Apple IWork \'09 Formulas And Functions User Guide Manual I Work

User Manual: Apple iWork \'09 iWork \'09 Formulas and Functions User Guide

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iWork
Formulas and
Functions User Guide

KKApple Inc.
© 2009 Apple Inc. All rights reserved.
Under the copyright laws, this manual may not be
copied, in whole or in part, without the written consent
of Apple. Your rights to the software are governed by
the accompanying software license agreement.

Apple, the Apple logo, iWork, Keynote, Mac, Mac OS,
Numbers, and Pages are trademarks of Apple Inc.,
registered in the U.S. and other countries.
Adobe and Acrobat are trademarks or registered
trademarks of Adobe Systems Incorporated in the U.S.
and/or other countries.

The Apple logo is a trademark of Apple Inc., registered
in the U.S. and other countries. Use of the “keyboard”
Apple logo (Option-Shift-K) for commercial purposes
without the prior written consent of Apple may
constitute trademark infringement and unfair
competition in violation of federal and state laws.

Other company and product names mentioned herein
are trademarks of their respective companies. Mention
of third-party products is for informational purposes
only and constitutes neither an endorsement nor a
recommendation. Apple assumes no responsibility with
regard to the performance or use of these products.

Every effort has been made to ensure that the
information in this manual is accurate. Apple is not
responsible for printing or clerical errors.

019-1588 09/2009

Apple
1 Infinite Loop
Cupertino, CA 95014-2084
408-996-1010
www.apple.com

Contents

13

Preface:  Welcome to iWork Formulas & Functions

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Chapter 1:  Using Formulas in Tables

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The Elements of Formulas
Performing Instant Calculations in Numbers
Using Predefined Quick Formulas
Creating Your Own Formulas
Adding and Editing Formulas Using the Formula Editor
Adding and Editing Formulas Using the Formula Bar
Adding Functions to Formulas
Handling Errors and Warnings in Formulas
Removing Formulas
Referring to Cells in Formulas
Using the Keyboard and Mouse to Create and Edit Formulas
Distinguishing Absolute and Relative Cell References
Using Operators in Formulas
The Arithmetic Operators
The Comparison Operators
The String Operator and the Wildcards
Copying or Moving Formulas and Their Computed Values
Viewing All Formulas in a Spreadsheet
Finding and Replacing Formula Elements

Chapter 2:  Overview of the iWork Functions
An Introduction to Functions
Information About Functions
Syntax Elements and Terms Used In Function Definitions
Value Types
Listing of Function Categories
Pasting from Examples in Help

Chapter 3:  Date and Time Functions
Listing of Date and Time Functions
DATE

		

3

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DATEDIF
DATEVALUE
DAY
DAYNAME
DAYS360
EDATE
EOMONTH
HOUR
MINUTE
MONTH
MONTHNAME
NETWORKDAYS
NOW
SECOND
TIME
TIMEVALUE
TODAY
WEEKDAY
WEEKNUM
WORKDAY
YEAR
YEARFRAC

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71

Chapter 4:  Duration Functions

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Chapter 5:  Engineering Functions

4		

Listing of Duration Functions
DUR2DAYS
DUR2HOURS
DUR2MILLISECONDS
DUR2MINUTES
DUR2SECONDS
DUR2WEEKS
DURATION
STRIPDURATION
Listing of Engineering Functions
BASETONUM
BESSELJ
BESSELY
BIN2DEC
BIN2HEX
BIN2OCT
CONVERT

Contents

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95

Supported Conversion Units
Weight and mass
Distance
Duration
Speed
Pressure
Force
Energy
Power
Magnetism
Temperature
Liquid
Metric prefixes
DEC2BIN
DEC2HEX
DEC2OCT
DELTA
ERF
ERFC
GESTEP
HEX2BIN
HEX2DEC
HEX2OCT
NUMTOBASE
OCT2BIN
OCT2DEC
OCT2HEX

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105
107
108
109
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114
116
117

Chapter 6:  Financial Functions
Listing of Financial Functions
ACCRINT
ACCRINTM
BONDDURATION
BONDMDURATION
COUPDAYBS
COUPDAYS
COUPDAYSNC
COUPNUM
CUMIPMT
CUMPRINC
DB
DDB
DISC

Contents

5

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EFFECT
FV
INTRATE
IPMT
IRR
ISPMT
MIRR
NOMINAL
NPER
NPV
PMT
PPMT
PRICE
PRICEDISC
PRICEMAT
PV
RATE
RECEIVED
SLN
SYD
VDB
YIELD
YIELDDISC
YIELDMAT

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166

Chapter 7:  Logical and Information Functions
Listing of Logical and Information Functions
AND
FALSE
IF
IFERROR
ISBLANK
ISERROR
ISEVEN
ISODD
NOT
OR
TRUE

167 Chapter 8:  Numeric Functions
167 Listing of Numeric Functions
170 ABS
170 CEILING

6		

Contents

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204

COMBIN
EVEN
EXP
FACT
FACTDOUBLE
FLOOR
GCD
INT
LCM
LN
LOG
LOG10
MOD
MROUND
MULTINOMIAL
ODD
PI
POWER
PRODUCT
QUOTIENT
RAND
RANDBETWEEN
ROMAN
ROUND
ROUNDDOWN
ROUNDUP
SIGN
SQRT
SQRTPI
SUM
SUMIF
SUMIFS
SUMPRODUCT
SUMSQ
SUMX2MY2
SUMX2PY2
SUMXMY2
TRUNC

206 Chapter 9:  Reference Functions
206 Listing of Reference Functions
207 ADDRESS
209 AREAS

Contents

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223

CHOOSE
COLUMN
COLUMNS
HLOOKUP
HYPERLINK
INDEX
INDIRECT
LOOKUP
MATCH
OFFSET
ROW
ROWS
TRANSPOSE
VLOOKUP

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257

Chapter 10:  Statistical Functions

8		

Listing of Statistical Functions
AVEDEV
AVERAGE
AVERAGEA
AVERAGEIF
AVERAGEIFS
BETADIST
BETAINV
BINOMDIST
CHIDIST
CHIINV
CHITEST
CONFIDENCE
CORREL
COUNT
COUNTA
COUNTBLANK
COUNTIF
COUNTIFS
COVAR
CRITBINOM
DEVSQ
EXPONDIST
FDIST
FINV
FORECAST
FREQUENCY

Contents

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GAMMADIST
GAMMAINV
GAMMALN
GEOMEAN
HARMEAN
INTERCEPT
LARGE
LINEST
Additional Statistics
LOGINV
LOGNORMDIST
MAX
MAXA
MEDIAN
MIN
MINA
MODE
NEGBINOMDIST
NORMDIST
NORMINV
NORMSDIST
NORMSINV
PERCENTILE
PERCENTRANK
PERMUT
POISSON
PROB
QUARTILE
RANK
SLOPE
SMALL
STANDARDIZE
STDEV
STDEVA
STDEVP
STDEVPA
TDIST
TINV
TTEST
VAR
VARA
VARP
VARPA
Contents

9

305 ZTEST
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Chapter 11:  Text Functions

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Chapter 12:  Trigonometric Functions

10		

Listing of Text Functions
CHAR
CLEAN
CODE
CONCATENATE
DOLLAR
EXACT
FIND
FIXED
LEFT
LEN
LOWER
MID
PROPER
REPLACE
REPT
RIGHT
SEARCH
SUBSTITUTE
T
TRIM
UPPER
VALUE
Listing of Trigonometric Functions
ACOS
ACOSH
ASIN
ASINH
ATAN
ATAN2
ATANH
COS
COSH
DEGREES
RADIANS
SIN
SINH
TAN

Contents

339 TANH
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Chapter 13:  Additional Examples and Topics

365

Index

Additional Examples and Topics Included
Common Arguments Used in Financial Functions
Choosing Which Time Value of Money Function to Use
Regular Cash Flows and Time Intervals
Irregular Cash Flows and Time Intervals
Which Function Should You Use to Solve Common Financial Questions?
Example of a Loan Amortization Table
More on Rounding
Using Logical and Information Functions Together
Adding Comments Based on Cell Contents
Trapping Division by Zero
Specifying Conditions and Using Wildcards
Survey Results Example

Contents

11

Preface

Welcome to iWork Formulas &
Functions

iWork comes with more than 250 functions you can use
to simplify statistical, financial, engineering, and other
computations. The built-in Function Browser gives you
a quick way to learn about functions and add them to a
formula.
To get started, just type the equal sign in an empty table cell to open the Formula
Editor. Then choose Insert > Function > Show Function Browser.

This user guide provides detailed instructions to help you write formulas and use
functions. In addition to this book, other resources are available to help you.
Onscreen help
Onscreen help contains all of the information in this book in an easy-to-search format
that’s always available on your computer. You can open iWork Formulas & Functions
Help from the Help menu in any iWork application. With Numbers, Pages, or Keynote
open, choose Help > “iWork Formulas & Functions Help.”

		

13

iWork website
Read the latest news and information about iWork at www.apple.com/iwork.
Support website
Find detailed information about solving problems at www.apple.com/support/iwork.
Help tags
iWork applications provide help tags—brief text descriptions—for most onscreen
items. To see a help tag, hold the pointer over an item for a few seconds.
Online video tutorials
Online video tutorials at www.apple.com/iwork/tutorials provide how-to videos about
performing common tasks in Keynote, Numbers, and Pages. The first time you open
an iWork application, a message appears with a link to these tutorials on the web. You
can view these video tutorials anytime by choosing Help > Video Tutorials in Keynote,
Numbers, and Pages.

14		

Preface    Welcome to iWork Formulas & Functions

Using Formulas in Tables

1

This chapter explains how to perform calculations in table
cells by using formulas.
The Elements of Formulas

A formula performs a calculation and displays the result in the cell where you place
the formula. A cell containing a formula is referred to as a formula cell.
For example, in the bottom cell of a column you can insert a formula that sums the
numbers in all the cells above it. If any of the values in the cells above the formula cell
change, the sum displayed in the formula cell updates automatically.
A formula performs calculations using specific values you provide. The values can
be numbers or text (constants) you type into the formula. Or they can be values that
reside in table cells you identify in the formula by using cell references. Formulas use
operators and functions to perform calculations using the values you provide:
ÂÂ Operators are symbols that initiate arithmetic, comparison, or string operations. You

use the symbols in formulas to indicate the operation you want to use. For example,
the symbol + adds values, and the symbol = compares two values to determine
whether they’re equal.
=A2 + 16:  A formula that uses an operator to add two values.
=:  Always precedes a formula.
A2:  A cell reference. A2 refers to the second cell in the first column.
+:  An arithmetic operator that adds the value that precedes it with the value that
follows it.
16:  A numeric constant.
ÂÂ Functions are predefined, named operations, such as SUM and AVERAGE. To use a

function, you enter its name and, in parentheses following the name, you provide
the arguments the function needs. Arguments specify the values the function will
use when it performs its operations.

		

15

=SUM(A2:A10):  A formula that uses the function SUM to add the values in a range
of cells (nine cells in the first column).
A2:A10:  A cell reference that refers to the values in cells A2 through A10.
To learn how to

Go to

Instantly display the sum, average, minimum
value, maximum value, and count of values in
selected cells and optionally save the formula
used to derive these values in Numbers

“Performing Instant Calculations in
Numbers” (page 17)

Quickly add a formula that displays the sum,
average, minimum value, maximum value, count,
or product of values in selected cells

“Using Predefined Quick Formulas” (page 18)

Use tools and techniques to create and modify
your formulas in Numbers

“Adding and Editing Formulas Using the Formula
Editor” (page 19)
“Adding and Editing Formulas Using the Formula
Bar” (page 20)
“Adding Functions to Formulas” (page 21)
“Removing Formulas” (page 24)

Use tools and techniques to create and modify
your formulas in Pages and Keynote

“Adding and Editing Formulas Using the Formula
Editor” (page 19)

Use the hundreds of iWork functions and review
examples illustrating ways to apply the functions
in financial, engineering, statistical, and other
contexts

Help > “iWork Formulas and Functions Help”
Help > “iWork Formulas and Functions User
Guide”

Add cell references of different kinds to a formula “Referring to Cells in Formulas” (page 24)
in Numbers
“Using the Keyboard and Mouse to Create and
Edit Formulas” (page 26)
“Distinguishing Absolute and Relative Cell
References” (page 27)
Use operators in formulas

“The Arithmetic Operators” (page 28)
“The Comparison Operators” (page 29)
“The String Operator and the Wildcards” (page 30)

Copy or move formulas or the value they
compute among table cells

“Copying or Moving Formulas and Their
Computed Values” (page 30)

Find formulas and formula elements in Numbers

“Viewing All Formulas in a Spreadsheet” (page 31)
“Finding and Replacing Formula
Elements” (page 32)

16		

Chapter 1    Using Formulas in Tables

Performing Instant Calculations in Numbers

In the lower left of the Numbers window, you can view the results of common
calculations using values in two or more selected table cells.
To perform instant calculations:
1 Select two or more cells in a table. They don’t have to be adjacent.
The results of calculations using the values in those cells are instantly displayed in the
lower left corner of the window.

The results in the lower left
are based on values in these
two selected cells.

sum:  Shows the sum of numeric values in selected cells.
avg:  Shows the average of numeric values in selected cells.
min:  Shows the smallest numeric value in selected cells.
max:  Shows the largest numeric value in selected cells.
count:  Shows the number of numeric values and date/time values in selected cells.
Empty cells and cells that contain types of values not listed above aren’t used in the
calculations.
2 To perform another set of instant calculations, select different cells.
If you find a particular calculation very useful and you want to incorporate it into a
table, you can add it as a formula to an empty table cell. Simply drag sum, avg, or one
of the other items in the lower left to an empty cell. The cell doesn’t have to be in the
same table as the cells used in the calculations.

Chapter 1    Using Formulas in Tables

17

Using Predefined Quick Formulas

An easy way to perform a basic calculation using values in a range of adjacent
table cells is to select the cells and then add a quick formula. In Numbers, this is
accomplished using the Function pop-up menu in the toolbar. In Keynote and Pages,
use the Function pop-up menu in the Format pane of the Table inspector.

Sum:  Calculates the sum of numeric values in selected cells.
Average:  Calculates the average of numeric values in selected cells.
Minimum:  Determines the smallest numeric value in selected cells.
Maximum:  Determines the largest numeric value in selected cells
Count:  Determines the number of numeric values and date/time values in selected cells.
Product:  Multiplies all the numeric values in selected cells.
You can also choose Insert > Function and use the submenu that appears.
Empty cells and cells containing types of values not listed are ignored.
Here are ways to add a quick formula:
mm To use selected values in a column or a row, select the cells. In Numbers, click Function
in the toolbar, and choose a calculation from the pop-up menu. In Keynote or Pages,
choose Insert > Function and use the submenu that appears.
If the cells are in the same column, the result is placed in the first empty cell beneath
the selected cells. If there is no empty cell, a row is added to hold the result. Clicking
on the cell will display the formula.
If the cells are in the same row, the result is placed in the first empty cell to the right
of the selected cells. If there is no empty cell, a column is added to hold the result.
Clicking on the cell will display the formula.
mm To use all the values in a column’s body cells, first click the column’s header cell or
reference tab. Then, in Numbers, click Function in the toolbar, and choose a calculation
from the pop-up menu. In Keynote or Pages, choose Insert > Function and use the
submenu that appears.
The result is placed in a footer row. If a footer row doesn’t exist, one is added. Clicking
on the cell will display the formula.

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Chapter 1    Using Formulas in Tables

mm To use all the values in a row, first click the row’s header cell or reference tab. Then,
in Numbers, click Function in the toolbar, and choose a calculation from the popup menu. In Keynote or Pages, choose Insert > Function and use the submenu that
appears.
The result is placed in a new column. Clicking on the cell will display the formula.

Creating Your Own Formulas

Although you can use several shortcut techniques to add formulas that perform
simple calculations (see “Performing Instant Calculations in Numbers” on page 17 and
“Using Predefined Quick Formulas” on page 18), when you want more control you use
the formula tools to add formulas.
To learn how to

Go to

Use the Formula Editor to work with a formula

“Adding and Editing Formulas Using the Formula
Editor” (page 19)

Use the resizable formula bar to work with a
formula in Numbers

“Adding and Editing Formulas Using the Formula
Bar” (page 20)

Use the Function Browser to quickly add
functions to formulas when using the Formula
Editor or the formula bar

“Adding Functions to Formulas” (page 21)

Detect an erroneous formula

“Handling Errors and Warnings in
Formulas” (page 23)

Adding and Editing Formulas Using the Formula Editor
The Formula Editor may be used as an alternative to editing a formula directly in the
formula bar (see “Adding and Editing Formulas Using the Formula Bar” on page 20).
The Formula Editor has a text field that holds your formula. As you add cell references,
operators, functions, or constants to a formula, they look like this in the Formula Editor.
A reference to a
range of three cells.

The Subtraction
operator.

References to cells
using their names.

All formulas must begin
with the equal sign.
The Sum function.

Here are ways to work with the Formula Editor:
mm To open the Formula Editor, do one of the following:
ÂÂ Select a table cell and then type the equal sign (=).
ÂÂ In Numbers, double-click a table cell that contains a formula. In Keynote and Pages,

select the table, and then double-click a table cell that contains a formula.
ÂÂ In Numbers only, select a table cell, click Function in the toolbar, and then choose

Formula Editor from the pop-up menu.
Chapter 1    Using Formulas in Tables

19

ÂÂ In Numbers only, select a table cell and then choose Insert > Function > Formula

Editor. In Keynote and Pages, choose Formula Editor from the Function pop-up
menu in the Format pane of the Table inspector.
ÂÂ Select a cell that contains a formula, and then press Option-Return.

The Formula Editor opens over the selected cell, but you can move it.
mm To move the Formula Editor, hold the pointer over the left side of the Formula Editor
until it changes into a hand, and then drag.
mm To build your formula, do the following:
ÂÂ To add an operator or a constant to the text field, place the insertion point and type.

You can use the arrow keys to move the insertion point around in the text field. See
“Using Operators in Formulas” on page 28 to learn about operators you can use.
Note:  When your formula requires an operator and you haven’t added one, the
+ operator is inserted automatically. Select the + operator and type a different
operator if needed.
ÂÂ To add cell references to the text field, place the insertion point and follow the

instructions in “Referring to Cells in Formulas” on page 24.
ÂÂ To add functions to the text field, place the insertion point and follow the

instructions in “Adding Functions to Formulas” on page 21.
mm To remove an element from the text field, select the element and press Delete.
mm To accept changes, press Return, press Enter, or click the Accept button in the Formula
Editor. You can also click outside the table.
To close the Formula Editor and not accept any changes you made, press Esc or click
the Cancel button in the Formula Editor.

Adding and Editing Formulas Using the Formula Bar
In Numbers, the formula bar, located beneath the format bar, lets you create and
modify formulas for a selected cell. As you add cell references, operators, functions,
or constants to a formula, they appear like this.
The Sum function.

References to cells
using their names.

All formulas must begin
with the equal sign.
The Subtraction operator.
A reference to a
range of three cells.

Here are ways to work with the formula bar:
mm To add or edit a formula, select the cell and add or change formula elements in the
formula bar.
mm To add elements to your formula, do the following:
20		

Chapter 1    Using Formulas in Tables

ÂÂ To add an operator or a constant, place the insertion point in the formula bar and

type. You can use the arrow keys to move the insertion point around. See “Using
Operators in Formulas” on page 28 to learn about operators you can use.
When your formula requires an operator and you haven’t added one, the + operator is
inserted automatically. Select the + operator and type a different operator if needed.
ÂÂ To add cell references to the formula, place the insertion point and follow the

instructions in “Referring to Cells in Formulas” on page 24.
ÂÂ To add functions to the formula, place the insertion point and follow the

instructions in “Adding Functions to Formulas” on page 21.
mm To increase or decrease the display size of formula elements in the formula bar, choose
an option from the Formula Text Size pop-up menu above the formula bar.
To increase or decrease the height of the formula bar, drag the resize control at the
far right of the formula bar down or up, or double-click the resize control to auto-fit
the formula.
mm To remove an element from the formula, select the element and press Delete.
mm To save changes, press Return, press Enter, or click the Accept button above the
formula bar. You can also click outside the formula bar.
To avoid saving any changes you made, click the Cancel button above the formula bar.

Adding Functions to Formulas
A function is a predefined, named operation (such as SUM and AVERAGE) that you can
use to perform a calculation. A function can be one of several elements in a formula,
or it can be the only element in a formula.
There are several categories of functions, ranging from financial functions that
calculate interest rates, investment values, and other information to statistical functions
that calculate averages, probabilities, standard deviations, and so on. To learn about all
the iWork function categories and their functions, and to review numerous examples
that illustrate how to use them, choose Help > “iWork Formulas and Functions Help”
or Help > “iWork Formulas and Functions User Guide”.

Chapter 1    Using Formulas in Tables

21

Although you can type a function into the text field of the Formula Editor or into the
formula bar (Numbers only), the Function Browser offers a convenient way to add a
function to a formula.
Select a category
to view functions in
that category.

Search for a function.

Select a function to
view information
about it.

Insert the selected function.

Left pane:  Lists categories of functions. Select a category to view functions in that
category. Most categories represent families of related functions. The All category lists
all the functions in alphabetical order. The Recent category lists the ten functions most
recently inserted using the Function Browser.
Right pane:  Lists individual functions. Select a function to view information about it
and to optionally add it to a formula.
Lower pane:  Displays detailed information about the selected function.
To use the Function Browser to add a function:
1 In the Formula Editor or the formula bar (Numbers only), place the insertion point
where you want the function added.
Note:  When your formula requires an operator before or after a function and you
haven’t added one, the + operator is inserted automatically. Select the + operator and
type a different operator if needed.

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Chapter 1    Using Formulas in Tables

2 In Pages or Keynote, choose Insert > Function > Show Function Browser to open
the Function Browser. In Numbers, open the Function Browser by doing one of the
following:
ÂÂ Click the Function Browser button in the formula bar.
ÂÂ Click the Function button in the toolbar and choose Show Function Browser.
ÂÂ Choose Insert > Function > Show Function Browser.
ÂÂ Choose View > Show Function Browser.

3 Select a function category.
4 Choose a function by double-clicking it or by selecting it and clicking Insert Function.
5 In the Formula Editor or formula bar (Numbers only), replace each argument
placeholder in the inserted function with a value.
Click to see a list of valid values.

Help for the “issue” argument
appears when the pointer is over
the placeholder.

Placeholders for optional
arguments are light gray.

To review a brief description of an argument’s value:  Hold the pointer over the
argument placeholder. You can also refer to information about the argument in the
Function Browser window.
To specify a value to replace any argument placeholder:  Click the argument
placeholder and type a constant or insert a cell reference (see “Referring to Cells
in Formulas” on page 24 for instructions). If the argument placeholder is light gray,
providing a value is optional.
To specify a value to replace an argument placeholder that has a disclosure
triangle:  Click the disclosure triangle and then choose a value from the pop-up menu.
To review information about a value in the pop-up menu, hold the pointer over the
value. To review help for the function, select Function Help.

Handling Errors and Warnings in Formulas
When a formula in a table cell is incomplete, contains invalid cell references, or is
otherwise incorrect, or when an import operation creates an error condition in a cell,
Number or Pages displays an icon in the cell. A blue triangle in the upper left of a cell
indicates one or more warnings. A red triangle in the middle of a cell means that a
formula error occurred.

Chapter 1    Using Formulas in Tables

23

To view error and warning messages:
mm Click the icon.
A message window summarizes each error and warning condition associated with
"the cell.

To have Numbers issue a warning when a cell referenced in a formula is empty, choose
Numbers > Preferences and in the General pane select “Show warnings when formulas
reference empty cells.” This option is not available in Keynote or Pages.

Removing Formulas

If you no longer want to use a formula that’s associated with a cell, you can quickly
remove the formula.
To remove a formula from a cell:
1 Select the cell.
2 Press the Delete key.
In Numbers, if you need to review formulas in a spreadsheet before deciding what to
delete, choose View > Show Formula List.

Referring to Cells in Formulas

All tables have reference tabs. These are the row numbers and column headings. In
Numbers, the reference tabs are visible anytime the table has focus; for example, a cell
in the table is currently selected. In Keynote and Pages, reference tabs appear only when
a formula within a table cell is selected. In Numbers, the reference tabs look like this:

The reference tabs are the gray box at the top of each column or at the left of each
row containing the column letters (for example, “A”) or row numbers (for example, “3”).
The look of the reference tabs in Keynote and Pages is similar to the look in Numbers.
You use cell references to identify cells whose values you want to use in formulas.
In Numbers, the cells can be in the same table as the formula cell, or they can be in
another table on the same or a different sheet.

24		

Chapter 1    Using Formulas in Tables

Cell references have different formats, depending on such factors as whether the cell’s
table has headers, whether you want to refer to a single cell or a range of cells, and so
on. Here’s a summary of the formats that you can use for cell references.
To refer to

Use this format

Any cell in the table containing
the formula

The reference tab letter followed C55 refers to the 55th row in the
by the reference tab number for third column.
the cell

A cell in a table that has a
header row and a header
column

The column name followed by
the row name

2006 Revenue refers to a cell
whose header row contains
2006 and header column
contains Revenue.

A cell in a table that has
multiple header rows or
columns

The name of the header whose
columns or rows you want to
refer to

If 2006 is a header that spans
two columns (Revenue and
Expenses), 2006 refers to all
the cells in the Revenue and
Expenses columns.

A range of cells

A colon (:) between the first
and last cell in the range, using
reference tab notation to
identify the cells

B2:B5 refers to four cells in the
second column.

All the cells in a row

The row name or rownumber:row-number

1:1 refers to all the cells in the
first row.

All the cells in a column

The column letter or name

C refers to all the cells in the
third column.

All the cells in a range of rows

2:6 refers to all the cells in five
A colon (:) between the row
number or name of the first and rows.
last row in the range

All the cells in a range of
columns

A colon (:) between the column
letter or name of the first and
last column in the range

B:C refers to all the cells in the
second and third columns.

In Numbers, a cell in another
table on the same sheet

If the cell name is unique in the
spreadsheet then only the cell
name is required; otherwise,
the table name followed by
two colons (::) and then the cell
identifier

Table 2::B5 refers to cell B5 in
a table named Table 2. Table
2::2006 Class Enrollment refers to
a cell by name.

In Numbers, a cell in a table on
another sheet

If the cell name is unique in the
spreadsheet then only the cell
name is required; otherwise,
the sheet name followed by
two colons (::), the table name,
two more colons, then the cell
identifier

Sheet 2::Table 2::2006 Class
Enrollment refers to a cell in a
table named Table 2 on a sheet
named Sheet 2.

Chapter 1    Using Formulas in Tables

Example

25

In Numbers, you can omit a table or sheet name if the cell or cells referenced have
names unique in the spreadsheet.
In Numbers, when you reference a cell in a multirow or multicolumn header, you’ll
notice the following behavior:
ÂÂ The name in the header cell closest to the cell referring to it is used. For example, if

a table has two header rows, and B1 contains “Dog” and B2 contains “Cat,” when you
save a formula that uses “Dog,” “Cat” is saved instead.
ÂÂ However, if “Cat” appears in another header cell in the spreadsheet, “Dog” is retained.

To learn how to insert cell references into a formula, see “Using the Keyboard and
Mouse to Create and Edit Formulas” below. See “Distinguishing Absolute and Relative
Cell References” on page 27 to learn about absolute and relative forms of cell
references, which are important when you need to copy or move a formula.

Using the Keyboard and Mouse to Create and Edit Formulas
You can type cell references into a formula, or you can insert cell references using
mouse or keyboard shortcuts.
Here are ways to insert cell references:
mm To use a keyboard shortcut to enter a cell reference, place the insertion point in the
Formula Editor or formula bar (Numbers only) and do one of the following:
ÂÂ To refer to a single cell, press Option and then use the arrow keys to select the cell.
ÂÂ To refer to a range of cells, press and hold Shift-Option after selecting the first cell in

the range until the last cell in the range is selected.
ÂÂ In Numbers, to refer to cells in another table on the same or a different sheet, select

the table by pressing Option-Command–Page Down to move downward through
tables or Option-Command–Page Up to move upward through tables. Once the
desired table is selected, continue holding down Option, but release Command, and
use the arrow keys to select the desired cell or range (using Shift-Option) of cells.
ÂÂ To specify absolute and relative attributes of a cell reference after inserting one,

click the inserted reference and press Command-K to cycle through the options.
See “Distinguishing Absolute and Relative Cell References” on page 27 for more
information.
mm To use the mouse to enter a cell reference, place the insertion point in the Formula
Editor or the formula bar (Numbers only) and do one of the following in the same
table as the formula cell or, for Numbers only, in a different table on the same or a
different sheet:
ÂÂ To refer to a single cell, click the cell.
ÂÂ To refer to all the cells in a column or a row, click the reference tab for the column

or row.

26		

Chapter 1    Using Formulas in Tables

ÂÂ To refer to a range of cells, click a cell in the range and drag up, down, left, or right

to select or resize the cell range.
ÂÂ To specify absolute and relative attributes of a cell reference, click the disclosure

triangle of the inserted reference and choose an option from the pop-up menu.
See “Distinguishing Absolute and Relative Cell References” on page 27 for more
information.
In Numbers, the cell reference inserted uses names instead of reference tab notation
unless the “Use header cell names as references” is deselected in the General pane of
Numbers preferences. In Keynote and Pages, the cell reference inserted uses names
instead of reference tab notation if referenced cells have headers.
mm To type a cell reference, place the insertion point in the Formula Editor or the formula
bar (Numbers only), and enter the cell reference using one of the formats listed in
“Referring to Cells in Formulas” on page 24.
When you type a cell reference that includes the name of a header cell (all
applications), table (Numbers only), or sheet (Numbers only), after typing 3 characters
a list of suggestions pops up if the characters you typed match one or more names
in your spreadsheet. You can select from the list or continue typing. To disable name
suggestions in Numbers, choose Numbers > Preferences and deselect “Use header cell
names as references” in the General pane.

Distinguishing Absolute and Relative Cell References
Use absolute and relative forms of a cell reference to indicate the cell to which you
want the reference to point if you copy or move its formula.
If a cell reference is relative (A1):  When its formula moves, it stays the same. However,
when the formula is cut or copied and then pasted, the cell reference changes so
that it retains the same position relative to the formula cell. For example, if a formula
containing A1 appears in C4 and you copy the formula and paste it in C5, the cell
reference in C5 becomes A2.
If the row and column components of a cell reference are absolute ($A$1):  When
its formula is copied, the cell reference doesn’t change. You use the dollar sign ($) to
designate a row or column component absolute. For example, if a formula containing
$A$1 appears in C4 and you copy the formula and paste it in C5 or in D5, the cell
reference in C5 or D5 remains $A$1.
If the row component of a cell reference is absolute (A$1):  The column component is
relative and may change to retain its position relative to the formula cell. For example,
if a formula containing A$1 appears in C4 and you copy the formula and paste it in D5,
the cell reference in D5 becomes B$1.

Chapter 1    Using Formulas in Tables

27

If the column component of a cell reference is absolute ($A1):  The row component
is relative and may change to retain its position relative to the formula cell. For
example, if a formula containing $A1 appears in C4 and you copy the formula and
paste it in C5 or in D5, the cell reference in C5 and D5 becomes $A2.
Here are ways to specify the absoluteness of cell reference components:
mm Type the cell reference using one of the conventions described above.
mm Click the disclosure triangle of a cell reference and choose an option from the pop-up
menu.
mm Select a cell reference and press Command-K to cycle through options.

Using Operators in Formulas

Use operators in formulas to perform arithmetic operations and to compare values:
ÂÂ Arithmetic operators perform arithmetic operations, such as addition and subtraction,

and return numerical results. See “The Arithmetic Operators” on page 28 to learn more.
ÂÂ Comparison operators compare two values and return TRUE or FALSE. See “The

Comparison Operators” on page 29 to learn more.

The Arithmetic Operators
You can use arithmetic operators to perform arithmetic operations in formulas.
When you want to

Use this arithmetic operator

For example, if A2 contains 20
and B2 contains 2, the formula

Add two values

+ (plus sign)

A2 + B2 returns 22.

Subtract one value from another – (minus sign)
value

A2 – B2 returns 18.

Multiply two values

* (asterisk)

A2 * B2 returns 40.

Divide one value by another
value

/ (forward slash)

A2 / B2 returns 10.

Raise one value to the power of
another value

^ (caret)

A2 ^ B2 returns 400.

Calculate a percentage

% (percent sign)

A2% returns 0.2, formatted for
display as 20%.

Using a string with an arithmetic operator returns an error. For example, 3 + “hello” is
not a correct arithmetic operation.

28		

Chapter 1    Using Formulas in Tables

The Comparison Operators
You can use comparison operators to compare two values in formulas. Comparison
operations always return the values TRUE or FALSE. Comparison operators can also
used to build the conditions used by some functions. See “condition” in the table
“Syntax Elements and Terms Used In Function Definitions” on page 34
When you want to determine
whether

Use this comparison operator

For example, if A2 contains 20
and B2 contains 2, the formula

Two values are equal

=

A2 = B2 returns FALSE.

Two values aren’t equal

<>

A2 <> B2 returns TRUE.

The first value is greater than
the second value

>

A2 > B2 returns TRUE.

The first value is less than the
second value

<

A2 < B2 returns FALSE.

The first value is greater than or
equal to the second value

>=

A2 >= B2 returns TRUE.

The first value is less than or
equal to the second value

<=

A2 <= B2 returns FALSE.

Strings are larger than numbers. For example, “hello” > 5 returns TRUE.
TRUE and FALSE can be compared with each other, but not with numbers or strings.
TRUE > FALSE, and FALSE < TRUE, because TRUE is interpreted as 1 and FALSE is
interpreted as 0. TRUE = 1 returns FALSE, and TRUE = “SomeText” returns FALSE.
Comparison operations are used primarily in functions, such as IF, which compare two
values and then perform other operations depending on whether the comparison
returns TRUE or FALSE. For more information about this topic, choose Help > “iWork
Formulas and Functions Help” or Help > “iWork Formulas and Functions User Guide.”

Chapter 1    Using Formulas in Tables

29

The String Operator and the Wildcards

The string operator can be used in formulas and wildcards can be used in conditions.
When you want to

Use this string operator or
wildcard

For example

Concatenate strings or the
contents of cells

&

“abc”&”def” returns “abcdef”
“abc”&A1 returns “abc2” if cell A1
contains 2.
A1&A2 returns “12” if cell A1
contains 1 and cell A2 contains 2.

Match a single character

?

“ea?” will match any string
beginning with “ea” and
containing exactly one
additional character.

Match any number of characters *

“*ed” will match a string of any
length ending with “ed”.

Literally match a wildcard
character

“~?” will match the question
mark, instead of using the
question mark to match any
single character.

~

For more information on the use of wildcards in conditions, see “Specifying Conditions
and Using Wildcards” on page 360.

Copying or Moving Formulas and Their Computed Values
Here are techniques for copying and moving cells related to a formula:
mm To copy the computed value in a formula cell but not the formula, select the cell,
choose Edit > Copy, select the cell you want to hold the value, and then choose Edit >
Paste Values.
mm To copy or move a formula cell or a cell that a formula refers to, follow the instructions
in “Copying and Moving Cells” in Numbers Help or the Numbers User Guide.
In Numbers, if the table is large and you want to move the formula to a cell that’s out
of view, select the cell, choose Edit > “Mark for Move,” select the other cell, and then
choose Edit > Move. For example, if the formula =A1 is in cell D1 and you want to
move the same formula to cell X1, select D1, choose Edit > “Mark for Move,” select X1,
and then choose Edit > Move. The formula =A1 appears in cell X1.
If you copy or move a formula cell:  Change cell references as “Distinguishing
Absolute and Relative Cell References” on page 27 describes if needed.
If you move a cell that a formula refers to:  The cell reference in the formula is
automatically updated. For example, if a reference to A1 appears in a formula and you
move A1 to D95, the cell reference in the formula becomes D95.

30		

Chapter 1    Using Formulas in Tables

Viewing All Formulas in a Spreadsheet

In Numbers, to view a list of all the formulas in a spreadsheet, choose View > Show
Formula List or click on the formula list button in the toolbar.

Location: Identifies the sheet and table in which the formula is located.
Results:  Displays the current value computed by the formula.
Formula:  Shows the formula.
Here are ways to use the formula list window:
mm To identify the cell containing a formula, click the formula. The table is shown above
the formula list window with the formula cell selected.
mm To edit the formula, double-click it.
mm To change the size of the formula list window, drag the selection handle in its upper
right corner up or down.
mm To find formulas that contain a particular element, type the element in the search field
and press Return.

Chapter 1    Using Formulas in Tables

31

Finding and Replacing Formula Elements

In Numbers, using the Find & Replace window, you can search through all of a
spreadsheet’s formulas to find and optionally change elements.
Here are ways to open the Find & Replace window:
mm Choose Edit > Find > Show Search, and then click Find & Replace.
mm Choose View > Show Formula List, and then click Find & Replace.

Find: Type the formula element (cell reference, operator, function, and so on) you
want to find.
In:  Choose Formulas Only from this pop-up menu.
Match case:  Select to find only elements whose uppercase and lowercase letters
match exactly what’s in the Find field.
Whole words:  Select to find only elements whose entire contents match what’s in
the Find field.
Replace:  Optionally type what you want to use to replace what’s in the Find field.
Repeat search (loop):  Select to continue looking for what’s in the Find field even
after the entire spreadsheet has been searched.
Next or Previous:  Click to search for the next or previous instance of what’s in the
Find field. When an element is found, the Formula Editor opens and displays the
formula containing the instance of the element.
Replace All:  Click to replace all instances of what’s in the Find field with what’s in
the Replace field.
Replace:  Click to replace the current instance of what’s in the Find field with what’s
in the Replace field.
Replace & Find:  Click to replace the current instance of what’s in the Find field and
to locate the next instance.

32		

Chapter 1    Using Formulas in Tables

Overview of the iWork Functions

2

This chapter introduces the functions available in iWork.
An Introduction to Functions

A function is a named operation that you can include in a formula to perform a
calculation or to manipulate data in a table cell.
iWork provides functions that do things such as perform mathematical or financial
operations, retrieve cell values based on a search, manipulate strings of text, or get the
current date and time. Each function has a name followed by one or more arguments
enclosed in parentheses. You use arguments to provide the values that the function
needs to perform its work.
For example, the following formula contains a function named SUM with a single
argument (a range of cells) that adds the values in column A, rows 2 through 10:
=SUM(A2:A10)
The number and types of arguments vary for each function. The number and
description of the arguments are included with the function in the alphabetical
“Listing of Function Categories” on page 40. The descriptions also include additional
information and examples for each function.

		

33

Information About Functions
For further information on

Go to

Syntax used in function definitions

“Syntax Elements and Terms Used In Function
Definitions” on page 34

Types of arguments that are used by functions

“Value Types” on page 36

Categories of functions, such as duration and
statistical

“Listing of Function Categories” on page 40.
Functions are listed alphabetically within each
category.

Arguments common to several financial functions “Common Arguments Used in Financial
Functions” on page 341
Supplemental examples and topics

“Additional Examples and Topics Included” on
page 340

Syntax Elements and Terms Used In Function Definitions
Functions are described using specific syntax elements and terms.

34		

Term or symbol

Meaning

uppercase text

Function names are shown in all uppercase text.
However, a function name can be entered using
any combination of uppercase or lowercase
letters.

parentheses

Function arguments are enclosed in parentheses.
Parentheses are required, although in limited
circumstances iWork can automatically insert the
final closing parenthesis for you.

italic text

Italic text indicates that you must replace the
argument name with a value the function will
use to calculate a result. Arguments have a value
type, such as “number,” “date/time,” or “string.”
Value types are discussed in “Value Types” on
page 36.

commas and semicolons

The syntax descriptions for functions use commas
to separate arguments. If your Language and Text
preferences (Mac OS X version 10.6 or higher) or
International preferences (earlier versions of Max
OS X) are set up to use the comma as a decimal
separator, separate arguments using a semicolon
instead of a comma.

Chapter 2    Overview of the iWork Functions

Term or symbol

Meaning

ellipsis (…)

An argument followed by an ellipsis can be
repeated as many times as necessary. Any
limitations are described in the argument
definition.

array

An array is a sequence of values used by a
function, or returned by a function.

array constant

An array constant is a set of values enclosed
within braces ({}) and is typed directly into the
function. For example, {1, 2, 5, 7} or {“12/31/2008”,
“3/15/2009”, “8/20/2010”}.

array function

A small number of functions are described as
“array function,” meaning the function returns an
array of values rather than a single value. These
functions are commonly used to provide values
to another function.

Boolean expression

A Boolean expression is an expression that
evaluates to the Boolean value TRUE or FALSE.

constant

A constant is a value specified directly within
the formula that contains no function calls
or references. For example, in the formula
=CONCATENATE(”cat”, “s”), “cat” and “s” are
constants.

modal argument

A modal argument is one that can have one of
several possible specified values. Usually, modal
arguments specify something about the type of
calculation the function should perform or about
the type of data the function should return.
If a modal argument has a default value, it is
specified in the argument description.

condition

A condition is an expression that can include
comparison operators, constants, the ampersand
string operator, and references. The contents
of the condition must be such that the result
of comparing the condition to another value
results in the Boolean value TRUE or FALSE.
Further information and examples are included in
“Specifying Conditions and Using Wildcards” on
page 360.

Chapter 2    Overview of the iWork Functions

35

Value Types

A function argument has a type, which specifies what type of information the
argument can contain. Functions also return a value of a particular type.
Value Type

Description

any

If an argument is specified as “any,” it can be a
Boolean value, date/time value, duration value,
number value, or string value.

Boolean

A Boolean value is a logical TRUE (1) or FALSE
(0) value or a reference to a cell containing or
resulting in a logical TRUE or FALSE value. It is
generally the result of evaluating a Boolean
expression, but a Boolean value can be specified
directly as an argument to a function or as the
content of a cell. A common use of a Boolean
value is to determine which expression is to be
returned by the IF function.

collection

An argument that is specified as a collection can
be a reference to a single table cell range, an
array constant, or an array returned by an array
function. An argument specified as collection will
have an additional attribute defining the type of
values it can contain.

date/time

This is a date/time value or a reference to a
cell containing a date/time value in any of the
formats supported by iWork. If a date/time value
is typed into the function, it should be enclosed
in quotation marks. You can choose to display
only a date or time in a cell, but all date/time
values contain both a date and a time.
Although dates can usually be entered directly
as strings (for example, “12/31/2010”), using the
DATE function insures the date will be interpreted
consistently regardless of the date format
selected in System Preferences (search for “date
format” in the System Preferences window).

36		

Chapter 2    Overview of the iWork Functions

Value Type

Description

duration

A duration is a length of time or a reference
to a cell containing a length of time. Duration
values consist of weeks (w or weeks), days (d or
days), hours (h or hours), minutes (m or minutes),
seconds (s or seconds), and milliseconds (ms or
milliseconds). A duration value can be entered in
one of two formats.
The first format consists of a number, followed
by a time period (such as h for hours), optionally
followed by a space, and is repeated for other
time periods. You can use either the abbreviation
for specifying the period, such as “h”, or the full
name, such as “hours.” For example, 12h 5d 3m
represents a duration of 12 hours, 5 days, and 3
minutes. TIme periods do not have to be entered
in order and spaces are not required. 5d 5h is the
same as 5h5d. If typed directly into a formula, the
string should be enclosed in quotation marks, as
in “12h 5d 3m”.
A duration can also be entered as a series of
numbers delimited by colons. If this format is
used, the seconds argument should be included
and end with a decimal followed by the number
of milliseconds, which can be 0, if the duration
value could be confused with a date/time
value. For example, 12:15:30.0 would represent a
duration of 12 hours, 15 minutes, and 30 seconds,
whereas 12:15:30 would be 12:15:30 a.m. 5:00.0
would represent a duration of exactly 5 minutes.
If typed directly into a function, the string
should be enclosed in quotation marks, as in
“12:15:30.0” or “5:00.0”. If the cell is formatted to a
particular duration display, the duration units are
applied relative to that duration display and the
milliseconds need not be specified.

Chapter 2    Overview of the iWork Functions

37

38		

Value Type

Description

list

A list is a comma-separated sequence of other
values. For example, =CHOOSE(3, “1st”, “second”,
7, “last”). In some cases, the list is enclosed in
an additional set of parentheses. For example,
=AREAS((B1:B5, C10:C12)).

modal

A modal value is a single value, often a number,
representing a specific mode for a modal
argument. “Modal argument” is defined in
“Syntax Elements and Terms Used In Function
Definitions” on page 34.

number

A number value is a number, a numeric
expression, or a reference to a cell containing a
numeric expression. If the acceptable values of
a number are limited (for example, the number
must be greater than 0), this is included within
the argument description.

range value

A range value is a reference to a single range of
cells (can be a single cell). A range value will have
an additional attribute defining the type of values
it should contain. This will be included within the
argument description.

Chapter 2    Overview of the iWork Functions

Value Type

Description

reference

This is a reference to a single cell or a range
of cells. If the range is more than one cell, the
starting and ending cell are separated by a single
colon. For example, =COUNT(A3:D7).
Unless the cell name is unique within all tables,
the reference must contain the name of the table
if the reference is to a cell on another table. For
example, =Table 2::B2. Note that the table name
and cell reference are separated by a double
colon (::).
If the table is on another sheet, the sheet name
must also be included, unless the cell name is
unique within all the the sheets. For example,
=SUM(Sheet 2::Table 1::C2:G2). The sheet name,
table name and cell reference are separated by
double colons.
Some functions that accept ranges can operate
on ranges that span multiple tables. Assume
that you have a file open that has one sheet
containing three tables (Table 1, Table 2, Table
3). Assume further that cell C2 in each table
contains the number 1. The table-spanning
formula =SUM(Table 1:Table 2 :: C2) would sum
cell C2 in all tables between Table 1 and Table 2.
So the result would be 2. If you drag Table 3 so
that it appears between Table 1 and Table 2 in
the sidebar, the function will return 3, since it is
now summing cell C2 in all three tables (Table 3
is between Table 1 and Table 2).

string

Chapter 2    Overview of the iWork Functions

A string is zero or more characters, or a reference
to a cell containing one or more characters. The
characters can consist of any printable characters,
including numbers. If a string value is typed into
the formula, it must be enclosed in quotation
marks. If the string value is somehow limited (for
example, the string must represent a date), this is
included within the argument description.

39

Listing of Function Categories

There are several categories of functions. For example, some functions perform
calculations on date/time values, logical functions give a Boolean (TRUE or FALSE)
result, and other functions perform financial calculations. Each of the categories of
functions is discussed in a separate chapter.
“Listing of Date and Time Functions” on page 42
“Listing of Duration Functions” on page 64
“Listing of Engineering Functions” on page 72
“Listing of Financial Functions” on page 96
“Listing of Logical and Information Functions” on page 155
“Listing of Numeric Functions” on page 167
“Listing of Reference Functions” on page 206
“Listing of Statistical Functions” on page 225
“Listing of Text Functions” on page 306
“Listing of Trigonometric Functions” on page 326

40		

Chapter 2    Overview of the iWork Functions

Pasting from Examples in Help

Many of the examples in help can be copied and pasted directly into a table or,
in Numbers, onto a blank canvas. There are two groups of examples which can be
copied from help and pasted into a table. The first are individual examples included
within help. All such examples begin with an equal sign (=). In the help for the HOUR
function, there are two such examples.

To use one of these examples, select the text beginning with the equal sign through
the end of the example.

Once this text is highlighted, you can copy it and then paste it into any cell in a table.
An alternative to copy and paste is to drag the selection from the example and drop it
onto any cell in a table.
The second kind of example that can be copied are example tables included within
help. This is the help example table for ACCRINT.

To use an example table, select all the cells in the example table, including the first row.

Once this text is highlighted, you can copy it and then paste it into any cell in a table
or onto a blank canvas in a Numbers sheet. Drag and drop cannot be used for this
type of example.
Chapter 2    Overview of the iWork Functions

41

Date and Time Functions

3

The date and time functions help you work with dates and
times to solve problems such as finding the number of
working days between two dates or finding the name of the
day of the week a date will fall on.
Listing of Date and Time Functions

iWork includes these date and time functions for use with tables.

42

Function

Description

“DATE” (page 44)

The DATE function combines separate values for
year, month, and day and returns a date/time
value. Although dates can usually be entered
directly as strings (for example, “12/31/2010”),
using the DATE function ensures the date will be
interpreted consistently regardless of the date
format specified in System Preferences (search for
“date format” in the System Preferences window).

“DATEDIF” (page 45)

The DATEDIF function returns the number of
days, months, or years between two dates.

“DATEVALUE” (page 47)

The DATEVALUE function converts a date
text string and returns a date/time value. This
function is provided for compatibility with other
spreadsheet programs.

“DAY” (page 47)

The DAY function returns the day of the month
for a given date/time value.

“DAYNAME” (page 48)

The DAYNAME function returns the name of
the day of the week from a date/time value or a
number. Day 1 is Sunday.

“DAYS360” (page 49)

The DAYS360 function returns the number of
days between two dates based on twelve 30-day
months and a 360-day year.

Function

Description

“EDATE” (page 50)

The EDATE function returns a date that is some
number of months before or after a given date.

“EOMONTH” (page 51)

The EOMONTH function returns a date that is the
last day of the month some number of months
before or after a given date.

“HOUR” (page 51)

The HOUR function returns the hour for a given
date/time value.

“MINUTE” (page 52)

The MINUTE function returns the minutes for a
given date/time value.

“MONTH” (page 53)

The MONTH function returns the month for a
given date/time value.

“MONTHNAME” (page 54)

The MONTHNAME function returns the name of
the month from a number. Month 1 is January.

“NETWORKDAYS” (page 54)

The NETWORKDAYS function returns the number
of working days between two dates. Working
days exclude weekends and any other specified
dates.

“NOW” (page 55)

The NOW function returns the current date/time
value from the system clock.

“SECOND” (page 56)

The SECOND function returns the seconds for a
given date/time value.

“TIME” (page 56)

The TIME function converts separate values for
hours, minutes, and seconds into a date/time
value.

“TIMEVALUE” (page 57)

The TIMEVALUE function returns the time as a
decimal fraction of a 24-hour day from a given
date/time value or from a text string.

“TODAY” (page 58)

The TODAY function returns the current system
date. The time is set to 12:00 a.m.

Chapter 3    Date and Time Functions

43

Function

Description

“WEEKDAY” (page 59)

The WEEKDAY function returns a number that is
the day of the week for a given date.

“WEEKNUM” (page 60)

The WEEKNUM function returns the number of
the week within the year for a given date.

“WORKDAY” (page 61)

The WORKDAY function returns the date that is
the given number of working days before or after
a given date. Working days exclude weekends
and any other dates specifically excluded.

“YEAR” (page 62)

The YEAR function returns the year for a given
date/time value.

“YEARFRAC” (page 63)

The YEARFRAC function finds the fraction of a
year represented by the number of whole days
between two dates.

DATE

The DATE function combines separate values for year, month, and day and returns a
date/time value. Although dates can usually be entered directly as strings (for example,
“12/31/2010”), using the DATE function ensures the date will be interpreted consistently
regardless of the date format specified in System Preferences (search for “date format”
in the System Preferences window).
DATE(year, month, day)
ÂÂ year:  The year to include in the value returned. year is a number value. The value

isn’t converted. If you specify 10, the year 10 is used, not the year 1910 or 2010.
ÂÂ month:  The month to include in the value returned. month is a number and should

be in the range 1 to 12.
ÂÂ day:  The day to include in the value returned. day is a number value and should be

in the range 1 to the number of days in month.
Examples
If A1 contains 2014, A2 contains 11, and A3 contains 10:
=DATE(A1, A2, A3) returns Nov 10, 2014, which is displayed according to the cell’s current format.
=DATE(A1, A3, A2) returns Oct 11, 2014.
=DATE(2012, 2, 14) returns Feb 14, 2012.

Related Topics
For related functions and additional information, see:
“DURATION” on page 70

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Chapter 3    Date and Time Functions

“TIME” on page 56
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

DATEDIF

The DATEDIF function returns the number of days, months, or years between two
dates.
DATEDIF(start-date, end-date, calc-method)
ÂÂ start-date:  The starting date. start-date is a date/time value.
ÂÂ end-date:  The ending date. end-date is a date/time value.
ÂÂ calc-method:  Specifies how to express the time difference and how dates in

different years or months are handled.
“D”:  Count the number of days between the start and end dates.
“M”:  Count the number of months between the start and end dates.
“Y”:  Count the number of years between the start and end dates.
“MD”:  Count the days between the start and end dates, ignoring months and years.
The month in end-date is considered to be the month in start-date. If the starting
day is after the ending day, the count starts from the ending day as if it were in the
preceding month. The year of the end-date is used to check for a leap year.
“YM”:  Count the number of whole months between the start and end dates,
ignoring the year. If the starting month/day is before the ending month/day, the
dates are treated as though they are in the same year. If the starting month/day is
after the ending month/day, the dates are treated as though they are in consecutive
years.
“YD”:  Count the number of days between the start and end dates, ignoring the
year. If the starting month/day is before the ending month/day, the dates are treated
as though they are in the same year. If the starting month/day is after the ending
month/day, the dates are treated as though they are in consecutive years.

Chapter 3    Date and Time Functions

45

Examples
If A1 contains the date/time value 4/6/88 and A2 contains the date/time value 10/30/06:
=DATEDIF(A1, A2, “D”) returns 6781, the number of days between April 6, 1988, and October 30, 2006.
=DATEDIF(A1, A2, “M”) returns 222, the number of whole months between April 6, 1988, and October
30, 2006.
=DATEDIF(A1, A2, “Y”) returns 18, the number of whole years between April 6, 1988, and October 30,
2006.
=DATEDIF(A1, A2, “MD”) returns 24, the number of days between the sixth day of a month and the
thirtieth day of the same month.
=DATEDIF(A1, A2, “YM”) returns 6, the number of months between April and the following October in
any year.
=DATEDIF(A1, A2, “YD”) returns 207, the number of days between April 6 and the following October
30 in any year.
=DATEDIF(”04/06/1988”, NOW(), “Y”) & “ years, “ & DATEDIF(”04/06/1988”, NOW(), “YM”) & “ months, and
“ & DATEDIF(”04/06/1988”, NOW(), “MD”) & “ days” returns the current age of someone born on April 6,
1988.

Related Topics
For related functions and additional information, see:
“DAYS360” on page 49
“NETWORKDAYS” on page 54
“NOW” on page 55
“YEARFRAC” on page 63
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

46		

Chapter 3    Date and Time Functions

DATEVALUE

The DATEVALUE function converts a date text string and returns a date/time value. This
function is provided for compatibility with other spreadsheet programs.
DATEVALUE(date-text)
ÂÂ date-text:  The date string to be converted. date-text is a string value. It must be a

date specified within quotations or a date/time value. If date-text is not a valid date,
an error is returned.
Examples
If cell B1 contains the date/time value August 2, 1979 06:30:00 and cell C1 contains the string
10/16/2008:
=DATEVALUE(B1) returns Aug 2, 1979, and is treated as a date value if referenced in other formulas.
The value returned is formatted according to the current cell format. A cell formatted as Automatic
uses the date format specified in System Preferences (search for “date format” in the System
Preferences window).
=DATEVALUE(C1) returns Oct 16, 2008.
=DATEVALUE(“12/29/1974”) returns Dec 29, 1979.

Related Topics
For related functions and additional information, see:
“DATE” on page 44
“TIME” on page 56
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

DAY

The DAY function returns the day of the month for a given date/time value.
DAY(date)
ÂÂ date:  The date the function should use. date is a date/time value. The time portion

is ignored by this function.

Chapter 3    Date and Time Functions

47

Examples
=DAY(”4/6/88 11:59:22 PM”) returns 6.
=DAY(“5/12/2009”) returns 12.

Related Topics
For related functions and additional information, see:
“DAYNAME” on page 48
“HOUR” on page 51
“MINUTE” on page 52
“MONTH” on page 53
“SECOND” on page 56
“YEAR” on page 62
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

DAYNAME

The DAYNAME function returns the name of the day of the week from a date/time
value or a number. Day 1 is Sunday.
DAYNAME(day-num)
ÂÂ day-num:  The desired day of the week. day-num is a date/time value, or number

value in the range 1 to 7. If day-num has a decimal portion, it is ignored.
Examples
If B1 contains the date/time value August 2, 1979 06:30:00, C1 contains the string 10/16/2008, and D1
contains 6:
=DAYNAME(B1) returns Thursday.
=DAYNAME(C1) returns Thursday.
=DAYNAME(D1) returns Friday.
=DAYNAME(“12/29/1974”) returns Sunday.

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Chapter 3    Date and Time Functions

Related Topics
For related functions and additional information, see:
“DAY” on page 47
“MONTHNAME” on page 54
“WEEKDAY” on page 59
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

DAYS360

The DAYS360 function returns the number of days between two dates based on
twelve 30-day months and a 360-day year.
DAYS360(start-date, end-date, use-euro-method)
ÂÂ start-date:  The starting date. start-date is a date/time value.
ÂÂ end-date:  The ending date. end-date is a date/time value.
ÂÂ use-euro-method:  An optional value that specifies whether to use the NASD or

European method for dates falling on the 31st of a month.
NASD method (0, FALSE, or omitted):  Use the NASD method for dates falling on
the 31st of a month.
EURO method (1 or TRUE):  Use the European method for dates falling on the 31st
of a month.
Examples
=DAYS360(”12/20/2008”, “3/31/2009”) returns 101d.
=DAYS360(”2/27/2008”, “3/31/2009”,0) returns 394d.
=DAYS360(”2/27/2008”, “3/31/2009”,1) returns 393d, as the European calculation method is used.

Related Topics
For related functions and additional information, see:
“DATEDIF” on page 45
“NETWORKDAYS” on page 54

Chapter 3    Date and Time Functions

49

“YEARFRAC” on page 63
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

EDATE

The EDATE function returns a date that is some number of months before or after a
given date.
EDATE(start-date, month-offset)
ÂÂ start-date:  The starting date. start-date is a date/time value.
ÂÂ month-offset: The number of months before or after the starting date. month-offset

is a number value. A negative month-offset is used to specify a number of months
before the starting date and a positive month-offset is used to specify a number of
months after the starting date.
Examples
=EDATE(”1/15/2000”, 1) returns 2/15/2000, the date one month later.
=EDATE(”1/15/2000”, -24) returns 1/15/1998, the date 24 months earlier.

Related Topics
For related functions and additional information, see:
“EOMONTH” on page 51
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

50		

Chapter 3    Date and Time Functions

EOMONTH

The EOMONTH function returns a date that is the last day of the month some number
of months before or after a given date.
EOMONTH(start-date, month-offset)
ÂÂ start-date:  The starting date. start-date is a date/time value.
ÂÂ month-offset: The number of months before or after the starting date. month-offset

is a number value. A negative month-offset is used to specify a number of months
before the starting date and a positive month-offset is used to specify a number of
months after the starting date.
Examples
=EOMONTH(”5/15/2010”, 5) returns Oct 31, 2010, the last day of the month five months after May 2010.
=EOMONTH(”5/15/2010”, -5) returns Dec 31, 2009, the last day of the month five months before May
2010.

Related Topics
For related functions and additional information, see:
“EDATE” on page 50
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

HOUR

The HOUR function returns the hour for a given date/time value.
HOUR(time)
ÂÂ time:  The time the function should use. time is a date/time value. The date portion

is ignored by this function.
Usage Notes
ÂÂ The hour returned is in 24-hour format (0 is midnight, 23 is 11:00 p.m.).
Examples
=HOUR(NOW()) returns the current hour of the day.
=HOUR(”4/6/88 11:59:22 AM”) returns 11.

Chapter 3    Date and Time Functions

51

Related Topics
For related functions and additional information, see:
“DAY” on page 47
“MINUTE” on page 52
“MONTH” on page 53
“SECOND” on page 56
“YEAR” on page 62
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

MINUTE

The MINUTE function returns the minutes for a given date/time value.
MINUTE(time)
ÂÂ time:  The time the function should use. time is a date/time value. The date portion

is ignored by this function.
Example
=MINUTE(”4/6/88 11:59:22 AM”) returns 59.

Related Topics
For related functions and additional information, see:
“DAY” on page 47
“HOUR” on page 51
“MONTH” on page 53
“SECOND” on page 56
“YEAR” on page 62
“Listing of Date and Time Functions” on page 42

52		

Chapter 3    Date and Time Functions

“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

MONTH

The MONTH function returns the month for a given date/time value.
MONTH(date)
ÂÂ date:  The date the function should use. date is a date/time value. The time portion

is ignored by this function.
Example
=MONTH(”April 6, 1988 11:59:22 AM”) returns 4.

Related Topics
For related functions and additional information, see:
“DAY” on page 47
“HOUR” on page 51
“MINUTE” on page 52
“MONTHNAME” on page 54
“SECOND” on page 56
“YEAR” on page 62
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 3    Date and Time Functions

53

MONTHNAME

The MONTHNAME function returns the name of the month from a number. Month 1 is
January.
MONTHNAME(month-num)
ÂÂ month-num:  The desired month. month-num is a number value and must be in the

range 1 to 12. If month-num has a decimal portion, it is ignored.
Examples
=MONTHNAME(9) returns September.
=MONTHNAME(6) returns June.

Related Topics
For related functions and additional information, see:
“DAYNAME” on page 48
“MONTH” on page 53
“WEEKDAY” on page 59
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

NETWORKDAYS

The NETWORKDAYS function returns the number of working days between two dates.
Working days exclude weekends and any other specified dates.
NETWORKDAYS(start-date, end-date, exclude-dates)
ÂÂ start-date:  The starting date. start-date is a date/time value.
ÂÂ end-date:  The ending date. end-date is a date/time value.
ÂÂ exclude-dates:  An optional collection of dates that should be excluded from the

count. exclude-dates is a collection containing date/time values.
Example
=NETWORKDAYS(”11/01/2009”, “11/30/2009”, {”11/11/2009”,”11/26/2009”}) returns 19d, the number of
working days in November 2009 excluding weekends and the two holidays specifically excluded.

54		

Chapter 3    Date and Time Functions

Related Topics
For related functions and additional information, see:
“DATEDIF” on page 45
“DAYS360” on page 49
“WORKDAY” on page 61
“YEARFRAC” on page 63
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

NOW

The NOW function returns the current date/time value from the system clock.
NOW()
Usage Notes
ÂÂ The NOW function does not have any arguments. However, you must include the
parentheses: =NOW().
Example
=NOW() returns October 4, 2008 10:47 am, if your file is updated on October 4, 2008, at 10:47 a.m.

Related Topics
For related functions and additional information, see:
“TODAY” on page 58
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 3    Date and Time Functions

55

SECOND

The SECOND function returns the seconds for a given date/time value.
SECOND(time)
ÂÂ time:  The time the function should use. time is a date/time value. The date portion

is ignored by this function.
Example
=SECOND(”4/6/88 11:59:22 am”) returns 22.

Related Topics
For related functions and additional information, see:
“DAY” on page 47
“HOUR” on page 51
“MINUTE” on page 52
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

TIME

The TIME function converts separate values for hours, minutes, and seconds into a
date/time value.
TIME(hours, minutes, seconds)
ÂÂ hours:  The number of hours to include in the value returned. hours is a number

value. If hours has a decimal portion, it is ignored.
ÂÂ minutes:  The number of minutes to include in the value returned. minutes is a

number value. If minutes has a decimal portion, it is ignored.
ÂÂ seconds:  The number of seconds to include in the value returned. seconds is a

number value. If seconds has a decimal portion, it is ignored.
Usage Notes
ÂÂ You can specify hour, minute, and second values greater than 24, 60, and 60,
respectively. If the hours, minutes, and seconds add up to more than 24 hours, 24
hours are repeatedly subtracted until the value is less than 24 hours.
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Chapter 3    Date and Time Functions

Examples
=TIME(12, 0, 0) returns 12:00 pm.
=TIME(16, 45, 30) returns 4:45 pm.
=TIME(0, 900, 0) returns 3:00 pm.
=TIME(60, 0, 0) returns 12:00 pm.
=TIME(4.25, 0, 0) returns 4:00 am.

Related Topics
For related functions and additional information, see:
“DATE” on page 44
“DATEVALUE” on page 47
“DURATION” on page 70
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

TIMEVALUE

The TIMEVALUE function returns the time as a decimal fraction of a 24-hour day from a
given date/time value or from a text string.
TIMEVALUE(time)
ÂÂ time:  The time the function should use. time is a date/time value. The date portion

is ignored by this function.
Examples
=TIMEVALUE(”4/6/88 12:00”) returns 0.5 (noon represents one-half of the day).
=TIMEVALUE(”12:00:59”) returns 0.5007 (rounded to four decimal places of accuracy).
=TIMEVALUE(”9:00 pm”) returns 0.875 (21 hours, or 9:00 p.m., divided by 24).

Related Topics
For related functions and additional information, see:
“Listing of Date and Time Functions” on page 42

Chapter 3    Date and Time Functions

57

“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

TODAY

The TODAY function returns the current system date. The time is set to 12:00 a.m.
TODAY()
Usage Notes
ÂÂ The TODAY function does not have any arguments. However, you must include the
parentheses: =TODAY().
ÂÂ The displayed date is updated every time you open or modify your file.
ÂÂ You can use the NOW function to get the current date and time and to format the

cell to display both.
Example
=TODAY() returns Apr 6, 2008, when calculated on April 6, 2008.

Related Topics
For related functions and additional information, see:
“NOW” on page 55
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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Chapter 3    Date and Time Functions

WEEKDAY

The WEEKDAY function returns a number that is the day of the week for a given date.
WEEKDAY(date, first-day)
ÂÂ date:  The date the function should use. date is a date/time value. The time portion

is ignored by this function.
ÂÂ first-day: An optional value that specifies how days are numbered.

Sunday is 1 (1 or omitted):  Sunday is the first day (day 1) of the week and Saturday
is day 7.
Monday is 1 (2):  Monday is the first day (day 1) of the week and Sunday is day 7.
Monday is 0 (3):  Monday is the first day (day 0) of the week and Sunday is day 6.
Examples
=WEEKDAY(”Apr 6, 1988”, 1) returns 4 (Wednesday, the fourth day if you start counting Sunday as day
1).
=WEEKDAY(”Apr 6, 1988”) returns the same value as the preceding example (numbering scheme 1 is
used if no number-scheme argument is specified).
=WEEKDAY(”Apr 6, 1988”, 2) returns 3 (Wednesday, the third day if you start counting Monday as day
1).
=WEEKDAY(”Apr 6, 1988”, 3) returns 2 (Wednesday, day number 2 if you start counting Monday as day
0).

Related Topics
For related functions and additional information, see:
“DAYNAME” on page 48
“MONTHNAME” on page 54
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 3    Date and Time Functions

59

WEEKNUM

The WEEKNUM function returns the number of the week within the year for a given date.
WEEKNUM(date, first-day)
ÂÂ date:  The date the function should use. date is a date/time value. The time portion

is ignored by this function.
ÂÂ first-day: An optional value that specifies whether weeks should begin on Sunday

or Monday.
Sunday is 1 (1 or omitted):  Sunday is the first day (day 1) of the week and Saturday
is day 7.
Monday is 1 (2):  Monday is the first day (day 1) of the week and Sunday is day 7.
Example
=WEEKNUM(”7/12/2009”,1) returns 29.
=WEEKNUM(”7/12/2009”,2) returns 28.

Related Topics
For related functions and additional information, see:
“DAY” on page 47
“HOUR” on page 51
“MINUTE” on page 52
“MONTH” on page 53
“SECOND” on page 56
“YEAR” on page 62
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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Chapter 3    Date and Time Functions

WORKDAY

The WORKDAY function returns the date that is the given number of working days
before or after a given date. Working days exclude weekends and any other dates
specifically excluded.
WORKDAY(date, work-days, exclude-dates)
ÂÂ date:  The date the function should use. date is a date/time value. The time portion

is ignored by this function.
ÂÂ work-days:  The number of working days before or after the given date. work-days

is a number value. It is positive if the desired date is after date and negative if the
desired date is before date.
ÂÂ exclude-dates:  An optional collection of dates that should be excluded from the

count. exclude-dates is a collection containing date/time values.
Example
=WORKDAY(”11/01/2009”, 20, {”11/11/2009”,”11/26/2009”}) returns Dec 1, 2009, the work day 20 days
after 11/01/2009 excluding weekends and the two holidays specifically excluded.

Related Topics
For related functions and additional information, see:
“NETWORKDAYS” on page 54
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 3    Date and Time Functions

61

YEAR

The YEAR function returns the year for a given date/time value.
YEAR(date)
ÂÂ date:  The date the function should use. date is a date/time value. The time portion

is ignored by this function.
Examples
=YEAR(”April 6, 2008”) returns 2008.
=YEAR(NOW()) returns 2009 when evaluated on June 4, 2009.

Related Topics
For related functions and additional information, see:
“DAY” on page 47
“HOUR” on page 51
“MINUTE” on page 52
“MONTH” on page 53
“SECOND” on page 56
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

62		

Chapter 3    Date and Time Functions

YEARFRAC

The YEARFRAC function finds the fraction of a year represented by the number of
whole days between two dates.
YEARFRAC(start-date, end-date, days-basis)
ÂÂ start-date:  The starting date. start-date is a date/time value.
ÂÂ end-date:  The ending date. end-date is a date/time value.
ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.
actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Examples
=YEARFRAC(”12/15/2009”, “6/30/2010”,0) returns 0.541666667.
=YEARFRAC(”12/15/2009”, “6/30/2010”,1) returns 0.539726027.
=YEARFRAC(”12/15/2009”, “6/30/2010”,2) returns 0.547222222.
=YEARFRAC(”12/15/2009”, “6/30/2010”,3) returns 0.539726027.
=YEARFRAC(”12/15/2009”, “6/30/2010”,4) returns 0.541666667.

Related Topics
For related functions and additional information, see:
“DATEDIF” on page 45
“DAYS360” on page 49
“NETWORKDAYS” on page 54
“Listing of Date and Time Functions” on page 42
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 3    Date and Time Functions

63

4

Duration Functions

The duration functions help you work with periods of time
(durations) by converting between different time periods,
such as hours, days, and weeks.
Listing of Duration Functions

iWork provides these duration functions for use with tables.

64

Function

Description

“DUR2DAYS” (page 65)

The DUR2DAYS function converts a duration
value to a number of days.

“DUR2HOURS” (page 65)

The DUR2HOURS function converts a duration
value to a number of hours.

“DUR2MILLISECONDS” (page 66)

The DUR2MILLISECONDS function converts a
duration value to a number of milliseconds.

“DUR2MINUTES” (page 67)

The DUR2MINUTES function converts a duration
value to a number of minutes.

“DUR2SECONDS” (page 68)

The DUR2SECONDS function converts a duration
value to a number of seconds.

“DUR2WEEKS” (page 69)

The DUR2WEEKS function converts a duration
value to a number of weeks.

“DURATION” (page 70)

The DURATION function combines separate
values for weeks, days, hours, minutes, seconds,
and milliseconds and returns a duration value.

“STRIPDURATION” (page 71)

The STRIPDURATION function evaluates a given
value and returns either the number of days
represented, if a duration value, or the given
value. This function is included for compatibility
with other spreadsheet applications.

DUR2DAYS

The DUR2DAYS function converts a duration value to a number of days.
DUR2DAYS(duration)
ÂÂ duration:  The length of time to be converted. duration is a duration value.
Examples
=DUR2DAYS(”2w 3d 2h 10m 0s 5ms”) returns 17.09027784.
=DUR2DAYS(”10:0:13:00:05.500”) returns 70.5417302.

Related Topics
For related functions and additional information, see:
“DUR2HOURS” on page 65
“DUR2MILLISECONDS” on page 66
“DUR2MINUTES” on page 67
“DUR2SECONDS” on page 68
“DUR2WEEKS” on page 69
“Listing of Duration Functions” on page 64
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

DUR2HOURS

The DUR2HOURS function converts a duration value to a number of hours.
DUR2HOURS(duration)
ÂÂ duration:  The length of time to be converted. duration is a duration value.
Examples
=DUR2HOURS(”2w 3d 2h 10m 0s 5ms”) returns 410.1666681.
=DUR2HOURS(”10:0:13:00:05.500”) returns 1693.001528.

Chapter 4    Duration Functions

65

Related Topics
For related functions and additional information, see:
“DUR2DAYS” on page 65
“DUR2MILLISECONDS” on page 66
“DUR2MINUTES” on page 67
“DUR2SECONDS” on page 68
“DUR2WEEKS” on page 69
“Listing of Duration Functions” on page 64
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

DUR2MILLISECONDS

The DUR2MILLISECONDS function converts a duration value to a number of milliseconds.
DUR2MILLISECONDS(duration)
ÂÂ duration:  The length of time to be converted. duration is a duration value.
Examples
=DUR2MILLISECONDS(”2w 3d 2h 10m 0s 5ms”) returns 1476600005.
=DUR2MILLISECONDS(”10:0:13:00:05.500”) returns 6094805500.

Related Topics
For related functions and additional information, see:
“DUR2DAYS” on page 65
“DUR2HOURS” on page 65
“DUR2MINUTES” on page 67
“DUR2SECONDS” on page 68
“DUR2WEEKS” on page 69
“Listing of Duration Functions” on page 64

66		

Chapter 4    Duration Functions

“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

DUR2MINUTES

The DUR2MINUTES function converts a duration value to a number of minutes.
DUR2MINUTES(duration)
ÂÂ duration:  The length of time to be converted. duration is a duration value.
Examples
=DUR2MINUTES(”2w 3d 2h 10m 0s 5ms”) returns 24610.0000833333.
=DUR2MINUTES(”10:0:13:00:05.500”) returns 101580.091666667.

Related Topics
For related functions and additional information, see:
“DUR2DAYS” on page 65
“DUR2HOURS” on page 65
“DUR2MILLISECONDS” on page 66
“DUR2SECONDS” on page 68
“DUR2WEEKS” on page 69
“Listing of Duration Functions” on page 64
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 4    Duration Functions

67

DUR2SECONDS

The DUR2SECONDS function converts a duration value to a number of seconds.
DUR2SECONDS(duration)
ÂÂ duration:  The length of time to be converted. duration is a duration value.
Examples
=DUR2SECONDS(”2w 3d 2h 10m 0s 5ms”) returns 1476600.005.
=DUR2SECONDS(”10:0:13:00:05.500”) returns 6094805.5.

Related Topics
For related functions and additional information, see:
“DUR2DAYS” on page 65
“DUR2HOURS” on page 65
“DUR2MILLISECONDS” on page 66
“DUR2MINUTES” on page 67
“DUR2WEEKS” on page 69
“Listing of Duration Functions” on page 64
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

68		

Chapter 4    Duration Functions

DUR2WEEKS

The DUR2WEEKS function converts a duration value to a number of weeks.
DUR2WEEKS(duration)
ÂÂ duration:  The length of time to be converted. duration is a duration value.
Examples
=DUR2WEEKS(”2w 3d 2h 10m 0s 5ms”) returns 2.44146826223545.
=DUR2WEEKS(”10:0:13:00:05.500”) returns 10.0773900462963.

Related Topics
For related functions and additional information, see:
“DUR2DAYS” on page 65
“DUR2HOURS” on page 65
“DUR2MILLISECONDS” on page 66
“DUR2MINUTES” on page 67
“DUR2SECONDS” on page 68
“Listing of Duration Functions” on page 64
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 4    Duration Functions

69

DURATION

The DURATION function combines separate values for weeks, days, hours, minutes,
seconds, and milliseconds and returns a duration value.
DURATION(weeks, days, hours, minutes, seconds, milliseconds)
ÂÂ weeks:  A value representing the number of weeks. weeks is a number value.
ÂÂ days:  An optional value representing the number of days. days is a number value.
ÂÂ hours:  An optional value representing the number of hours. hours is a number value.
ÂÂ minutes:  An optional value representing the number of minutes. minutes is a

number value.
ÂÂ seconds:  An optional value representing the number of seconds. seconds is a

number value.
ÂÂ milliseconds:  An optional value representing the number of milliseconds.

milliseconds is a number value.
Usage Notes
ÂÂ An argument that is 0 can be omitted, but the comma must be included if later
values are included. For example, =DURATION(, ,12, 3) would return a duration value
of 12h 3m (12 hours and 3 minutes).
ÂÂ Negative values are permitted. For example, =DURATION(0, 2, -24) would return a

duration of 1 day (2 days minus 24 hours).
Examples
=DURATION(1) returns 1w (1 week).
=DURATION(,,1) returns 1h (1 hour).
=DURATION(1.5) returns 1w 3d 12h (1 week, 3 days, 12 hours or 1.5 weeks).
=DURATION(3, 2, 7, 10, 15.3505) returns 3w 2d 7h 10m 15s 350ms (3 weeks, 2 days, 7 hours, 10 minutes,
15 seconds, 350 milliseconds).

Related Topics
For related functions and additional information, see:
“DATE” on page 44
“TIME” on page 56
“Listing of Duration Functions” on page 64
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41
70		

Chapter 4    Duration Functions

STRIPDURATION

The STRIPDURATION function evaluates a given value and returns either the number
of days represented, if a duration value, or the given value. This function is included for
compatibility with other spreadsheet applications.
STRIPDURATION(any-value)
ÂÂ any-value:  A value. any-value can contain any value type.

Usage Notes
ÂÂ If any-value is a duration value, the result is the same as for DUR2DAYS; otherwise
any-value is returned.
ÂÂ This function may be automatically inserted when a Numbers ’08 document is

upgraded, or an Excel or Appleworks document is imported. It is removed in any
copy of the file saved as a Numbers ’08 or Excel document.
Examples
=STRIPDURATION(”1w”) returns 7, the equivalent of one week in days.
=STRIPDURATION(12) returns 12; since it was not a duration value it is returned.
=STRIPDURATION (”abc”) returns “abc”.

Related Topics
For related functions and additional information, see:
“Listing of Duration Functions” on page 64
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 4    Duration Functions

71

Engineering Functions

5

The engineering functions help you calculate some common
engineering values and convert between different numeric
bases.
Listing of Engineering Functions

iWork provides these engineering functions for use with tables.

72

Function

Description

“BASETONUM” (page 73)

The BASETONUM function converts a number of
the specified base into a number in base 10.

“BESSELJ” (page 74)

The BESSELJ function returns the integer Bessel
function Jn(x).

“BESSELY” (page 75)

The BESSELY function returns the integer Bessel
function Yn(x).

“BIN2DEC” (page 76)

The BIN2DEC function converts a binary number
to the corresponding decimal number.

“BIN2HEX” (page 77)

The BIN2HEX function converts a binary number
to the corresponding hexadecimal number.

“BIN2OCT” (page 78)

The BIN2OCT function converts a binary number
to the corresponding octal number.

“CONVERT” (page 79)

The CONVERT function converts a number from
one measurement system to its corresponding
value in another measurement system.

“DEC2BIN” (page 83)

The DEC2BIN function converts a decimal
number to the corresponding binary number.

“DEC2HEX” (page 84)

The DEC2HEX function converts a decimal
number to the corresponding hexadecimal
number.

Function

Description

“DEC2OCT” (page 85)

The DEC2OCT function converts a decimal
number to the corresponding octal number.

“DELTA” (page 86)

The DELTA function determines whether two
values are exactly equal.

“ERF” (page 87)

The ERF function returns the error function
integrated between two values.

“ERFC” (page 87)

The ERFC function returns the complementary
ERF function integrated between a given lower
bound and infinity.

“GESTEP” (page 88)

The GESTEP function determines if one value is
greater than or exactly equal to another value.

“HEX2BIN” (page 89)

The HEX2BIN function converts a hexadecimal
number to the corresponding binary number.

“HEX2DEC” (page 90)

The HEX2DEC function converts a hexadecimal
number to the corresponding decimal number.

“HEX2OCT” (page 91)

The HEX2OCT function converts a hexadecimal
number to the corresponding octal number.

“NUMTOBASE” (page 92)

The NUMTOBASE function converts a number
from base 10 into a number in the specified base.

“OCT2BIN” (page 93)

The OCT2BIN function converts an octal number
to the corresponding binary number.

“OCT2DEC” (page 94)

The OCT2DEC function converts an octal number
to the corresponding decimal number.

“OCT2HEX” (page 95)

The OCT2HEX function converts an octal number
to the corresponding hexadecimal number.

BASETONUM

The BASETONUM function converts a number of the specified base into a number
in base 10.
BASETONUM(convert-string, base)
ÂÂ convert-string:  The string representing the number to be converted. convert-string

is a string value. It must contain only numbers and letters that apply in the base of
the number being converted.
ÂÂ base:  The current base of the number to be converted. base is a number value and

must be in the range 1 to 36.

Chapter 5    Engineering Functions

73

Usage Notes
ÂÂ This function returns a number value and can properly be used in a formula
containing other number values. Some other spreadsheet applications return
a string value.
Examples
=BASETONUM(”3f”, 16) returns 63.
=BASETONUM(1000100, 2) returns 68.
=BASETONUM(”7279”, 8) returns an error, since the digit “9” is not valid in base 8.

Related Topics
For related functions and additional information, see:
“BIN2DEC” on page 76
“HEX2DEC” on page 90
“NUMTOBASE” on page 92
“OCT2DEC” on page 94
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

BESSELJ

The BESSELJ function returns the integer Bessel function Jn(x).
BESSELJ(any-x-value, n-value)
ÂÂ any-x-value:  The x value at which you want to evaluate the function. any-x-value is

a number value.
ÂÂ n-value:  The order of the function. n-value is a number value and must be greater

than or equal to 0. If n-value has a decimal portion, it is ignored.
Examples
=BESSELJ(25, 3) returns 0.108343081061509.
=BESSELJ(25, 3.9) also returns 0.108343081061509, since any decimal portion of n-value is ignored.
=BESSELJ(-25, 3) returns -0.108343081061509.

74		

Chapter 5    Engineering Functions

Related Topics
For related functions and additional information, see:
“BESSELY” on page 75
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

BESSELY

The BESSELY function returns the integer Bessel function Yn(x).
BESSELY(pos-x-value, n-value)
ÂÂ pos-x-value:  The positive x value at which you want to evaluate the function.

pos-x-value is a number value and must be greater than 0.
ÂÂ n-value:  The order of the function. n-value is a number value and must be greater

than or equal to 0. If n-value has a decimal portion, it is ignored.
Usage Notes
ÂÂ This form of the Bessel function is also known as the Neumann function.
Examples
=BESSELY(25, 3) returns 0.117924850396893.
=BESSELY(25, 3.9) also returns 0.117924850396893, since any decimal portion of n-value is ignored.
=BESSELY(-25, 3) returns an error, since negative or zero values are not permitted.

Related Topics
For related functions and additional information, see:
“BESSELJ” on page 74
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 5    Engineering Functions

75

BIN2DEC

The BIN2DEC function converts a binary number to the corresponding decimal
number.
BIN2DEC(binary-string, convert-length)
ÂÂ binary-string:  The string representing the number to be converted. binary-string is

a string value. It must contain only 0s and 1s.
ÂÂ convert-length:  An optional value specifying minimum length of the number

returned. convert-length is a number value and must be in the range 1 to 32. If
omitted, it is assumed to be 1. If included, convert-string is padded with leading
zeros, if necessary, so that it is at least the length specified by convert-length.
Examples
=BIN2DEC(”1001”) returns 9.
=BIN2DEC(”100111”, 3) returns 039.
=BIN2DEC(101101) returns 45.

Related Topics
For related functions and additional information, see:
“BIN2HEX” on page 77
“BIN2OCT” on page 78
“DEC2BIN” on page 83
“HEX2DEC” on page 90
“OCT2DEC” on page 94
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

76		

Chapter 5    Engineering Functions

BIN2HEX

The BIN2HEX function converts a binary number to the corresponding hexadecimal
number.
BIN2HEX(binary-string, convert-length)
ÂÂ binary-string:  The string representing the number to be converted. binary-string is

a string value. It must contain only 0s and 1s.
ÂÂ convert-length:  An optional value specifying minimum length of the number

returned. convert-length is a number value and must be in the range 1 to 32. If
omitted, it is assumed to be 1. If included, convert-string is padded with leading
zeros, if necessary, so that it is at least the length specified by convert-length.
Usage Notes
ÂÂ This function uses two’s complement notation, based on 32 bits. Therefore, negative
numbers will always be 8 digits in length.
Examples
=BIN2HEX(”100101”) returns 25.
=BIN2HEX(”100111”, 3) returns 027.
=BIN2HEX(101101) returns 2D.

Related Topics
For related functions and additional information, see:
“BIN2DEC” on page 76
“BIN2OCT” on page 78
“DEC2HEX” on page 84
“HEX2BIN” on page 89
“OCT2HEX” on page 95
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 5    Engineering Functions

77

BIN2OCT

The BIN2OCT function converts a binary number to the corresponding octal number.
BIN2OCT(binary-string, convert-length)
ÂÂ binary-string:  The string representing the number to be converted. binary-string is

a string value. It must contain only 0s and 1s.
ÂÂ convert-length:  An optional value specifying minimum length of the number

returned. convert-length is a number value and must be in the range 1 to 32. If
omitted, it is assumed to be 1. If included, convert-string is padded with leading
zeros, if necessary, so that it is at least the length specified by convert-length.
Usage Notes
ÂÂ This function uses two’s complement notation, based on 32 bits. Therefore, negative
numbers will always be 11 digits in length.
Examples
=BIN2OCT(”10011”) returns 23.
=BIN2OCT(”100111”, 3) returns 047.

Related Topics
For related functions and additional information, see:
“BIN2HEX” on page 77
“DEC2OCT” on page 85
“HEX2OCT” on page 91
“OCT2BIN” on page 93
“BIN2DEC” on page 76
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

78		

Chapter 5    Engineering Functions

CONVERT

The CONVERT function converts a number from one measurement system to its
corresponding value in another measurement system.
CONVERT(convert-num, from-unit, to-unit)
ÂÂ convert-num:  The number to be converted. convert-num is a number value.
ÂÂ from-unit:  The current unit of the number to be converted. from-unit is a string

value. It must be one of the specified constants.
ÂÂ to-unit:  The new unit of the number to be converted. to-unit is a string value.

It must be one of the specified constants.
Usage Notes
ÂÂ The possible values for from-unit and to-unit are contained in tables that follow
the examples (“Supported Conversion Units” on page 80). The tables are organized
by category. If the value is entered into a referenced cell, instead of being typed
directly into the function, the quotes included in the tables are not required. Case is
important and must be strictly followed.
Examples
=CONVERT(9, “lbm”, “kg”) returns 4.08233133 (9 pounds is approximately 4.08 kilograms).
=CONVERT (26.2, “mi”, “m”) returns 42164.8128 (26.2 miles is approximately 42,164.8 meters).
=CONVERT(1, “tsp”, “ml”) returns 4.92892159375 (1 teaspoon is approximately 4.9 milliliters).

Related Topics
For related functions and additional information, see:

“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 5    Engineering Functions

79

Supported Conversion Units
Weight and mass
Measure

Constant

Gram

“g” (can be used with metric prefixes)

Slug

“sg”

Pound mass (avoirdupois)

“lbm”

U (atomic mass unit)

“u” (can be used with metric prefixes)

Ounce mass (avoirdupois)

“ozm”

Distance
Measure

Constant

Meter

“m” (can be used with metric prefixes)

Statute mile

“mi”

Nautical mile

“Nmi”

Inch

“in”

Foot

“ft”

Yard

“yd”

Angstrom

“ang” (can be used with metric prefixes)

Pica (1/6 in., Postscript Pica)

“Pica”

Duration

80		

Measure

Constant

Year

“yr”

Week

“wk”

Day

“day”

Hour

“hr”

Minute

“mn”

Second

“sec” (can be used with metric prefixes)

Chapter 5    Engineering Functions

Speed
Measure

Constant

Miles per hour

“mi/h”

Miles per minute

“mi/mn”

Meters per hour

“m/h” (can be used with metric prefixes)

Meters per minute

“m/mn” (can be used with metric prefixes)

Meters per second

“m/s” (can be used with metric prefixes)

Feet per minute

“ft/mn”

Feet per second

“ft/s”

Knot

“kt”

Pressure
Measure

Constant

Pascal

“Pa” (can be used with metric prefixes)

Atmosphere

“atm” (can be used with metric prefixes)

Millimeters of mercury

“mmHg” (can be used with metric prefixes)

Force
Measure

Constant

Newton

“N” (can be used with metric prefixes)

Dyne

“dyn” (can be used with metric prefixes)

Pound force

“lbf”

Energy
Measure

Constant

Joule

“J” (can be used with metric prefixes)

Erg

“e” (can be used with metric prefixes)

Thermodynamic calorie

“c” (can be used with metric prefixes)

IT calorie

“cal” (can be used with metric prefixes)

Electron volt

“eV” (can be used with metric prefixes)

Horsepower-hour

“HPh”

Chapter 5    Engineering Functions

81

Measure

Constant

Watt-hour

“Wh” (can be used with metric prefixes)

Foot-pound

“flb”

BTU

“BTU”

Power
Measure

Constant

Horsepower

“HP”

Watt

“W” (can be used with metric prefixes)

Magnetism
Measure

Constant

Tesla

“T” (can be used with metric prefixes)

Gauss

“ga” (can be used with metric prefixes)

Temperature
Measure

Constant

Degrees Celsius

“C”

Degrees Fahrenheit

“F”

Kelvins

“K” (can be used with metric prefixes)

Liquid

82		

Measure

Constant

Teaspoon

“tsp”

Tablespoon

“tbs”

Fluid ounce

“oz”

Cup

“cup”

U.S. pint

“pt”

U.K. pint

“uk_pt”

Quart

“qt”

Gallon

“gal”

Liter

“l” (can be used with metric prefixes)

Chapter 5    Engineering Functions

Metric prefixes
Measure

Constant

Multiplier

exa

“E”

1E+18

peta

“P”

1E+15

tera

“T”

1E+12

giga

“G”

1E+09

mega

“M”

1E+06

kilo

“k”

1E+03

hecto

“h”

1E+02

deca

“e”

1E+01

deci

“d”

1E-01

centi

“c”

1E-02

milli

“m”

1E-03

micro

“u” or “µ”

1E-06

nano

“n”

1E-09

pico

“p”

1E-12

femto

“f”

1E-15

atto

“a”

1E-18

Usage Notes
ÂÂ These prefixes can only be used with the metric constants “g”, “u”, “m”, “ang”, “sec”, “m/h”,
“m/mn”, “m/s”, “Pa”, “atm”, “mmHg”, “N”, “dyn”, “J”, “e”, “c”, “cal”, “eV”, “Wh”, “W”, “T”, “ga”, “K”, and “l”.

DEC2BIN

The DEC2BIN function converts a decimal number to the corresponding binary
number.
DEC2BIN(decimal-string, convert-length)
ÂÂ decimal-string:  The string representing the number to be converted. decimal-string

is a string value. It must contain only the numbers 0 through 9.
ÂÂ convert-length:  An optional value specifying minimum length of the number

returned. convert-length is a number value and must be in the range 1 to 32. If
omitted, it is assumed to be 1. If included, convert-string is padded with leading
zeros, if necessary, so that it is at least the length specified by convert-length.

Chapter 5    Engineering Functions

83

Examples
=DEC2BIN(100) returns 01100100.
=DEC2BIN(”1001”, 12) returns 001111101001.

Related Topics
For related functions and additional information, see:
“BIN2DEC” on page 76
“DEC2HEX” on page 84
“DEC2OCT” on page 85
“HEX2BIN” on page 89
“OCT2BIN” on page 93
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

DEC2HEX

The DEC2HEX function converts a decimal number to the corresponding hexadecimal
number.
DEC2HEX(decimal-string, convert-length)
ÂÂ decimal-string:  The string representing the number to be converted. decimal-string

is a string value. It must contain only the numbers 0 through 9.
ÂÂ convert-length:  An optional value specifying minimum length of the number

returned. convert-length is a number value and must be in the range 1 to 32. If
omitted, it is assumed to be 1. If included, convert-string is padded with leading
zeros, if necessary, so that it is at least the length specified by convert-length.
Examples
=DEC2HEX(100) returns 64.
=DEC2HEX(”1001”, 4) returns 03E9.

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Related Topics
For related functions and additional information, see:
“BIN2HEX” on page 77
“DEC2BIN” on page 83
“DEC2OCT” on page 85
“HEX2DEC” on page 90
“OCT2HEX” on page 95
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

DEC2OCT

The DEC2OCT function converts a decimal number to the corresponding octal number.
DEC2OCT(decimal-string, convert-length)
ÂÂ decimal-string:  The string representing the number to be converted. decimal-string

is a string value. It must contain only the numbers 0 through 9.
ÂÂ convert-length:  An optional value specifying minimum length of the number

returned. convert-length is a number value and must be in the range 1 to 32. If
omitted, it is assumed to be 1. If included, convert-string is padded with leading
zeros, if necessary, so that it is at least the length specified by convert-length.
Examples
=DEC2OCT(100) returns 144.
=DEC2OCT(”1001”, 4) returns 1751.

Related Topics
For related functions and additional information, see:
“BIN2OCT” on page 78
“DEC2BIN” on page 83
“DEC2HEX” on page 84

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“HEX2OCT” on page 91
“OCT2DEC” on page 94
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

DELTA

The DELTA function determines whether two values are exactly equal. This function
uses exact equality. By comparison, the = operator uses string-based equality.
DELTA(compare-from, compare-to)
ÂÂ compare-from:  A number. compare-from is a number value.
ÂÂ compare-to:  A number. compare-to is a number value.

Usage Notes
ÂÂ DELTA returns 1 (TRUE) if compare-from is exactly equal to compare-to; otherwise
0 (FALSE) is returned.
Examples
=DELTA(5, 5) returns 1 (TRUE).
=DELTA(5, -5) returns 0 (FALSE).
=DELTA(5, 5.000) returns 1 (TRUE).

Related Topics
For related functions and additional information, see:
“GESTEP” on page 88
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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ERF

The ERF function returns the error function integrated between two values.
ERF(lower, upper)
ÂÂ lower:  The lower limit or bound. lower is a number value.
ÂÂ upper:  An optional argument specifying the upper limit or bound. upper is a

number value. If upper is omitted it is assumed to be 0.
Usage Notes
ÂÂ This function is also known as the Gauss error function.
Examples
=ERF(0, 1) returns 0.842700792949715.
=ERF(-1, 1) returns 1.68540158589943.
=ERF(1, 8) returns 0.157299207050285.

Related Topics
For related functions and additional information, see:
“ERFC” on page 87
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

ERFC

The ERFC function returns the complementary ERF function integrated between a
given lower bound and infinity.
ERFC(lower)
ÂÂ lower:  The lower limit or bound. lower is a number value.
Examples
=ERFC(-1) returns 1.84270079294971.
=ERFC(1) returns 0.157299207050285.
=ERFC(12) returns 1.3562611692059E-64.

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Related Topics
For related functions and additional information, see:
“ERF” on page 87
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

GESTEP

The GESTEP function determines if one value is greater than or exactly equal to
another value. This function uses exact equality. By comparison, the = operator uses
string-based equality.
GESTEP(compare-num, step-number)
ÂÂ compare-num:  The number to compare. compare-num is a number value.
ÂÂ step-number:  The size of the step. step-number is a number value.

Usage Notes
ÂÂ GESTEP returns 1 (TRUE) if compare-num is greater than or exactly equal to stepnumber; otherwise 0 (FALSE) is returned.
Examples
=GESTEP(-4, -5) returns 1 (TRUE), since -4 is greater than -5.
=GESTEP(4, 5) returns 0 (FALSE), since 4 is less than 5.
=GESTEP(5, 4) returns 1 (TRUE), since 5 is greater than 4.
=GESTEP(20, 20) returns 1 (TRUE), since 20 is exactly equal to 20.

Related Topics
For related functions and additional information, see:
“DELTA” on page 86
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15

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“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

HEX2BIN

The HEX2BIN function converts a hexadecimal number to the corresponding binary
number.
HEX2BIN(hex-string, convert-length)
ÂÂ hex-string:  The string representing the number to be converted. hex-string is a string

value. It must contain only the numbers 0 through 9 and the letters A through F.
ÂÂ convert-length:  An optional value specifying minimum length of the number

returned. convert-length is a number value and must be in the range 1 to 32. If
omitted, it is assumed to be 1. If included, convert-string is padded with leading
zeros, if necessary, so that it is at least the length specified by convert-length.
Usage Notes
ÂÂ This function uses two’s complement notation, based on 32 bits. Therefore, negative
numbers will always be 32 digits in length.
Examples
=HEX2BIN(”F”, 8) returns 00001111.
=HEX2BIN(“3F”) returns 0111111.

Related Topics
For related functions and additional information, see:
“BIN2HEX” on page 77
“HEX2DEC” on page 90
“HEX2OCT” on page 91
“OCT2BIN” on page 93
“DEC2BIN” on page 83
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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89

HEX2DEC

The HEX2DEC function converts a hexadecimal number to the corresponding decimal
number.
HEX2DEC(hex-string, convert-length)
ÂÂ hex-string:  The string representing the number to be converted. hex-string is a

string value. It must contain only the numbers 0 through 9 and the letters A through
F.
ÂÂ convert-length:  An optional value specifying minimum length of the number

returned. convert-length is a number value and must be in the range 1 to 32. If
omitted, it is assumed to be 1. If included, convert-string is padded with leading
zeros, if necessary, so that it is at least the length specified by convert-length.
Examples
=HEX2DEC(”F”, 3) returns 015.
=HEX2DEC(“3F”) returns 63.

Related Topics
For related functions and additional information, see:
“BIN2DEC” on page 76
“DEC2HEX” on page 84
“HEX2BIN” on page 89
“HEX2OCT” on page 91
“OCT2DEC” on page 94
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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HEX2OCT

The HEX2OCT function converts a hexadecimal number to the corresponding octal
number.
HEX2OCT(hex-string, convert-length)
ÂÂ hex-string:  The string representing the number to be converted. hex-string is a

string value. It must contain only the numbers 0 through 9 and the letters A through
F.
ÂÂ convert-length:  An optional value specifying minimum length of the number

returned. convert-length is a number value and must be in the range 1 to 32. If
omitted, it is assumed to be 1. If included, convert-string is padded with leading
zeros, if necessary, so that it is at least the length specified by convert-length.
Usage Notes
ÂÂ This function uses two’s complement notation, based on 32 bits. Therefore, negative
numbers will always be 11 digits in length.
Examples
=HEX2OCT(”F”, 3) returns 017.
=HEX2OCT(“4E”) returns 116.

Related Topics
For related functions and additional information, see:
“BIN2OCT” on page 78
“DEC2OCT” on page 85
“HEX2BIN” on page 89
“HEX2DEC” on page 90
“OCT2HEX” on page 95
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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91

NUMTOBASE

The NUMTOBASE function converts a number from base 10 into a number in the
specified base.
NUMTOBASE(decimal-string, base, convert-length)
ÂÂ decimal-string:  The string representing the number to be converted. decimal-string

is a string value. It must contain only the numbers 0 through 9.
ÂÂ base:  The new base of the number to be converted. base is a number value and

must be in the range 1 to 36.
ÂÂ convert-length:  An optional value specifying minimum length of the number

returned. convert-length is a number value and must be in the range 1 to 32. If
omitted, it is assumed to be 1. If included, convert-string is padded with leading
zeros, if necessary, so that it is at least the length specified by convert-length.
Examples
=NUMTOBASE(16, 16) returns 10.
=NUMTOBASE(100, 32, 4) returns 0034.
=NUMTOBASE(100,2) returns 1100100.

Related Topics
For related functions and additional information, see:
“BASETONUM” on page 73
“DEC2BIN” on page 83
“DEC2HEX” on page 84
“DEC2OCT” on page 85
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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OCT2BIN

The OCT2BIN function converts an octal number to the corresponding binary number.
OCT2BIN(octal-string, convert-length)
ÂÂ octal-string:  The string representing the number to be converted. octal-string is a

string value. It must contain only the numbers 0 through 7.
ÂÂ convert-length:  An optional value specifying minimum length of the number

returned. convert-length is a number value and must be in the range 1 to 32. If
omitted, it is assumed to be 1. If included, convert-string is padded with leading
zeros, if necessary, so that it is at least the length specified by convert-length.
Usage Notes
ÂÂ This function uses two’s complement notation, based on 32 bits. Therefore, negative
numbers will always be 32 digits in length.
Examples
=OCT2BIN(127,8) returns 01010111.
=OCT2BIN(15) returns 01101.

Related Topics
For related functions and additional information, see:
“BIN2OCT” on page 78
“DEC2BIN” on page 83
“HEX2BIN” on page 89
“OCT2DEC” on page 94
“OCT2HEX” on page 95
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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93

OCT2DEC

The OCT2DEC function converts an octal number to the corresponding decimal
number.
OCT2DEC(octal-string, convert-length)
ÂÂ octal-string:  The string representing the number to be converted. octal-string is a

string value. It must contain only the numbers 0 through 7.
ÂÂ convert-length:  An optional value specifying minimum length of the number

returned. convert-length is a number value and must be in the range 1 to 32. If
omitted, it is assumed to be 1. If included, convert-string is padded with leading
zeros, if necessary, so that it is at least the length specified by convert-length.
Examples
=OCT2DEC(127,4) returns 0087.
=OCT2DEC(15) returns 13.

Related Topics
For related functions and additional information, see:
“BIN2DEC” on page 76
“DEC2OCT” on page 85
“OCT2BIN” on page 93
“OCT2HEX” on page 95
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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OCT2HEX

The OCT2HEX function converts an octal number to the corresponding hexadecimal
number.
OCT2HEX(octal-string, convert-length)
ÂÂ octal-string:  The string representing the number to be converted. octal-string is a

string value. It must contain only the numbers 0 through 7.
ÂÂ convert-length:  An optional value specifying minimum length of the number

returned. convert-length is a number value and must be in the range 1 to 32. If
omitted, it is assumed to be 1. If included, convert-string is padded with leading
zeros, if necessary, so that it is at least the length specified by convert-length.
Usage Notes
ÂÂ This function uses two’s complement notation, based on 32 bits. Therefore, negative
numbers will always be 8 digits in length.
Examples
=OCT2HEX(127,4) returns 0057.
=OCT2HEX(15) returns 0D.

Related Topics
For related functions and additional information, see:
“BIN2HEX” on page 77
“DEC2HEX” on page 84
“HEX2OCT” on page 91
“OCT2BIN” on page 93
“OCT2DEC” on page 94
“Listing of Engineering Functions” on page 72
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 5    Engineering Functions

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6

Financial Functions

The financial functions help you work with cash flows,
depreciable assets, annuities, and investments by solving
problems such as the amount of annual depreciation of an
asset, the interest earned on an investment, and the current
market price of a bond.
Listing of Financial Functions

iWork provides these financial functions for use with tables.

96

Function

Description

“ACCRINT” (page 99)

The ACCRINT function calculates the accrued
interest added to the purchase price of a security
and paid to the seller when the security pays
periodic interest.

“ACCRINTM” (page 101)

The ACCRINTM function calculates the total
accrued interest added to the purchase price of a
security and paid to the seller when the security
pays interest only at maturity.

“BONDDURATION” (page 103)

The BONDDURATION function calculates the
weighted average of the present value of the
cash flows for an assumed par value of $100.

“BONDMDURATION” (page 104)

The BONDMDURATION function calculates the
modified weighted average of the present value
of the cash flows for an assumed par value of
$100.

“COUPDAYBS” (page 105)

The COUPDAYBS function returns the number
of days between the beginning of the coupon
period in which settlement occurs and the
settlement date.

“COUPDAYS” (page 107)

The COUPDAYS function returns the number of
days in the coupon period in which settlement
occurs.

Function

Description

“COUPDAYSNC” (page 108)

The COUPDAYSNC function returns the number
of days between the settlement date and the end
of the coupon period in which settlement occurs.

“COUPNUM” (page 109)

The COUPNUM function returns the number
of coupons remaining to be paid between the
settlement date and the maturity date.

“CUMIPMT” (page 110)

The CUMIPMT function returns the total interest
included in loan or annuity payments over a
chosen time interval based on fixed periodic
payments and a fixed interest rate.

“CUMPRINC” (page 112)

The CUMPRINC function returns the total
principal included in loan or annuity payments
over a chosen time interval based on fixed
periodic payments and a fixed interest rate.

“DB” (page 114)

The DB function returns the amount of
depreciation of an asset for a specified period
using the fixed-declining balance method.

“DDB” (page 116)

The DDB function returns the amount of
depreciation of an asset based on a specified
depreciation rate.

“DISC” (page 117)

The DISC function returns the annual discount
rate of a security that pays no interest and is sold
at a discount to its redemption value.

“EFFECT” (page 119)

The EFFECT function returns the effective annual
interest rate from the nominal annual interest
rate based on the number of compounding
periods per year.

“FV” (page 120)

The FV function returns the future value of an
investment based on a series of regular periodic
cash flows (payments of a constant amount and
all cash flows at constant intervals) and a fixed
interest rate.

“INTRATE” (page 122)

The INTRATE function returns the effective annual
interest rate for a security that pays interest only
at maturity.

“IPMT” (page 123)

The IPMT function returns the interest portion
of a specified loan or annuity payment based on
fixed, periodic payments and a fixed interest rate.

“IRR” (page 125)

The IRR function returns the internal rate of
return for an investment that is based on a series
of potentially irregular cash flows that occur at
regular time intervals.

Chapter 6    Financial Functions

97

98		

Function

Description

“ISPMT” (page 126)

The ISPMT function returns the interest portion
of a specified loan or annuity payment based
on fixed, periodic payments and a fixed interest
rate. This function is provided for compatibility
with tables imported from other spreadsheet
applications.

“MIRR” (page 128)

The MIRR function returns the modified internal
rate of return for an investment that is based on
a series of potentially irregular cash flows that
occur at regular time intervals. The rate earned on
positive cash flows and the rate paid to finance
negative cash flows can differ.

“NOMINAL” (page 129)

The NOMINAL function returns the nominal
annual interest rate from the effective
annual interest rate based on the number of
compounding periods per year.

“NPER” (page 130)

The NPER function returns the number of
payment periods for a loan or annuity based on a
series of regular periodic cash flows (payments of
a constant amount and all cash flows at constant
intervals) and a fixed interest rate.

“NPV” (page 132)

The NPV function returns the net present value
of an investment based on a series of potentially
irregular cash flows that occur at regular time
intervals.

“PMT” (page 134)

The PMT function returns the fixed periodic
payment for a loan or annuity based on a series
of regular periodic cash flows (payments of a
constant amount and all cash flows at constant
intervals) and a fixed interest rate.

“PPMT” (page 135)

The PPMT function returns the principal portion
of a specified loan or annuity payment based on
fixed periodic payments and a fixed interest rate.

“PRICE” (page 137)

The PRICE function returns the price of a
security that pays periodic interest per $100 of
redemption (par) value.

“PRICEDISC” (page 138)

The PRICEDISC function returns the price of a
security that is sold at a discount to redemption
value and does not pay interest per $100 of
redemption (par) value.

“PRICEMAT” (page 140)

The PRICEMAT function returns the price of a
security that pays interest only at maturity per
$100 of redemption (par) value.

Chapter 6    Financial Functions

Function

Description

“PV” (page 141)

The PV function returns the present value of
an investment or annuity based on a series
of regular periodic cash flows (payments of a
constant amount and all cash flows at constant
intervals) and a fixed interest rate.

“RATE” (page 144)

The RATE function returns the interest rate of an
investment, loan, or annuity based on a series
of regular periodic cash flows (payments of a
constant amount and all cash flows at constant
intervals) and a fixed interest rate.

“RECEIVED” (page 146)

The RECEIVED function returns the maturity value
for a security that pays interest only at maturity.

“SLN” (page 147)

The SLN function returns the amount of
depreciation of an asset for a single period using
the straight-line method.

“SYD” (page 148)

The SYD function returns the amount of
depreciation of an asset for a specified period
using the sum-of-the-years-digits method.

“VDB” (page 149)

The VDB function returns the amount of
depreciation of an asset over a chosen time
interval, based on a specified depreciation rate.

“YIELD” (page 150)

The YIELD function returns the effective annual
interest rate for a security that pays regular
periodic interest.

“YIELDDISC” (page 152)

The YIELDDISC function returns the effective
annual interest rate for a security that is sold at a
discount to redemption value and pays
no interest.

“YIELDMAT” (page 153)

The YIELDMAT function returns the effective
annual interest rate for a security that pays
interest only at maturity.

ACCRINT

The ACCRINT function calculates the accrued interest added to the purchase price of a
security and paid to the seller when the security pays periodic interest.
ACCRINT(issue, first, settle, annual-rate, par, frequency, days-basis)
ÂÂ issue:  The date the security was originally issued. issue is a date/time value and

must be the earliest date given.
ÂÂ first: The date of the first interest payment. first is a date/time value and must be

after issue.

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99

ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ annual-rate:  The annual coupon rate or stated annual interest rate of the security.

annual-rate is a number value and is either entered as a decimal (for example, 0.08)
or with a percent sign (for example, 8%).
ÂÂ par:  The face (par) or maturity value of the security. par is a number value. If

omitted (comma, but no value), par is assumed to be 1000.
ÂÂ frequency:  The number of coupon payments each year.

annual (1): One payment per year.
semiannual (2): Two payments per year.
quarterly (4): Four payments per year.
ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.
actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Usage Notes
ÂÂ If settle is before first, the function returns the interest accrued since issue. If settle is
after first, the function returns the interest accrued since the coupon payment date
that most immediately precedes settle.
ÂÂ Use ACCRINTM for a security that pays interest only at maturity.
Example 1
Assume you are considering the purchase of the hypothetical security described by the values listed.
The settlement date is assumed to be before the first coupon date.
You could use the ACCRINT function to determine the amount of accrued interest that would be
added to the purchase/sale price. The function evaluates to $38.06, which represents the interest
accrued between the issue date and the settlement date.

=ACCRINT
(B2, C2, D2,
E2, F2, G2,
H2)

issue

first

settle

annual-rate

par

frequency

days-basis

12/14/2008

07/01/2009

05/01/2009

0.10

1000

2

0

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Chapter 6    Financial Functions

Example 2
Assume you are considering the purchase of the hypothetical security described by the values listed.
The settlement date is assumed to be after the first coupon date.
You could use the ACCRINT function to determine the amount of accrued interest that would be
added to the purchase/sale price. The function evaluates to approximately $20.56, which represents
the interest accrued between the immediately preceding coupon payment date and the settlement
date.

=ACCRINT
(B2, C2, D2,
E2, F2, G2,
H2)

issue

first

settle

annual-rate

par

frequency

days-basis

12/14/2008

07/01/2009

09/15/2009

0.10

1000

2

0

Related Topics
For related functions and additional information, see:
“ACCRINTM” on page 101
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

ACCRINTM

The ACCRINTM function calculates the total accrued interest added to the purchase price
of a security and paid to the seller when the security pays interest only at maturity.
ACCRINTM(issue, settle, annual-rate, par, days-basis)
ÂÂ issue:  The date the security was originally issued. issue is a date/time value and

must be the earliest date given.
ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ annual-rate:  The annual coupon rate or stated annual interest rate of the security.

annual-rate is a number value and is either entered as a decimal (for example, 0.08)
or with a percent sign (for example, 8%).

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ÂÂ par:  The face (par) or maturity value of the security. par is a number value. If

omitted (comma, but no value), par is assumed to be 1000.
ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.
actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Usage Notes
ÂÂ Use ACCRINT for a security that pays periodic interest.
Example
Assume you are considering the purchase of the hypothetical security described by the values listed.
This security pays interest only at maturity.
You could use the ACCRINTM function to determine the amount of accrued interest that would be
added to the purchase/sale price. The function evaluates to approximately $138.06, which represents
the interest accrued between the issue date and the settlement date.

=ACCRINTM(B2,
C2, D2, E2, F2)

issue

settle

annual-rate

par

days-basis

12/14/2007

05/01/2009

0.10

1000

0

Related Topics
For related functions and additional information, see:
“ACCRINT” on page 99
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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Chapter 6    Financial Functions

BONDDURATION

The BONDDURATION function returns the weighted average of the present value of
the cash flows for an assumed par value of $100.
BONDDURATION(settle, maturity, annual-rate, annual-yield, frequency, days-basis)
ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ maturity:  The date when the security matures. maturity is a date/time value. It must

be after settle.
ÂÂ annual-rate:  The annual coupon rate or stated annual interest rate of the security.

annual-rate is a number value and is either entered as a decimal (for example, 0.08)
or with a percent sign (for example, 8%).
ÂÂ annual-yield:  The annual yield of the security. annual-yield is a number value and is

either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).
ÂÂ frequency:  The number of coupon payments each year.

annual (1): One payment per year.
semiannual (2): Two payments per year.
quarterly (4): Four payments per year.
ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.
actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Usage Notes
ÂÂ This function returns a value known as the Macauley duration.
Example
Assume you are considering the purchase of a hypothetical security. The purchase will settle April 2,
2010 and the maturity will mature on December 31, 2015. The coupon rate is 5%, resulting in a yield
of approximately 5.284% (the yield was calculated using the YIELD function). The bond pays interest
quarterly, based on actual days.
=BONDDURATION(“4/2/2010”, “12/31/2015”, 0.05, 0.05284, 4, 1) returns approximately 5.0208, the
present value of the future cash flows (the bond duration), based on the Macauley duration. The cash
flows consist of the price paid, interest received, and principal received at maturity.

Chapter 6    Financial Functions

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Related Topics
For related functions and additional information, see:
“BONDMDURATION” on page 104
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

BONDMDURATION

The BONDMDURATION function returns the modified weighted average of the present
value of the cash flows for an assumed par value of $100.
BONDMDURATION(settle, maturity, annual-rate, annual-yield, frequency, days-basis)
ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ maturity:  The date when the security matures. maturity is a date/time value. It must

be after settle.
ÂÂ annual-rate:  The annual coupon rate or stated annual interest rate of the security.

annual-rate is a number value and is either entered as a decimal (for example, 0.08)
or with a percent sign (for example, 8%).
ÂÂ annual-yield:  The annual yield of the security. annual-yield is a number value and is

either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).
ÂÂ frequency:  The number of coupon payments each year.

annual (1): One payment per year.
semiannual (2): Two payments per year.
quarterly (4): Four payments per year.
ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.

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actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Usage Notes
ÂÂ This function returns a value known as the modified Macauley duration.
Example
Assume you are considering the purchase of a hypothetical security. The purchase will settle April 2,
2010 and the maturity will mature on December 31, 2015. The coupon rate is 5%, resulting in a yield
of approximately 5.284% (the yield was calculated using the YIELD function). The bond pays interest
quarterly, based on actual days.
=BONDMDURATION(“4/2/2010”, “12/31/2015”, 0.05, 0.05284, 4, 1) returns approximately 4.9554, the
present value of the future cash flows (the bond duration), based on the modified Macauley duration.
The cash flows consist of the price paid, interest received, and principal received at maturity.

Related Topics
For related functions and additional information, see:
“BONDDURATION” on page 103
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

COUPDAYBS

The COUPDAYBS function returns the number of days between the beginning of the
coupon period in which settlement occurs and the settlement date.
COUPDAYBS(settle, maturity, frequency, days-basis)
ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ maturity:  The date when the security matures. maturity is a date/time value. It must

be after settle.
ÂÂ frequency:  The number of coupon payments each year.

annual (1): One payment per year.

Chapter 6    Financial Functions

105

semiannual (2): Two payments per year.
quarterly (4): Four payments per year.
ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.
actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Example
Assume you are considering the purchase of the hypothetical security described by the values listed.
You could use the COUPDAYBS function to determine the number of days from the last coupon
payment date until the settlement date. This would be the number of days included in the
computation of the accrued interest that would be added to the bond’s purchase price. The function
returns 2, since there are 2 days between the last coupon payment date of March 31, 2010, and the
settlement date of April 2, 2010.

=COUPDAYBS(B2, C2,
D2, E2, F2, G2)

settle

maturity

frequency

days-basis

4/2/2010

12/31/2015

4

1

Related Topics
For related functions and additional information, see:
“COUPDAYS” on page 107
“COUPDAYSNC” on page 108
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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Chapter 6    Financial Functions

COUPDAYS

The COUPDAYS function returns the number of days in the coupon period in which
settlement occurs.
COUPDAYS(settle, maturity, frequency, days-basis)
ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ maturity:  The date when the security matures. maturity is a date/time value. It must

be after settle.
ÂÂ frequency:  The number of coupon payments each year.

annual (1): One payment per year.
semiannual (2): Two payments per year.
quarterly (4): Four payments per year.
ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.
actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Example
Assume you are considering the purchase of the hypothetical security described by the values listed.
You could use the COUPDAYS function to determine the number of days in the settlement date
coupon period. The function returns 91, since there are 91 days in the coupon period beginning
April 1, 2010, and ending on June 30, 2010.

=COUPDAYS(B2, C2,
D2, E2, F2, G2)

settle

maturity

frequency

days-basis

4/2/2010

12/31/2015

4

1

Chapter 6    Financial Functions

107

Related Topics
For related functions and additional information, see:
“COUPDAYBS” on page 105
“COUPDAYSNC” on page 108
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

COUPDAYSNC

The COUPDAYSNC function returns the number of days between the settlement date
and the end of the coupon period in which settlement occurs.
COUPDAYSNC(settle, maturity, frequency, days-basis)
ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ maturity:  The date when the security matures. maturity is a date/time value. It must

be after settle.
ÂÂ frequency:  The number of coupon payments each year.

annual (1): One payment per year.
semiannual (2): Two payments per year.
quarterly (4): Four payments per year.
ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.
actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).

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Chapter 6    Financial Functions

Example
Assume you are considering the purchase of the hypothetical security described by the values listed.
You could use the COUPDAYSNC function to determine the number of days until the next coupon
payment date. This would be the number of days until the first coupon payment you would receive.
The function returns 89, since there are 89 days between settlement date of April 2, 2010, and the
next coupon payment date of June 30, 2010.
settle
=COUPDAYSNC(B2, C2, 4/2/2010
D2, E2, F2, G2)

maturity

frequency

days-basis

12/31/2015

4

1

Related Topics
For related functions and additional information, see:
“COUPDAYS” on page 107
“COUPDAYBS” on page 105
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

COUPNUM

The COUPNUM function returns the number of coupons remaining to be paid
between the settlement date and the maturity date.
COUPNUM(settle, maturity, frequency, days-basis)
ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ maturity:  The date when the security matures. maturity is a date/time value. It must

be after settle.
ÂÂ frequency:  The number of coupon payments each year.

annual (1): One payment per year.
semiannual (2): Two payments per year.
quarterly (4): Four payments per year.

Chapter 6    Financial Functions

109

ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.
actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Example
Assume you are considering the purchase of the hypothetical security described by the values listed.
You could use the COUPNUM function to determine the number of coupons you could expect
between the settlement date and the security’s maturity date. The function returns 23, since there
are 23 quarterly coupon payment dates between April 2, 2010, and December 31, 2015, with the first
being on June 30, 2010.

=COUPNUM(B2, C2,
D2, E2, F2, G2)

settle

maturity

frequency

days-basis

4/2/2010

12/31/2015

4

1

Related Topics
For related functions and additional information, see:
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

CUMIPMT

The CUMIPMT function returns the total interest included in loan or annuity payments
over a chosen time interval based on fixed periodic payments and a fixed interest rate.
CUMIPMT(periodic-rate, num-periods, present-value, starting-per, ending-per, when-due)
ÂÂ periodic-rate:  The interest rate per period. periodic-rate is a number value and is

either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).
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Chapter 6    Financial Functions

ÂÂ num-periods:  The number of periods. num-periods is a number value and must be

greater than or equal to 0.
ÂÂ present-value:  The value of the initial investment, or the amount of the loan or

annuity. present-value is a number value. At time 0, an amount received is a positive
amount and an amount invested is a negative amount. For example, it could be an
amount borrowed (positive) or the initial payment made on an annuity contract
(negative).
ÂÂ starting-per:  First period to include in the calculation. starting-per is a number value.
ÂÂ ending-per:  Last period to include in the calculation. ending-per is a number value

and must be greater than 0 and also greater than starting-per.
ÂÂ when-due:  Specifies whether payments are due at the beginning or end of each

period.
end (0):  Payments are due at the end of each period.
beginning (1):  Payments are due at the beginning of each period.
Usage Notes
ÂÂ If settle is before first, the function returns the interest accrued since issue. If settle is
after first, the function returns the interest accrued since the coupon payment date
that most immediately precedes settle.
ÂÂ Use ACCRINTM for a security that pays interest only at maturity.
Examples
It is generally understood that the amount of interest paid on a loan is higher in the early years, as
compared to the later years. This example demonstrates just how much higher the early years can
be. Assume a mortgage loan with an initial loan amount of $550,000, an interest rate of 6%, and a
30-year term.
The CUMIPMT function can be used to determine the interest for any period. In the following table,
CUMIPMT has been used to determine the interest for the first year (payments 1 through 12) and for
the last year (payments 349 through 360) of the loan term. The function evaluates to $32,816.27 and
$1,256.58, respectively. The amount of interest paid in the first year is more than 26 times the amount
of interest paid in the last year.
periodic-rate

num-periods

present-value

starting-per

ending-per

when-due

=CUMIPMT (B2, =0.06/12
C2, D2, E2, F2,
G2)

360

=550000

1

12

0

=CUMIPMT (B2,   
C2, D2, E3, F3,
G2)

  

  

349

360

  

Chapter 6    Financial Functions

111

Related Topics
For related functions and additional information, see:
“CUMPRINC” on page 112
“IPMT” on page 123
“PMT” on page 134
“PPMT” on page 135
“Example of a Loan Amortization Table” on page 353
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

CUMPRINC

The CUMPRINC function returns the total principal included in loan or annuity
payments over a chosen time interval based on fixed periodic payments and a fixed
interest rate.
CUMPRINC(periodic-rate, num-periods, present-value, starting-per, ending-per, cum-when-due)
ÂÂ periodic-rate:  The interest rate per period. periodic-rate is a number value and is

either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).
ÂÂ num-periods:  The number of periods. num-periods is a number value and must be

greater than or equal to 0.
ÂÂ present-value:  The value of the initial investment, or the amount of the loan or

annuity. present-value is a number value. At time 0, an amount received is a positive
amount and an amount invested is a negative amount. For example, it could be an
amount borrowed (positive) or the initial payment made on an annuity contract
(negative).
ÂÂ starting-per:  First period to include in the calculation. starting-per is a number value.
ÂÂ ending-per:  Last period to include in the calculation. ending-per is a number value

and must be greater than 0 and greater than starting-per.
ÂÂ when-due:  Specifies whether payments are due at the beginning or end of each

period.

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Chapter 6    Financial Functions

end (0):  Payments are due at the end of each period.
beginning (1):  Payments are due at the beginning of each period.
Examples
It is generally understood that the amount of the principal reduction on a loan is higher in the later
years, as compared to the early years. This example demonstrates just how much higher the later
years can be. Assume a mortgage loan with an initial loan amount of $550,000, an interest rate of 6%,
and a 30-year term.
The CUMPRINC function can be used to determine the interest for any period. In the following table,
CUMPRINC has been used to determine the principal repaid in the first year (payments 1 through 12)
and in the last year (payments 349 through 360) of the loan term. The function evaluates to $6,754.06
and $38,313.75, respectively. The amount of principal paid in the first year is only about 18% of the
amount of principal paid in the last year.
periodic-rate

num-periods

present-value

starting-per

ending-per

when-due

=CUMPRINC
(B2, C2, D2, E2,
F2, G2)

=0.06/12

360

=550000

1

12

0

=CUMPRINC
(B2, C2, D2, E3,
F3, G2)

  

  

  

349

360

  

Related Topics
For related functions and additional information, see:
“CUMIPMT” on page 110
“IPMT” on page 123
“PMT” on page 134
“PPMT” on page 135
“Example of a Loan Amortization Table” on page 353
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 6    Financial Functions

113

DB

The DB function returns the amount of depreciation of an asset for a specified period
using the fixed-declining balance method.
DB(cost, salvage, life, depr-period, first-year-months)
ÂÂ cost:  The initial cost of the asset. cost is a number value and must be greater than or

equal to 0.
ÂÂ salvage:  The salvage value of the asset. salvage is a number value and must be

greater than or equal to 0.
ÂÂ life:  The number of periods over which the asset is depreciating. life is a number

value and must be greater than 0. A decimal (fractional) part of life is allowed (for
example, 5.5 for a five and one-half year depreciable life).
ÂÂ depr-period:  The period for which you want to calculate depreciation. depr-period

is a number value and must be greater than 0. Any decimal (fractional) part of deprperiod is ignored.
ÂÂ first-year-months: An optional argument specifying the number of months of

depreciation in the first year. first-year-months is a number value and must be in the
range 1 to 12. Any decimal (fractional) part of first-year-months is ignored.
Example 1
Constructing a Depreciation Schedule
Assume you have just purchased an asset with a cost of $1,000, a salvage value of $100, and an
expected useful life of 4 years. Assume the asset will be depreciated 12 months in the first year.
Using the DB function, you can construct a depreciation table showing the depreciation for each year.
  

cost

salvage

life

depr-period

first-year-months

  

1000

100

4

  

12

First year (returns
$438)

=DB(B2, C2, D2,
E3, F2)

  

  

1

  

Second year
(returns $246.16)

=DB(B2, C2, D2,
E4, F2)

  

  

2

  

Third year (returns =DB(B2, C2, D2,
$138.74)
E5, F2)

  

  

3

  

Fourth year
(returns $77.75)

  

  

4

  

114		

=DB(B2, C2, D2,
E6, F2)

Chapter 6    Financial Functions

Example 2
Depreciation for Partial First Year
Assume the same facts as Example 1, except that the asset will be depreciated for less than
12 months in the first year.
  

cost

salvage

life

depr-period

first-year-months

  

1000

100

4

1

  

Depreciate 9
months (returns
$328.50)

=DB(B2, C2, D2,
E2, F3)

  

  

  

9

Depreciate 6
months (returns
$219)

=DB(B2, C2, D2,
E2, F4)

  

  

  

3

Depreciate 3
months (returns
$109.50)

=DB(B2, C2, D2,
E2, F5)

  

  

  

6

Depreciate 1
month (returns
$36.50)

=DB(B2, C2, D2,
E2, F6)

  

  

  

1

Related Topics
For related functions and additional information, see:
“DDB” on page 116
“SLN” on page 147
“SYD” on page 148
“VDB” on page 149
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 6    Financial Functions

115

DDB

The DDB function returns the amount of depreciation of an asset based on a specified
depreciation rate.
DDB(cost, salvage, life, depr-period, depr-factor)
ÂÂ cost:  The initial cost of the asset. cost is a number value and must be greater than or

equal to 0.
ÂÂ salvage:  The salvage value of the asset. salvage is a number value and must be

greater than or equal to 0.
ÂÂ life:  The number of periods over which the asset is depreciating. life is a number

value and must be greater than 0. A decimal (fractional) part of life is allowed (for
example, 5.5 for a five and one-half year depreciable life).
ÂÂ depr-period:  The period for which you want to calculate depreciation. depr-period

is a number value and must be greater than 0. Any decimal (fractional) part of deprperiod is ignored.
ÂÂ depr-factor:  An optional number that determines the depreciation rate. depr-factor

is a number value. If omitted, 2 (200% for double-declining) is assumed. The higher
the number, the more rapid the depreciation. For example, if a depreciation rate of
one and one-half times the straight line depreciation is desired, use 1.5 or 150%.
Examples
Assume you have just purchased an asset with a cost of $1,000, a salvage value of $100, and an
expected useful life of 4 years.
Using the DDB function, you can determine the depreciation for different periods and different
depreciation rates.
  

cost

salvage

life

depr-period

depr-factor

  

1000

100

4

  

  

First year, doubledeclining balance
(returns $500)

=DDB(B2, C2, D2,
E3, F3)

  

  

1

2

Second year,
double-declining
balance (returns
$250)

=DDB(B2, C2, D2,
E4, F4)

  

  

2

2

Third year, double- =DDB(B2, C2, D2,
declining balance E5, F5)
(returns $125)

  

  

3

2

=DDB(B2, C2, D2,
E6, F6)

  

  

4

2

Fourth year,
double-declining
balance (returns
$25)

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Chapter 6    Financial Functions

  

salvage

life

depr-period

depr-factor

First year, straight- =DDB(B2, C2, D2,
line (returns $250) E7, F7)

  

  

1

1

=DDB(B2, C2, D2,
E8, F8)

  

  

3

1

First year, tripledeclining balance
(returns $750)

cost

Related Topics
For related functions and additional information, see:
“DB” on page 114
“SLN” on page 147
“SYD” on page 148
“VDB” on page 149
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

DISC

The DISC function returns the annual discount rate of a security that pays no interest
and is sold at a discount to its redemption value.
DISC(settle, maturity, price, redemption, days-basis)
ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ maturity:  The date when the security matures. maturity is a date/time value. It must

be after settle.
ÂÂ price:  The cost of the security per $100 of par value. price is a number value.
ÂÂ redemption:  The redemption value per $100 of par value. redemption is a number

value that must be greater than 0. redemption is the amount that will be received
per $100 of face value. Often, it is 100, meaning that the security’s redemption value
is equal to its face value.

Chapter 6    Financial Functions

117

ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.
actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Example
In this example, the DISC function is used to determine the annual discount rate of the hypothetical
security described by the values listed.
The function evaluates to 5.25%, the annual discount rate.

=DISC(B2, C2, D2,
E2, F2)

settle

maturity

price

redemption

days-basis

05/01/2009

06/30/2015

67.64

100

0

Related Topics
For related functions and additional information, see:
“PRICEDISC” on page 138
“YIELDDISC” on page 152
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

118		

Chapter 6    Financial Functions

EFFECT

The EFFECT function returns the effective annual interest rate from the nominal annual
interest rate based on the number of compounding periods per year.
EFFECT(nominal-rate, num-periods-year)
ÂÂ nominal-rate:  The nominal rate of interest of a security. nominal-rate is a number

value and is either entered as a decimal (for example, 0.08) or with a percent sign
(for example, 8%).
ÂÂ num-periods-year:  The number of compounding periods per year. num-periods-

year is a number value and must be greater than 0.
Examples
=EFFECT(0.05, 365) returns approximately 5.13%, the effective annual interest rate if 5% is
compounded daily.
=EFFECT(0.05, 12) returns approximately 5.12%, the effective annual interest rate if 5% is compounded
monthly.
=EFFECT(0.05, 4) returns approximately 5.09%, the effective annual interest rate if 5% is compounded
quarterly.
=EFFECT(0.05, 2) returns approximately 5.06%, the effective annual interest rate if 5% is compounded
semiannually.
=EFFECT(0.05, 1) returns approximately 5.00%, the effective annual interest rate if 5% is compounded
annually.

Related Topics
For related functions and additional information, see:
“NOMINAL” on page 129
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 6    Financial Functions

119

FV

The FV function returns the future value of an investment based on a series of regular
periodic cash flows (payments of a constant amount and all cash flows at constant
intervals) and a fixed interest rate.
FV(periodic-rate, num-periods, payment, present-value, when-due)
ÂÂ periodic-rate:  The interest rate per period. periodic-rate is a number value and is

either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).
ÂÂ num-periods:  The number of periods. num-periods is a number value and must be

greater than or equal to 0.
ÂÂ payment:  The payment made or amount received each period. payment is a

number value. At each period, an amount received is a positive amount and an
amount invested is a negative amount. For example, it could be a monthly loan
payment (negative) or the periodic payment received on an annuity (positive).
ÂÂ present-value:  An optional argument that specifies the value of the initial

investment, or the amount of the loan or annuity. present-value is a number value.
At time 0, an amount received is a positive amount and an amount invested is a
negative amount. For example, it could be an amount borrowed (positive) or the
initial payment made on an annuity contract (negative).
ÂÂ when-due:  An optional argument that specifies whether payments are due at the

beginning or end of each period. Most mortgage and other loans require the first
payment at the end of the first period (0), which is the default. Most lease and rent
payments, and some other types of payments, are due at the beginning of each
period (1).
end (0 or omitted):  Payments are due at the end of each period.
beginning (1):  Payments are due at the beginning of each period.
Usage Notes
ÂÂ If payment is specified and there is no initial investment, present-value may be omitted.
Example 1
Assume you are planning for your daughter’s college education. She has just turned 3 and you
expect she will begin college in 15 years. You have $50,000 to set aside in a savings account today
and can add $200 to the account at the end of each month. Over the next 15 years, the savings
account is expected to earn an annual interest rate of 4.5%, and pays interest monthly.
Using the FV function, you can determine the expected value of this savings account at the time your
daughter begins college. Based on the assumptions given, it would be $149,553.00.

=FV(B2, C2, D2,
E2, F2)

120		

periodic-rate

num-periods

payment

present-value

when-due

=0.045/12

=15*12

-200

-50000

1

Chapter 6    Financial Functions

Example 2
Assume you are presented with an investment opportunity. The opportunity requires that you invest
$50,000 in a discount security today and then nothing further. The discount security matures in 14
years and has a redemption value of $100,000. Your alternative is to leave your money in your money
market savings account where it is expected to earn an annual yield of 5.25%.
One way to evaluate this opportunity would be to consider how much the $50,000 would be worth
at the end of the investment period and compare that to the redemption value of the security.
Using the FV function, you can determine the expected future value of the money market account.
Based on the assumptions given, it would be $102,348.03. Therefore, if all assumptions happen as
expected, it would be better to keep the money in the money market account since its value after 14
years ($102,348.03) exceeds the redemption value of the security ($100,000).

=FV(B2, C2, D2,
E2, F2)

periodic-rate

num-periods

payment

present-value

when-due

0.0525

14

0

-50000

1

Related Topics
For related functions and additional information, see:
“NPER” on page 130
“NPV” on page 132
“PMT” on page 134
“PV” on page 141
“RATE” on page 144
“Choosing Which Time Value of Money Function to Use” on page 348
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 6    Financial Functions

121

INTRATE

The INTRATE function returns the effective annual interest rate for a security that pays
interest only at maturity.
INTRATE(settle, maturity, invest-amount, redemption, days-basis)
ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ maturity:  The date when the security matures. maturity is a date/time value. It must

be after settle.
ÂÂ invest-amount:  The amount invested in the security. invest-amount is a number

value and must be greater than or equal to 0.
ÂÂ redemption:  The redemption value per $100 of par value. redemption is a number

value that must be greater than 0. redemption is the amount that will be received
per $100 of face value. Often, it is 100, meaning that the security’s redemption value
is equal to its face value.
ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.
actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Example
In this example, the INTRATE function is used to determine the effective annual interest rate of the
hypothetical security described by the values listed. The security pays interest only at maturity. The
function evaluates to approximately 10.85%.

=INTRATE(B2, C2,
D2, E2, F2)

122		

settle

maturity

invest-amount

par

days-basis

05/01/2009

06/30/2015

990.02

1651.83

0

Chapter 6    Financial Functions

Related Topics
For related functions and additional information, see:
“RECEIVED” on page 146
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

IPMT

The IPMT function returns the interest portion of a specified loan or annuity payment
based on fixed, periodic payments and a fixed interest rate.
IPMT(periodic-rate, period, num-periods, present-value, future-value, when-due)
ÂÂ periodic-rate:  The interest rate per period. periodic-rate is a number value and is

either entered as a decimal (for example, 0.08) or with a percent sign (for example,
8%).
ÂÂ period:  The payment period for which you want to calculate the amount of

principal or interest. period is a number and must be greater than 0.
ÂÂ num-periods:  The number of periods. num-periods is a number value and must be

greater than or equal to 0.
ÂÂ present-value:  The value of the initial investment, or the amount of the loan or

annuity. present-value is a number value. At time 0, an amount received is a positive
amount and an amount invested is a negative amount. For example, it could be an
amount borrowed (positive) or the initial payment made on an annuity contract
(negative).
ÂÂ future-value:  An optional argument that represents the value of the investment

or remaining cash value of the annuity (positive amount), or the remaining loan
balance (negative amount), after the final payment. future-value is a number value.
At the end of the investment period, an amount received is a positive amount and
an amount invested is a negative amount. For example, It could be the balloon
payment due on a loan (negative) or the remaining value of an annuity contract
(positive). If omitted, it is assumed to be 0.

Chapter 6    Financial Functions

123

ÂÂ when-due:  An optional argument that specifies whether payments are due at the

beginning or end of each period. Most mortgage and other loans require the first
payment at the end of the first period (0), which is the default. Most lease and rent
payments, and some other types of payments, are due at the beginning of each
period (1).
end (0 or omitted):  Payments are due at the end of each period.
beginning (1):  Payments are due at the beginning of each period.
Example
In this example, IPMT is used to determine the interest portion of the first payment of the third
year of the loan term (payment 25) given the loan facts presented. The function evaluates to
approximately –$922.41 representing the interest portion of loan payment 25.

=IPMT(B2, C2,
D2, E2, F2, G2)

periodic-rate

period

num-periods

present-value

future-value

when-due

=0.06/12

25

=10*12

200000

-100000

0

Related Topics
For related functions and additional information, see:
“CUMIPMT” on page 110
“CUMPRINC” on page 112
“PMT” on page 134
“PPMT” on page 135
“Example of a Loan Amortization Table” on page 353
“Choosing Which Time Value of Money Function to Use” on page 348
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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Chapter 6    Financial Functions

IRR

The IRR function returns the internal rate of return for an investment that is based on a
series of potentially irregular cash flows (payments that do not need to be a constant
amount) that occur at regular time intervals.
IRR(flows-range, estimate)
ÂÂ flows-range: A collection that contains the cash flow values. flows-range is a

collection containing number values. Income (a cash inflow) is specified as a positive
number, and an expenditure (a cash outflow) is specified as a negative number.
There must be at least one positive and one negative value included within the
collection. Cash flows must be specified in chronological order and equally spaced
in time (for example, each month). If a period does not have a cash flow, use 0 for
that period.
ÂÂ estimate:  An optional argument specifying the initial estimate for the rate of return.

estimate is a number value and is either entered as a decimal (for example, 0.08) or
with a percent sign (for example, 8%). If omitted, 10% is assumed. If the default value
does not result in a solution, initially try a larger positive value. If this does not result
in an outcome, try a small negative value. The minimum value allowed is –1.
Usage Notes
ÂÂ If the periodic cash flows are the same, consider using the NPV function.
Example 1
Assume you are planning for your daughter’s college education. She has just turned 13 and you
expect she will begin college in 5 years. You have $75,000 to set aside in a savings account today and
will add the bonus you receive from your employer at the end of each year. Since you expect your
bonus to increase each year, you expect to be able to set aside $5,000, $7,000, $8,000, $9,000, and
$10,000, respectively, at the end of each of the next 5 years. You think you will need to have $150,000
set aside for her education by the time your daughter reaches college.
Using the IRR function, you can determine the rate you would need to receive on invested amounts
in order to have $150,000. Based on the assumptions given, the rate would be 5.70%.

=IRR(B2:H2)

Initial
Deposit

Year 1

Year 2

Year 3

Year 4

Year 5

Amount
Required

-75000

-5000

-7000

-8000

-9000

-10000

150000

Chapter 6    Financial Functions

125

Example 2
Assume you are presented with the opportunity to invest in a partnership. The initial investment
required is $50,000. Because the partnership is still developing its product, an additional $25,000 and
$10,000 must be invested at the end of the first and second years, respectively. In the third year the
partnership expects to be self-funding but not return any cash to investors. In the fourth and fifth
years, investors are projected to receive $10,000 and $30,000, respectively. At the end of the sixth
year, the company expects to sell and investors are projected to receive $100,000.
Using the IRR function, you can determine the expected rate of return on this investment. Based on
the assumptions given, the rate would be 10.24%.

=IRR(B2:H2)

Initial
Deposit

Year 1

Year 2

Year 3

Year 4

Year 5

Sales
proceeds

-50000

-25000

-10000

0

10000

30000

100000

Related Topics
For related functions and additional information, see:
“MIRR” on page 128
“NPV” on page 132
“Choosing Which Time Value of Money Function to Use” on page 348
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

ISPMT

The ISPMT function returns the interest portion of a specified loan or annuity payment
based on fixed, periodic payments and a fixed interest rate. This function is provided
for compatibility with tables imported from other spreadsheet applications.

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Chapter 6    Financial Functions

ISPMT(annual-rate, period, num-periods, present-value)
ÂÂ annual-rate:  The annual coupon rate or stated annual interest rate of the security.

annual-rate is a number value and is either entered as a decimal (for example, 0.08)
or with a percent sign (for example, 8%).
ÂÂ period:  The payment period for which you want to calculate the amount of

principal or interest. period is a number and must be greater than 0.
ÂÂ num-periods:  The number of periods. num-periods is a number value and must be

greater than or equal to 0.
ÂÂ present-value:  The value of the initial investment, or the amount of the loan or

annuity. present-value is a number value. At time 0, an amount received is a positive
amount and an amount invested is a negative amount. For example, it could be an
amount borrowed (positive) or the initial payment made on an annuity contract
(negative).
Usage Notes
ÂÂ The IPMT function has additional functionality and should be used instead of ISPMT.
Example
In this example, ISPMT is used to determine the interest portion of the first payment of the third year
of the loan term (payment 25) given the loan facts presented.
The function evaluates to approximately –$791.67, which represents the interest portion of loan
payment 25.

=ISPMT(B2, C2, D2, E2)

periodic-rate

period

num-periods

present-value

=0.06/12

25

=10*12

200000

Related Topics
For related functions and additional information, see:
“IPMT” on page 123
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 6    Financial Functions

127

MIRR

The MIRR function returns the modified internal rate of return for an investment that
is based on a series of potentially irregular cash flows (payments that do not need to
be a constant amount) that occur at regular time intervals. The rate earned on positive
cash flows and the rate paid to finance negative cash flows can differ.
MIRR(flows-range, finance-rate, reinvest-rate)
ÂÂ flows-range: A collection that contains the cash flow values. flows-range is a

collection containing number values. Income (a cash inflow) is specified as a positive
number, and an expenditure (a cash outflow) is specified as a negative number.
There must be at least one positive and one negative value included within the
collection. Cash flows must be specified in chronological order and equally spaced
in time (for example, each month). If a period does not have a cash flow, use 0 for
that period.
ÂÂ finance-rate: Interest rate paid on negative cash flows (outflows). finance-rate

is a number value and is either entered as a decimal (for example, 0.08) or with
a percent sign (for example, 8%) and represents the rate at which the amounts
invested (negative cash flows) can be financed. For example, a company’s cost of
capital might be used.
ÂÂ reinvest-rate:  Rate at which positive cash flows (inflows) can be reinvested. reinvest-

rate is a number value and is either entered as a decimal (for example, 0.08) or with
a percent sign (for example, 8%) and represents the rate at which the amounts
received (positive cash flows) can be reinvested. For example, a company’s shortterm investment rate might be used.
Usage Notes
ÂÂ Cash flows must be equally spaced in time. If there is no cash flow in a particular
time period, use 0.
Example 1
Assume you are presented with the opportunity to invest in a partnership. The initial investment
required is $50,000. Because the partnership is still developing its product, an additional $25,000 and
$10,000 must be invested at the end of the first and second years, respectively. In the third year the
partnership expects to be self-funding but not return any cash to investors. In the fourth and fifth years,
investors are projected to receive $10,000 and $30,000, respectively. At the end of the sixth year, the
company expects to sell and investors are projected to receive $100,000. Assume that you can currently
borrow money at 9.00% (finance-rate) and can earn 4.25% on short-term savings (reinvest-rate).
Using the IRR function, you can determine the expected rate of return on this investment. Based on
the assumptions given, the rate would be approximately 9.75%.

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Chapter 6    Financial Functions

=MIRR
(B2:H2, 0.09,
0.0425)

Initial
Deposit

Year 1

Year 2

Year 3

Year 4

Year 5

Sales
proceeds

-50000

-25000

-10000

0

10000

30000

100000

Example 2
Assume the same information as in Example 1, but rather than placing the cash flows in individual
cells, you specify the cash flows as an array constant. The MIRR function would then be as follows:
=MIRR({-50000, -25000, -10000, 0, 10000, 30000, 100000}, 0.09, 0.0425) returns approximately 9.75%.

Related Topics
For related functions and additional information, see:
“IRR” on page 125
“NPV” on page 132
“PV” on page 141
“Choosing Which Time Value of Money Function to Use” on page 348
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

NOMINAL

The NOMINAL function returns the nominal annual interest rate from the effective
annual interest rate based on the number of compounding periods per year.
NOMINAL(effective-int-rate, num-periods-year)
ÂÂ effective-int-rate: The effective interest rate of a security. effective-int-rate is a

number value and is either entered as a decimal (for example, 0.08) or with a
percent sign (for example, 8%).
ÂÂ num-periods-year:  The number of compounding periods per year. num-periods-

year is a number value and must be greater than 0.

Chapter 6    Financial Functions

129

Examples
=NOMINAL(0.0513, 365) returns approximately 5.00%, the nominal annual interest rate if the effective
rate of 5.13% was based on daily compounding.
=NOMINAL(0.0512, 12) returns approximately 5.00%, the nominal annual interest rate if the effective
rate of 5.12% was based on monthly compounding.
=NOMINAL(0.0509, 4) returns approximately 5.00%, the nominal annual interest rate if the effective
rate of 5.09% was based on quarterly compounding.
=NOMINAL(0.0506, 2) returns approximately 5.00%, the nominal annual interest rate if the effective
rate of 5.06% was based on semiannual compounding.
=NOMINAL(0.0500, 1) returns approximately 5.00%, the nominal annual interest rate if the effective
rate of 5.00% was based on annual compounding.

Related Topics
For related functions and additional information, see:
“EFFECT” on page 119
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

NPER

The NPER function returns the number of payment periods for a loan or annuity based
on a series of regular periodic cash flows (payments of a constant amount and all cash
flows at constant intervals) and a fixed interest rate.
NPER(periodic-rate, payment, present-value, future-value, when-due)
ÂÂ periodic-rate:  The interest rate per period. periodic-rate is a number value and is

either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).
ÂÂ payment:  The payment made or amount received each period. payment is a

number value. At each period, an amount received is a positive amount and an
amount invested is a negative amount. For example, it could be a monthly loan
payment (negative) or the periodic payment received on an annuity (positive).

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Chapter 6    Financial Functions

ÂÂ present value:  The value of the initial investment, or the amount of the loan or

annuity, specified as a negative number. present-value is a number value. At time
0, an amount received is a positive amount and an amount invested is a negative
amount. For example, It could be an amount borrowed (positive) or the initial
payment made on an annuity contract (negative).
ÂÂ future-value:  An optional argument specifying the value of the investment or

remaining cash value of the annuity (positive amount), or the remaining loan
balance (negative amount), after the final payment. future-value is a number value.
At the end of the investment period, an amount received is a positive amount and
an amount invested is a negative amount. For example, It could be the balloon
payment due on a loan (negative) or the remaining value of an annuity contract
(positive).
ÂÂ when-due:  An optional argument that specifies whether payments are due at the

beginning or end of each period. Most mortgage and other loans require the first
payment at the end of the first period (0), which is the default. Most lease and rent
payments, and some other types of payments, are due at the beginning of each
period (1).
end (0 or omitted):  Payments are due at the end of each period.
beginning (1):  Payments are due at the beginning of each period.
Example 1
Assume you are planning for your daughter’s college education. You have $50,000 to set aside in
a savings account today and can add $200 to the account at the end of each month. The savings
account is expected to earn an annual interest rate of 4.5%, and pays interest monthly. You believe
you will need to have set aside $150,000 by the time your daughter reaches college.
Using the NPER function, you can determine the number of periods you would need to make the
$200 payment. Based on the assumptions given, it would be approximately 181 periods or 15 years,
1 month.

=NPER(B2, C2, D2,
E2, F2)

periodic-rate

payment

present-value

future-value

when-due

=0.045/12

-200

-50000

150000

1

Example 2
Assume you are planning to purchase your uncle’s mountain cabin. You have $30,000 to use as a
down payment today and can afford to make a monthly payment of $1,500. Your uncle says he is
willing to lend you the difference between the cabin’s sale price of $200,000 and your down payment
(so you would borrow $170,000) at an annual rate of 7%.
Using the NPER function, you can determine the number of months it would take you to repay your
uncle’s loan. Based on the assumptions given, it would be approximately 184 months or 15 years,
4 months.

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131

=NPER(B2, C2, D2,
E2, F2)

periodic-rate

payment

present-value

future-value

when-due

=0.07/12

-1500

170000

0

1

Related Topics
For related functions and additional information, see:
“FV” on page 120
“PMT” on page 134
“PV” on page 141
“RATE” on page 144
“Choosing Which Time Value of Money Function to Use” on page 348
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

NPV

The NPV function returns the net present value of an investment based on a series of
potentially irregular cash flows that occur at regular time intervals.
NPV(periodic-discount-rate, cash-flow, cash-flow…)
ÂÂ periodic-discount-rate:  The discount rate per period. periodic-discount-rate is

a number value and is either entered as a decimal (for example, 0.08) or with a
percent sign (for example, 8%). periodic-discount-rate must be greater than or equal
to 0.
ÂÂ cash-flow: A cash flow. cash-flow is a number value. A positive value represents

income (cash inflow). A negative value represents an expenditure (cash outflow).
Cash flows must be equally spaced in time.
ÂÂ cash-flow…: Optionally include one or more additional cash flows.

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Usage Notes
ÂÂ periodic-discount-rate is specified using the same time frame as the time frame used
for the cash flows. For example, if the cash flows are monthly and the desired annual
discount rate is 8%, periodic-discount-rate must be specified as 0.00667 or 0.667%
(0.08 divided by 12).
ÂÂ If cash flows are irregular, use the IRR function.
Example
Assume you are presented with the opportunity to invest in a partnership. Because the partnership is
still developing its product, an additional $25,000 and $10,000 must be invested at the end of the first
and second years, respectively. In the third year the partnership expects to be self-funding but not
return any cash to investors. In the fourth and fifth years, investors are projected to receive $10,000
and $30,000, respectively. At the end of the sixth year, the company expects to sell and investors are
projected to receive $100,000. In order to invest, you want to achieve an annual return of at least 10%.
Using the NPV function, you can determine the maximum amount you are willing to initially invest.
Based on the assumptions given, the NPV would be $50,913.43. Therefore if the required initial
investment is this amount or less, this opportunity meets your 10% goal.

=NPV(B2,
C2:H2)

periodic-rate Year 1

Year 2

Year 3

Year 4

Year 5

Sales
proceeds

0.10

-10000

0

10000

30000

100000

-25000

Related Topics
For related functions and additional information, see:
“IRR” on page 125
“PV” on page 141
“Choosing Which Time Value of Money Function to Use” on page 348
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 6    Financial Functions

133

PMT

The PMT function returns the fixed periodic payment for a loan or annuity based on
a series of regular periodic cash flows (payments of a constant amount and all cash
flows at constant intervals) and a fixed interest rate.
PMT(periodic-rate, num-periods, present-value, future-value, when-due)
ÂÂ periodic-rate:  The interest rate per period. periodic-rate is a number value and is

either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).
ÂÂ num-periods:  The number of periods. num-periods is a number value and must be

greater than or equal to 0.
ÂÂ present-value:  The value of the initial investment, or the amount of the loan or

annuity. present-value is a number value. At time 0, an amount received is a positive
amount and an amount invested is a negative amount. For example, it could be an
amount borrowed (positive) or the initial payment made on an annuity contract
(negative).
ÂÂ future-value:  An optional argument that represents the value of the investment

or remaining cash value of the annuity (positive amount), or the remaining loan
balance (negative amount), after the final payment. future-value is a number value.
At the end of the investment period, an amount received is a positive amount and
an amount invested is a negative amount. For example, It could be the balloon
payment due on a loan (negative) or the remaining value of an annuity contract
(positive). If omitted, it is assumed to be 0.
ÂÂ when-due:  An optional argument that specifies whether payments are due at the

beginning or end of each period. Most mortgage and other loans require the first
payment at the end of the first period (0), which is the default. Most lease and rent
payments, and some other types of payments, are due at the beginning of each
period (1).
end (0 or omitted):  Payments are due at the end of each period.
beginning (1):  Payments are due at the beginning of each period.
Example
In this example, PMT is used to determine the fixed payment given the loan facts presented.
The function evaluates to –$1,610.21, which represents the fixed payment you would make (negative
because it is a cash outflow) for this loan.

=PMT(B2, C2, D2,
E2, F2)

134		

periodic-rate

num-periods

present-value

future-value

when-due

=0.06/12

=10*12

200000

-100000

0

Chapter 6    Financial Functions

Related Topics
For related functions and additional information, see:
“FV” on page 120
“IPMT” on page 123
“NPER” on page 130
“PPMT” on page 135
“PV” on page 141
“RATE” on page 144
“Example of a Loan Amortization Table” on page 353
“Choosing Which Time Value of Money Function to Use” on page 348
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

PPMT

The PPMT function returns the principal portion of a specified loan or annuity
payment based on fixed periodic payments and a fixed interest rate.
PPMT(periodic-rate, period, num-periods, present-value, future-value, when-due)
ÂÂ periodic-rate:  The interest rate per period. periodic-rate is a number value and is

either entered as a decimal (for example, 0.08) or with a percent sign (for example,
8%).
ÂÂ period:  The payment period for which you want to calculate the amount of

principal or interest. period is a number and must be greater than 0.
ÂÂ num-periods:  The number of periods. num-periods is a number value and must be

greater than or equal to 0.

Chapter 6    Financial Functions

135

ÂÂ present-value:  The value of the initial investment, or the amount of the loan or

annuity. present-value is a number value. At time 0, an amount received is a positive
amount and an amount invested is a negative amount. For example, it could be an
amount borrowed (positive) or the initial payment made on an annuity contract
(negative).
ÂÂ future-value:  An optional argument that represents the value of the investment

or remaining cash value of the annuity (positive amount), or the remaining loan
balance (negative amount), after the final payment. future-value is a number value.
At the end of the investment period, an amount received is a positive amount and
an amount invested is a negative amount. For example, It could be the balloon
payment due on a loan (negative) or the remaining value of an annuity contract
(positive). If omitted, it is assumed to be 0.
ÂÂ when-due:  An optional argument that specifies whether payments are due at the

beginning or end of each period. Most mortgage and other loans require the first
payment at the end of the first period (0), which is the default. Most lease and rent
payments, and some other types of payments, are due at the beginning of each
period (1).
end (0 or omitted):  Payments are due at the end of each period.
beginning (1):  Payments are due at the beginning of each period.
Example
In this example, PPMT is used to determine the principal portion of the first payment of the third
year of the loan term (payment 25) given the loan facts presented. The function evaluates to
approximately –$687.80, which represents the principal portion of payment 25.

=PPMT(B2, C2,
D2, E2, F2, G2)

periodic-rate

period

num-periods

present-value

future-value

when-due

=0.06/12

25

=10*12

200000

-100000

0

Related Topics
For related functions and additional information, see:
“CUMIPMT” on page 110
“CUMPRINC” on page 112
“IPMT” on page 123
“PMT” on page 134
“Example of a Loan Amortization Table” on page 353
“Choosing Which Time Value of Money Function to Use” on page 348
“Common Arguments Used in Financial Functions” on page 341
136		

Chapter 6    Financial Functions

“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

PRICE

The PRICE function returns the price of a security that pays periodic interest per $100
of redemption (par) value.
PRICE(settle, maturity, annual-rate, annual-yield, redemption, frequency, days-basis)
ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ maturity:  The date when the security matures. maturity is a date/time value. It must

be after settle.
ÂÂ annual-rate:  The annual coupon rate or stated annual interest rate of the security.

annual-rate is a number value and is either entered as a decimal (for example, 0.08)
or with a percent sign (for example, 8%).
ÂÂ annual-yield:  The annual yield of the security. annual-yield is a number value and is

either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).
ÂÂ redemption:  The redemption value per $100 of par value. redemption is a number

value that must be greater than 0. redemption is the amount that will be received
per $100 of face value. Often, it is 100, meaning that the security’s redemption value
is equal to its face value.
ÂÂ frequency:  The number of coupon payments each year.

annual (1): One payment per year.
semiannual (2): Two payments per year.
quarterly (4): Four payments per year.
ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.
actual/365 (3):  Actual days in each month, 365 days in a year.

Chapter 6    Financial Functions

137

30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Example
In this example, the PRICE function is used to determine the purchase price when trading the
hypothetical security described by the values listed. The security pays periodic interest.
The function evaluates to $106.50, which represents the price per $100 of face value.
settle
05/01/2009
=PRICE (B2,
C2, D2, E2, F2,
G2, H2)

maturity

annual-rate

annual-yield

redemption

frequency

days-basis

06/30/2015

0.065

0.0525

100

2

0

Related Topics
For related functions and additional information, see:
“PRICEDISC” on page 138
“PRICEMAT” on page 140
“YIELD” on page 150
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

PRICEDISC

The PRICEDISC function returns the price of a security that is sold at a discount to
redemption value and does not pay interest per $100 of redemption (par) value.
PRICEDISC(settle, maturity, annual-yield, redemption, days-basis)
ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ maturity:  The date when the security matures. maturity is a date/time value. It must

be after settle.
ÂÂ annual-yield:  The annual yield of the security. annual-yield is a number value and is

either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).

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Chapter 6    Financial Functions

ÂÂ redemption:  The redemption value per $100 of par value. redemption is a number

value that must be greater than 0. redemption is the amount that will be received
per $100 of face value. Often, it is 100, meaning that the security’s redemption value
is equal to its face value.
ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.
actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Example
In this example, the PRICEDISC function is used to determine the purchase price when trading the
hypothetical security described by the values listed. The security does not pay interest and is sold at
a discount.
The function evaluates to approximately $65.98, which represents the price per $100 of face value.

=PRICEDISC (B2,
C2, D2, E2, F2)

settle

maturity

discount

redemption

days-basis

05/01/2009

06/30/2015

0.0552

100

0

Related Topics
For related functions and additional information, see:
“PRICE” on page 137
“PRICEMAT” on page 140
“YIELDDISC” on page 152
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 6    Financial Functions

139

PRICEMAT

The PRICEMAT function returns the price of a security that pays interest only at
maturity per $100 of redemption (par) value.
PRICEMAT(settle, maturity, issue, annual-rate, annual-yield, days-basis)
ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ maturity:  The date when the security matures. maturity is a date/time value. It must

be after settle.
ÂÂ issue:  The date the security was originally issued. issue is a date/time value and

must be the earliest date given.
ÂÂ annual-rate:  The annual coupon rate or stated annual interest rate of the security.

annual-rate is a number value and is either entered as a decimal (for example, 0.08)
or with a percent sign (for example, 8%).
ÂÂ annual-yield:  The annual yield of the security. annual-yield is a number value and is

either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).
ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.
actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Example
In this example, the PRICEMAT function is used to determine the purchase price when trading the
hypothetical security described by the values listed. The security pays interest only at maturity. The
function evaluates to $99.002, which represents the price per $100 of face value.
settle
=PRICEMAT (B2, 05/01/2009
C2, D2, E2, F2,
G2)

140		

maturity

issue

annual-rate

annual-yield

days-basis

06/30/2015

12/14/2008

0.065

0.06565

0

Chapter 6    Financial Functions

Related Topics
For related functions and additional information, see:
“PRICE” on page 137
“PRICEDISC” on page 138
“YIELDMAT” on page 153
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

PV

The PV function returns the present value of an investment or annuity based on a
series of regular periodic cash flows (payments of a constant amount and all cash
flows at constant intervals) and a fixed interest rate.
PV(periodic-rate, num-periods, payment, future-value, when-due)
ÂÂ periodic-rate:  The interest rate per period. periodic-rate is a number value and is

either entered as a decimal (for example, 0.08) or with a percent sign (for example, 8%).
ÂÂ num-periods:  The number of periods. num-periods is a number value and must be

greater than or equal to 0.
ÂÂ payment:  The payment made or amount received each period. payment is a

number value. At each period, an amount received is a positive amount and an
amount invested is a negative amount. For example, it could be a monthly loan
payment (negative) or the periodic payment received on an annuity (positive).
ÂÂ future-value:  An optional argument specifying the value of the investment or

remaining cash value of the annuity (positive amount), or the remaining loan
balance (negative amount), after the final payment. future-value is a number value.
At the end of the investment period, an amount received is a positive amount and
an amount invested is a negative amount. For example, It could be the balloon
payment due on a loan (negative) or the remaining value of an annuity contract
(positive).

Chapter 6    Financial Functions

141

ÂÂ when-due:  An optional argument that specifies whether payments are due at the

beginning or end of each period. Most mortgage and other loans require the first
payment at the end of the first period (0), which is the default. Most lease and rent
payments, and some other types of payments, are due at the beginning of each
period (1).
end (0 or omitted):  Payments are due at the end of each period.
beginning (1):  Payments are due at the beginning of each period.
Usage Notes
ÂÂ periodic-rate is specified using the time frame of num-periods. For example, if numperiods represents months and the annual interest rate is 8%, periodic-rate must be
specified as 0.00667 or 0.667% (0.08 divided by 12).
ÂÂ If payment is specified and there is no investment value, cash value, or loan balance

remaining, future-value may be omitted.
ÂÂ If payment is omitted, you must include future-value.
Example 1
Assume you are planning for your daughter’s college education. She has just turned 3 and you
expect she will begin college in 15 years. You think you will need to have $150,000 set aside in a
savings account by the time she reaches college. You can add $200 to the account at the end of each
month. Over the next 15 years, the savings account is expected to earn an annual interest rate of
4.5%, and earns interest monthly.
Using the PV function, you can determine the amount that must be deposited to this savings
account today so that the value of the savings account will reach $150,000 by the time your daughter
begins college. Based on the assumptions given, the function returns –$50,227.88 as the amount that
would need to be deposited today (function returns a negative because the deposit to the savings
account today is a cash outflow).

=PV(B2, C2, D2,
E2, F2)

142		

periodic-rate

num-periods

payment

future-value

when-due

=0.045/12

=15*12

-200

150000

1

Chapter 6    Financial Functions

Example 2
In this example, you are presented with an investment opportunity. The opportunity is to invest in
a discount security today and then pay or receive nothing further until the security matures. The
discount security matures in 14 years and has a redemption value of $100,000. Your alternative is to
leave your money in your money market savings account where it is expected to earn an annual
yield of 5.25%.
Using the PV function, you can determine the maximum amount you should be willing to pay for this
discount security today, assuming you want at least as good an interest rate as you expect to get on
your money market account. Based on the assumptions given, it would be –$48,852.92 (the function
returns a negative amount since this is a cash outflow).

=PV(B2, C2, D2,
E2, F2)

periodic-rate

num-periods

payment

future-value

when-due

0.0525

14

0

100000

1

Related Topics
For related functions and additional information, see:
“FV” on page 120
“IRR” on page 125
“NPER” on page 130
“PMT” on page 134
“RATE” on page 144
“Choosing Which Time Value of Money Function to Use” on page 348
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 6    Financial Functions

143

RATE

The RATE function returns the interest rate of an investment, loan, or annuity based
on a series of regular periodic cash flows (payments of a constant amount and all cash
flows at constant intervals) and a fixed interest rate.
RATE(num-periods, payment, present-value, future-value, when-due, estimate)
ÂÂ num-periods:  The number of periods. num-periods is a number value and must be

greater than or equal to 0.
ÂÂ payment:  The payment made or amount received each period. payment is a

number value. At each period, an amount received is a positive amount and an
amount invested is a negative amount. For example, it could be a monthly loan
payment (negative) or the periodic payment received on an annuity (positive).
ÂÂ present-value:  The value of the initial investment, or the amount of the loan or

annuity. present-value is a number value. At time 0, an amount received is a positive
amount and an amount invested is a negative amount. For example, it could be an
amount borrowed (positive) or the initial payment made on an annuity contract
(negative).
ÂÂ future-value:  An optional argument that represents the value of the investment

or remaining cash value of the annuity (positive amount), or the remaining loan
balance (negative amount), after the final payment. future-value is a number value.
At the end of the investment period, an amount received is a positive amount and
an amount invested is a negative amount. For example, It could be the balloon
payment due on a loan (negative) or the remaining value of an annuity contract
(positive).
ÂÂ when-due:  An optional argument that specifies whether payments are due at the

beginning or end of each period. Most mortgage and other loans require the first
payment at the end of the first period (0), which is the default. Most lease and rent
payments, and some other types of payments, are due at the beginning of each
period (1).
end (0 or omitted):  Payments are due at the end of each period.
beginning (1):  Payments are due at the beginning of each period.
ÂÂ estimate:  An optional argument specifying the initial estimate for the rate of return.

estimate is a number value and is either entered as a decimal (for example, 0.08) or
with a percent sign (for example, 8%). If omitted, 10% is assumed. If the default value
does not result in a solution, initially try a larger positive value. If this does not result
in an outcome, try a small negative value. The minimum value allowed is –1.

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Chapter 6    Financial Functions

Example
Assume you are planning for your daughter’s college education. She has just turned 3 and you
expect she will begin college in 15 years. You think you will need to have $150,000 set aside in a
savings account by the time she reaches college. You can set aside $50,000 today and add $200 to
the account at the end of each month. Over the next 15 years, the savings account is expected to
earn an annual interest rate of 4.5%, and earns interest monthly.
Using the RATE function, you can determine the rate that must be earned on the savings account so
that it will reach $150,000 by the time your daughter begins college. Based on the assumptions given,
the rate returned by the function is approximately 0.377%, which is per month since num-periods was
monthly, or 4.52% annually.

=RATE(B2, C2,
D2, E2, F2, G2)

num-periods

payment

present-value

future-value

when-due

estimate

=15*12

-200

-50000

150000

1

=0.1/12

Related Topics
For related functions and additional information, see:
“FV” on page 120
“IRR” on page 125
“NPER” on page 130
“PMT” on page 134
“PV” on page 141
“Choosing Which Time Value of Money Function to Use” on page 348
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 6    Financial Functions

145

RECEIVED

The RECEIVED function returns the maturity value for a security that pays interest only
at maturity.
RECEIVED(settle, maturity, invest-amount, annual-rate, days-basis)
ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ maturity:  The date when the security matures. maturity is a date/time value. It must

be after settle.
ÂÂ invest-amount:  The amount invested in the security. invest-amount is a number

value and must be greater than or equal to 0.
ÂÂ annual-rate:  The annual coupon rate or stated annual interest rate of the security.

annual-rate is a number value and is either entered as a decimal (for example, 0.08)
or with a percent sign (for example, 8%).
ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.
actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Example
In this example, the RECEIVED function is used to determine the amount received at the maturity of
the hypothetical security described by the values listed. The security pays interest only at maturity.
The function evaluates to $1,651.83, the amount to be received at maturity including both principal
and interest.
settle
=RECEIVED (B2, C2, 05/01/2009
D2, E2, F2)

maturity

invest-amount

annual-rate

days-basis

06/30/2015

990.02

0.065

0

Related Topics
For related functions and additional information, see:
“INTRATE” on page 122
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
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“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

SLN

The SLN function returns the depreciation of an asset for a single period using the
straight-line method.
SLN(cost, salvage, life)
ÂÂ cost:  The initial cost of the asset. cost is a number value and must be greater than or

equal to 0.
ÂÂ salvage:  The salvage value of the asset. salvage is a number value and must be

greater than or equal to 0.
ÂÂ life:  The number of periods over which the asset is depreciating. life is a number

value and must be greater than 0. A decimal (fractional) part of life is allowed (for
example, 5.5 for a five and one-half year depreciable life).
Example
=SLN(10000, 1000, 6) returns $1500, the depreciation per year, in dollars, of an asset that originally
costs $10,000 and has an estimated salvage value of $1,000 after 6 years.

Related Topics
For related functions and additional information, see:
“DB” on page 114
“DDB” on page 116
“SYD” on page 148
“VDB” on page 149
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41
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SYD

The SYD function returns the amount of depreciation of an asset for a specified period
using the sum-of-the-years-digits method.
SYD(cost, salvage, life, depr-period)
ÂÂ cost:  The initial cost of the asset. cost is a number value and must be greater than or

equal to 0.
ÂÂ salvage:  The salvage value of the asset. salvage is a number value and must be

greater than or equal to 0.
ÂÂ life:  The number of periods over which the asset is depreciating. life is a number

value and must be greater than 0. A decimal (fractional) part of life is allowed (for
example, 5.5 for a five and one-half year depreciable life).
ÂÂ depr-period:  The period for which you want to calculate depreciation. depr-period

is a number value and must be greater than 0. Any decimal (fractional) part of deprperiod is ignored.
Examples
=SYD(10000, 1000, 9, 1) returns $1,800, the depreciation amount for the first year for an asset with an
initial cost of $10,000 and a salvage value of $1,000 after a 9-year life.
=SYD(10000, 1000, 9, 2) returns $1,600, the depreciation amount for the second year.
=SYD(10000, 1000, 9, 8) returns $400, the depreciation amount for the eighth year.

Related Topics
For related functions and additional information, see:
“DB” on page 114
“DDB” on page 116
“SLN” on page 147
“VDB” on page 149
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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VDB

The VDB (variable declining balance) function returns the amount of depreciation of
an asset over a chosen time interval, based on a specified depreciation rate.
VDB(cost, salvage, life, starting-per, ending-per, depr-factor, no-switch)
ÂÂ cost:  The initial cost of the asset. cost is a number value and must be greater than or

equal to 0.
ÂÂ salvage:  The salvage value of the asset. salvage is a number value and must be

greater than or equal to 0.
ÂÂ life:  The number of periods over which the asset is depreciating. life is a number

value and must be greater than 0. A decimal (fractional) part of life is allowed (for
example, 5.5 for a five and one-half year depreciable life).
ÂÂ starting-per:  First period to include in the calculation. starting-per is a number value.
ÂÂ ending-per:  Last period to include in the calculation. ending-per is a number value

and must be greater than 0 and greater than starting-per.
ÂÂ depr-factor:  An optional number that determines the depreciation rate. depr-factor

is a number value. If omitted, 2 (200% for double-declining) is assumed. The higher
the number, the more rapid the depreciation. For example, if a depreciation rate of
one and one-half times the straight line depreciation is desired, use 1.5 or 150%.
ÂÂ no-switch:  An optional value indicating whether depreciation switches over to the

straight-line method.
switch (0, FALSE, or omitted):  Switch to the straight line method in the year that
straight-line depreciation exceeds declining balance depreciation.
no switch (1, TRUE):  Do not switch to the straight-line method.
Usage Notes
ÂÂ starting-per should be specified as the period prior to the first period you wish to
include in the calculation. If you wish to include the first period, use 0 for starting-per.
ÂÂ If you wish to determine depreciation that includes only the first period, ending-per

should be 1.
Examples
Assume you have purchased an asset at a cost of $11,000.00, that it has a salvage value of $1,000.00,
and that it has an estimated useful life of 5 years. You intend to depreciate the asset using the 1.5
(150%) declining balance method.
=VDB(11000, 1000, 5, 0, 1, 1.5, 0) returns $3,300, the depreciation for the first year.
=VDB(11000, 1000, 5, 4, 5, 1.5, 0) returns $1,386.50, the depreciation for the fifth (last) year, assuming
straight-line depreciation is used when greater than the declining-balance depreciation.
=VDB(11000, 1000, 5, 4, 5, 1.5, 1) returns $792.33, the depreciation for the fifth (last) year, assuming that
declining-balance depreciation is used at all times (no-switch is TRUE).

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Related Topics
For related functions and additional information, see:
“DB” on page 114
“DDB” on page 116
“SLN” on page 147
“SYD” on page 148
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

YIELD

The YIELD function returns the effective annual interest rate for a security that pays
regular periodic interest.
YIELD(settle, maturity, annual-rate, price, redemption, frequency, days-basis)
ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ maturity:  The date when the security matures. maturity is a date/time value. It must

be after settle.
ÂÂ annual-rate:  The annual coupon rate or stated annual interest rate of the security.

annual-rate is a number value and is either entered as a decimal (for example, 0.08)
or with a percent sign (for example, 8%).
ÂÂ price:  The cost of the security per $100 of par value. price is a number value.
ÂÂ redemption:  The redemption value per $100 of par value. redemption is a number

value that must be greater than 0. redemption is the amount that will be received
per $100 of face value. Often, it is 100, meaning that the security’s redemption value
is equal to its face value.
ÂÂ frequency:  The number of coupon payments each year.

annual (1): One payment per year.
semiannual (2): Two payments per year.
quarterly (4): Four payments per year.
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ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.
actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Example
In this example, the YIELD function is used to determine the annual yield of the hypothetical security
described by the values listed. The security pays periodic interest.
The function evaluates to approximately 5.25%.
settle
05/01/2009
=YIELD (B2,
C2, D2, E2, F2,
G2, H2)

maturity

annual-rate

price

redemption

frequency

days-basis

06/30/2015

0.065

106.50

100

2

0

Related Topics
For related functions and additional information, see:
“PRICE” on page 137
“YIELDDISC” on page 152
“YIELDMAT” on page 153
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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YIELDDISC

The YIELDDISC function returns the effective annual interest rate for a security that is
sold at a discount to redemption value and pays no interest.
YIELDDISC(settle, maturity, price, redemption, days-basis)
ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ maturity:  The date when the security matures. maturity is a date/time value. It must

be after settle.
ÂÂ price:  The cost of the security per $100 of par value. price is a number value.
ÂÂ redemption:  The redemption value per $100 of par value. redemption is a number

value that must be greater than 0. redemption is the amount that will be received
per $100 of face value. Often, it is 100, meaning that the security’s redemption value
is equal to its face value.
ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.
actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Example
In this example, the YIELDDISC function is used to determine the effective annual yield of the
hypothetical security described by the values listed. The security does not pay interest and is sold at
a discount.
The function evaluates to approximately 8.37%, which represents the annual yield at a price of
approximately $65.98 per $100 of face value.

=YIELDDISC (B2,
C2, D2, E2, F2)

152		

settle

maturity

price

redemption

days-basis

05/01/2009

06/30/2015

65.98

100

0

Chapter 6    Financial Functions

Related Topics
For related functions and additional information, see:
“PRICEDISC” on page 138
“YIELD” on page 150
“YIELDMAT” on page 153
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

YIELDMAT

The YIELDMAT function returns the effective annual interest rate for a security that
only pays interest at maturity.
YIELDMAT(settle, maturity, issue, annual-rate, price, days-basis)
ÂÂ settle:  The trade settlement date. settle is a date/time value. The trade settlement

date is usually one or more days after the trade date.
ÂÂ maturity:  The date when the security matures. maturity is a date/time value. It must

be after settle.
ÂÂ issue:  The date the security was originally issued. issue is a date/time value and

must be the earliest date given.
ÂÂ annual-rate:  The annual coupon rate or stated annual interest rate of the security.

annual-rate is a number value and is either entered as a decimal (for example, 0.08)
or with a percent sign (for example, 8%).
ÂÂ price:  The cost of the security per $100 of par value. price is a number value.
ÂÂ days-basis:  An optional argument specifying the number of days per month and

days per year used in the calculations.
30/360 (0 or omitted):  30 days in a month, 360 days in a year, using the NASD
method for dates falling on the 31st of a month.
actual/actual (1):  Actual days in each month, actual days in each year.
actual/360 (2):  Actual days in each month, 360 days in a year.

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actual/365 (3):  Actual days in each month, 365 days in a year.
30E/360 (4):  30 days in a month, 360 days in a year, using the European method for
dates falling on the 31st of a month (European 30/360).
Example
In this example, the YIELDMAT function is used to determine the effective annual yield of the
hypothetical security described by the values listed. The security pays interest only at maturity.
The function evaluates to 6.565%.
settle
=YIELDMAT (B2, 05/01/2009
C2, D2, E2, F2,
G2)

maturity

issue

annual-rate

price

days-basis

06/30/2015

12/14/2008

0.065

99.002

0

Related Topics
For related functions and additional information, see:
“PRICEMAT” on page 140
“YIELD” on page 150
“YIELDDISC” on page 152
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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Logical and Information Functions

7

The logical and information functions help you to evaluate
the contents of cells and help in determining how to
evaluate or otherwise work with cell contents or formula
results.
Listing of Logical and Information Functions

iWork provides these logical and information functions for use with tables.
Function

Description

“AND” (page 156)

The AND function returns TRUE if all arguments
are true, and FALSE otherwise.

“FALSE” (page 157)

The FALSE function returns the Boolean value
FALSE. This function is included for compatibility
with tables imported from other spreadsheet
applications.

“IF” (page 158)

The IF function returns one of two values
depending on whether a specified expression
evaluates to a Boolean value of TRUE or FALSE.

“IFERROR” (page 159)

The IFERROR function returns a value that you
specify if a given value evaluates to an error;
otherwise it returns the given value.

“ISBLANK” (page 160)

The ISBLANK function returns TRUE if the
specified cell is empty and FALSE otherwise.

“ISERROR” (page 161)

The ISERROR function returns TRUE if a given
expression evaluates to an error and FALSE
otherwise.

		

155

Function

Description

“ISEVEN” (page 162)

The ISEVEN function returns TRUE if the value is
even (leaves no remainder when divided by 2);
otherwise it returns FALSE.

“ISODD” (page 163)

The ISODD function returns TRUE if the value
is odd (leaves a remainder when divided by 2);
otherwise it returns FALSE.

“NOT” (page 164)

The NOT function returns the opposite of the
Boolean value of a specified expression.

“OR” (page 165)

The OR function returns TRUE if any argument is
true; otherwise it returns FALSE.

“TRUE” (page 166)

The TRUE function returns the Boolean value
TRUE. This function is included for compatibility
with tables imported from other spreadsheet
applications.

AND

The AND function returns TRUE if all arguments are true, and FALSE otherwise.
AND(test-expression, test-expression…)
ÂÂ test-expression:  An expression. test-expression can contain anything as long as the

expression can be evaluated as a Boolean. If the expression evaluates to a number, 0
is considered to be FALSE, and any other number is considered to be TRUE.
ÂÂ test-expression…: Optionally include one or more additional expressions.

Usage Notes
ÂÂ The AND function is equivalent to the logical conjunction operator used in
mathematics or logic. It first evaluates each test-expression. If all the given
expressions evaluate to TRUE, the AND function returns TRUE; otherwise FALSE.
Examples
=AND(TRUE, TRUE) returns TRUE because both arguments are true.
=AND(1, 0, 1, 1) returns FALSE because one of the arguments is a numeric 0, which is interpreted as
FALSE.
=AND(A5>60, A5<=100) returns TRUE if cell A5 contains a number in the range 61 to 100, otherwise
FALSE.
The following two IF functions will return the same value:
=IF(B2>60, IF(B2<=100, TRUE, FALSE), FALSE)
=IF(AND(B2>60, B2<=100), TRUE, FALSE)

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Related Topics
For related functions and additional information, see:
“IF” on page 158
“NOT” on page 164
“OR” on page 165
“Specifying Conditions and Using Wildcards” on page 360
“Adding Comments Based on Cell Contents” on page 358
“Using Logical and Information Functions Together” on page 358
“Listing of Logical and Information Functions” on page 155
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

FALSE

The FALSE function returns the Boolean value FALSE. This function is included for
compatibility with tables imported from other spreadsheet applications.
FALSE()
Usage Notes
ÂÂ The FALSE function does not have any arguments. However, you must include the
parentheses: =FALSE().
ÂÂ Instead of using the FALSE function, you can specify a Boolean value of FALSE by

simply typing FALSE (or false) into a cell or as a function argument.
Examples
=FALSE() returns the Boolean value FALSE.
=AND(1, FALSE()) returns the Boolean value FALSE.

Related Topics
For related functions and additional information, see:
“TRUE” on page 166
“Listing of Logical and Information Functions” on page 155

Chapter 7    Logical and Information Functions

157

“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

IF

The IF function returns one of two values depending on whether a specified
expression evaluates to a Boolean value of TRUE or FALSE.
IF(if-expression, if-true, if-false)
ÂÂ if-expression:  A logical expression. if-expression can contain anything as long as the

expression can be evaluated as a Boolean. If the expression evaluates to a number, 0
is considered to be FALSE, and any other number is considered to be TRUE.
ÂÂ if-true:  The value returned if the expression is TRUE. if-true can contain any value

type. If omitted (comma but no value), IF will return 0.
ÂÂ if-false:  An optional argument specifying the value returned if the expression is

FALSE. if-false can contain any value type. If omitted (comma but no value), IF will
return 0. If entirely omitted (no comma after if-false) and if-expression evaluates to
FALSE, IF will return FALSE.
Usage Notes
ÂÂ If the Boolean value of if-expression is TRUE, the function returns the if-true
expression; otherwise it returns the if-false expression.
ÂÂ Both if-true and if-false can contain additional IF functions (nested IF functions).
Examples
=IF(A5>=0, “Nonnegative”, “Negative”) returns the text “Nonnegative” if cell A5 contains a number
greater than or equal to zero or a nonnumeric value. If cell A5 contains a value less than 0, the
function returns “Negative”.
=IF(IFERROR(OR(ISEVEN(B4+B5),ISODD(B4+B5), FALSE),), “All numbers”, “Not all numbers”) returns the
text “All numbers” if both cells B4 and B5 contain numbers; otherwise the text “Not all numbers.” This
is accomplished by testing to see if the sum of the two cells is either even or odd. If the cell is not a
number, the EVEN and ODD functions will return an error and the IFERROR function will return FALSE;
otherwise it will return TRUE since either EVEN or ODD is TRUE. So if either B4 or B5 is not a number
or Boolean, the IF statement will return the if-false expression, “Not all numbers”; otherwise it will
return the if-true expression “All numbers.”

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Related Topics
For related functions and additional information, see:
“AND” on page 156
“NOT” on page 164
“OR” on page 165
“Specifying Conditions and Using Wildcards” on page 360
“Trapping Division by Zero” on page 360
“Adding Comments Based on Cell Contents” on page 358
“Using Logical and Information Functions Together” on page 358
“Listing of Logical and Information Functions” on page 155
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

IFERROR

The IFERROR function returns a value that you specify if a given value evaluates to an
error; otherwise it returns the given value.
IFERROR(any-expression, if-error)
ÂÂ any-expression:  An expression to be tested. any-expression can contain any value

type.
ÂÂ if-error:  The value returned if any-expression evaluates to an error. if-error can

contain any value type.
Usage Notes
ÂÂ Use IFERROR to handle errors in a formula. For example, if you are working with
data where a valid value for cell D1 is 0, the formula =B1/D1 would result in an
error (division by zero). This error can be prevented by using a formula such as
=IFERROR(B1/D1, 0) which returns the actual division if D1 is not zero; otherwise it
returns 0.

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Examples
If B1 is a number value and D1 evaluates to 0, then:
=IFERROR(B1/D1,0) returns 0 since division by zero results in an error.
=IF(ISERROR(B1/D1),0,B1/D1) is equivalent to the previous IFERROR example, but requires the use of
both IF and ISERROR.
=IF(IFERROR(OR(ISEVEN(B4+B5),ISODD(B4+B5), FALSE),), “All numbers”, “Not all numbers”) returns the
text “All numbers” if both cells B4 and B5 contain numbers; otherwise the text “Not all numbers.” This
is accomplished by testing to see if the sum of the two cells is either even or odd. If the cell is not a
number, the EVEN and ODD functions will return an error and the IFERROR function will return FALSE;
otherwise it will return TRUE since either EVEN or ODD is TRUE. So if either B4 or B5 is not a number
or a Boolean, the IF statement will return the if-false expression, “Not all numbers”; otherwise it will
return the if-true expression “All numbers.”

Related Topics
For related functions and additional information, see:
“ISBLANK” on page 160
“ISERROR” on page 161
“Listing of Logical and Information Functions” on page 155
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

ISBLANK

The ISBLANK function returns TRUE if the specified cell is empty and FALSE otherwise.
ISBLANK(cell)
ÂÂ cell:  A reference to a single table cell. cell is a reference value to a single cell that

can contain any value or be empty.
Usage Notes
ÂÂ If the cell is completely blank (empty), the function returns TRUE; otherwise it
returns FALSE. If the cell contains a space or a nonprinting character, the function
will return FALSE, even though the cell appears to be blank.

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Examples
If the table cell A1 is empty and cell B2 is equal to 100:
=ISBLANK(A1) returns TRUE.
=ISBLANK(B2) returns FALSE.

Related Topics
For related functions and additional information, see:
“IFERROR” on page 159
“ISERROR” on page 161
“Adding Comments Based on Cell Contents” on page 358
“Using Logical and Information Functions Together” on page 358
“Listing of Logical and Information Functions” on page 155
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

ISERROR

The ISERROR function returns TRUE if a given expression evaluates to an error and
FALSE otherwise.
ISERROR(any-expression)
ÂÂ any-expression:  An expression to be tested. any-expression can contain any value

type.
Usage Notes
ÂÂ It is often better to use the IFERROR function. The IFERROR function provides all the
functionality of ISERROR, but allows for trapping, not just identifying, the error.
Examples
If B1 is a number value and D1 evaluates to 0, then
=IF(ISERROR(B1/D1),0,B1/D1) returns 0 since division by zero results in an error.
=IFERROR(B1/D1,0) is equivalent to the previous example, but requires only one function.

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161

Related Topics
For related functions and additional information, see:
“IFERROR” on page 159
“ISBLANK” on page 160
“Listing of Logical and Information Functions” on page 155
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

ISEVEN

The ISEVEN function returns TRUE if the given number is even (leaves no remainder
when divided by 2); otherwise it returns FALSE.
ISEVEN(num)
ÂÂ num:  A number. num is a number value.

Usage Notes
ÂÂ If num is text, the function returns an error. If num is the Boolean TRUE (value of 1),
the function returns FALSE. If num is the Boolean FALSE (value of 0), the function
returns TRUE.
Examples
=ISEVEN(2) returns TRUE.
=ISEVEN(2.75) returns TRUE.
=ISEVEN(3) returns FALSE.

Related Topics
For related functions and additional information, see:
“ISODD” on page 163
“Listing of Logical and Information Functions” on page 155
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41
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ISODD

The ISODD function returns TRUE if the given number is odd (leaves a remainder when
divided by 2); otherwise it returns FALSE.
ISODD(num)
ÂÂ num:  A number. num is a number value.

Usage Notes
ÂÂ If num is text, the function returns an error. If num is the Boolean TRUE (value of 1),
the function returns TRUE. If num is the Boolean FALSE (value of 0), the function
returns FALSE.
Examples
=ISODD(3) returns TRUE.
=ISODD(3.75) returns TRUE.
=ISODD(2) returns FALSE.

Related Topics
For related functions and additional information, see:
“ISEVEN” on page 162
“Listing of Logical and Information Functions” on page 155
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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163

NOT

The NOT function returns the opposite of the Boolean value of a specified expression.
NOT(any-expression)
ÂÂ any-expression:  An expression to be tested. any-expression can contain anything as

long as the expression can be evaluated as a Boolean. If the expression evaluates to
a number, 0 is considered to be FALSE, and any other number is considered to be
TRUE.
Examples
=NOT(0) returns TRUE because 0 is interpreted as FALSE.
=OR(A9, NOT(A9)) always returns TRUE because either A9 or its opposite will always be true.
=NOT(OR(FALSE, FALSE)) returns TRUE because neither argument of the logical OR is true.

Related Topics
For related functions and additional information, see:
“AND” on page 156
“IF” on page 158
“OR” on page 165
“Listing of Logical and Information Functions” on page 155
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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OR

The OR function returns TRUE if any argument is true; otherwise it returns FALSE.
OR(any-expression, any-expression…)
ÂÂ any-expression:  An expression to be tested. any-expression can contain anything as

long as the expression can be evaluated as a Boolean. If the expression evaluates to a
number, 0 is considered to be FALSE, and any other number is considered to be TRUE.
ÂÂ any-expression…: Optionally include one or more additional expressions to be tested.

Usage Notes
ÂÂ The OR function is equivalent to the logical disjunction or inclusive disjunction
used in mathematics or logic. It first evaluates each expression. If any of the given
expressions evaluate to TRUE, the OR function returns TRUE; otherwise FALSE.
ÂÂ If an expression is numeric, a value of 0 is interpreted as FALSE and any nonzero

value is interpreted as TRUE.
ÂÂ OR is often used with the IF function when more than one condition must be

considered.
Examples
=OR(A1+A2<100, B1+B2<100) returns FALSE if the sums of the indicated cells are both greater than
or equal to 100, and TRUE if at least one of the sums is less than 100.
=OR(5, 0, 6) returns TRUE because at least one argument is not zero.

Related Topics
For related functions and additional information, see:
“AND” on page 156
“IF” on page 158
“NOT” on page 164
“Specifying Conditions and Using Wildcards” on page 360
“Adding Comments Based on Cell Contents” on page 358
“Using Logical and Information Functions Together” on page 358
“Listing of Logical and Information Functions” on page 155
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41
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TRUE

The TRUE function returns the Boolean value TRUE. This function is included for
compatibility with tables imported from other spreadsheet applications.
TRUE()
Usage Notes
ÂÂ The TRUE function does not have any arguments. However, you must include the
parentheses: =TRUE().
ÂÂ Instead of using the TRUE function, you can specify a Boolean value of TRUE by

simply typing TRUE (or true) into a cell or function argument.
Examples
=TRUE() returns the Boolean value TRUE.
=AND(1, TRUE()) returns the Boolean value TRUE.
=AND(1, TRUE) works exactly the same as the preceding example.

Related Topics
For related functions and additional information, see:
“FALSE” on page 157
“Listing of Logical and Information Functions” on page 155
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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8

Numeric Functions

The numeric functions help you to calculate commonly used
mathematical values.
Listing of Numeric Functions

iWork provides these numeric functions for use with tables.
Function

Description

“ABS” (page 170)

The ABS function returns the absolute value of a
number or duration.

“CEILING” (page 170)

The CEILING function rounds a number away
from zero to the nearest multiple of the specified
factor.

“COMBIN” (page 172)

The COMBIN function returns the number of
different ways you can combine a number of
items into groups of a specific size, ignoring the
order within the groups.

“EVEN” (page 173)

The EVEN function rounds a number away from
zero to the next even number.

“EXP” (page 174)

The EXP function returns e (the base of natural
logarithms) raised to the specified power.

“FACT” (page 174)

The FACT function returns the factorial of a
number.

“FACTDOUBLE” (page 175)

The FACTDOUBLE function returns the double
factorial of a number.

“FLOOR” (page 176)

The FLOOR function rounds a number toward
zero to the nearest multiple of the specified
factor.

“GCD” (page 177)

The GCD function returns the greatest common
divisor of the specified numbers.

		

167

168		

Function

Description

“INT” (page 178)

The INT function returns the nearest integer that
is less than or equal to the number.

“LCM” (page 179)

The LCM function returns the least common
multiple of the specified numbers.

“LN” (page 179)

The LN function returns the natural logarithm of
a number, the power to which e must be raised
to result in the number.

“LOG” (page 180)

The LOG function returns the logarithm of a
number using a specified base.

“LOG10” (page 181)

The LOG10 function returns the base-10
logarithm of a number.

“MOD” (page 182)

The MOD function returns the remainder from a
division.

“MROUND” (page 183)

The MROUND function rounds a number to the
nearest multiple of a specified factor.

“MULTINOMIAL” (page 184)

The MULTINOMIAL function returns the closed
form of the multinomial coefficient of the given
numbers.

“ODD” (page 185)

The ODD function rounds a number away from
zero to the next odd number.

“PI” (page 186)

The PI function returns the approximate value of
π (pi), the ratio of a circle’s circumference to its
diameter.

“POWER” (page 186)

The POWER function returns a number raised to
a power.

“PRODUCT” (page 187)

The PRODUCT function returns the product of
one or more numbers.

“QUOTIENT” (page 188)

The QUOTIENT function returns the integer
quotient of two numbers.

“RAND” (page 189)

The RAND function returns a random number
that is greater than or equal to 0 and less than 1.

“RANDBETWEEN” (page 189)

The RANDBETWEEN function returns a random
integer within the specified range.

“ROMAN” (page 190)

The ROMAN function converts a number to
Roman numerals.

Chapter 8    Numeric Functions

Function

Description

“ROUND” (page 191)

The ROUND function returns a number rounded
to the specified number of places.

“ROUNDDOWN” (page 192)

The ROUNDDOWN function returns a number
rounded toward zero (rounded down) to the
specified number of places.

“ROUNDUP” (page 193)

The ROUNDUP function returns a number
rounded away from zero (rounded up) to the
specified number of places.

“SIGN” (page 195)

The SIGN function returns 1 when a given
number is positive, –1 when it is negative, and 0
when it is zero.

“SQRT” (page 195)

The SQRT function returns the square root of a
number.

“SQRTPI” (page 196)

The SQRTPI function returns the square root of a
number multiplied by π (pi).

“SUM” (page 196)

The SUM function returns the sum of a collection
of numbers.

“SUMIF” (page 197)

The SUMIF function returns the sum of a
collection of numbers, including only numbers
that satisfy a specified condition.

“SUMIFS” (page 198)

The SUMIFS function returns the sum of the cells
in a collection where the test values meet the
given conditions.

“SUMPRODUCT” (page 200)

The SUMPRODUCT function returns the sum of
the products of corresponding numbers in one or
more ranges.

“SUMSQ” (page 201)

The SUMSQ function returns the sum of the
squares of a collection of numbers.

“SUMX2MY2” (page 202)

The SUMX2MY2 function returns the sum of the
difference of the squares of corresponding values
in two collections.

“SUMX2PY2” (page 203)

The SUMX2PY2 function returns the sum of
the squares of corresponding values in two
collections.

“SUMXMY2” (page 204)

The SUMXMY2 function returns the sum
of the squares of the differences between
corresponding values in two collections.

“TRUNC” (page 204)

The TRUNC function truncates a number to the
specified number of digits.

Chapter 8    Numeric Functions

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ABS

The ABS function returns the absolute value of a number or duration.
ABS(num-dur)
ÂÂ num-dur:  A number or duration value. num-dur is a number or duration value.

Usage Notes
ÂÂ The result returned by ABS is either a positive number or 0.
Examples
=ABS(A1) returns 5, if cell A1 contains 5.
=ABS(8-5) returns 3.
=ABS(5-8) returns 3.
=ABS(0) returns 0.
=ABS(A1) returns 0, if cell A1 is empty.

Related Topics
For related functions and additional information, see:
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

CEILING

The CEILING function rounds a number away from zero to the nearest multiple of the
specified factor.
CEILING(num-to-round, multiple-factor)
ÂÂ num-to-round:  The number to be rounded. num-to-round is a number value.
ÂÂ multiple-factor:  The number to use to determine the closet multiple. multiple-factor

is a number value and must have the same sign as num-to-round.

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Examples
=CEILING(0.25, 1) returns 1.
=CEILING(1.25, 1) returns 2.
=CEILING(-1.25, -1) returns -2.
=CEILING(5, 2) returns 6.
=CEILING(73, 10) returns 80.
=CEILING(7, 2.5) returns 7.5.

Related Topics
For related functions and additional information, see:
“EVEN” on page 173
“FLOOR” on page 176
“INT” on page 178
“MROUND” on page 183
“ODD” on page 185
“ROUND” on page 191
“ROUNDDOWN” on page 192
“ROUNDUP” on page 193
“TRUNC” on page 204
“More on Rounding” on page 355
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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171

COMBIN

The COMBIN function returns the number of different ways you can combine a
number of items into groups of a specific size, ignoring the order within the groups.
COMBIN(total-items, group-size)
ÂÂ total-items:  The total number of items. total-items is a number value and must be

greater than or equal to 0. If total-items has a decimal (fractional) part, it is ignored.
ÂÂ group-size:  The number of items combined in each group. group-size is a number

value and must be greater than or equal to 0. If group-size has a decimal (fractional)
part, it is ignored.
Usage Notes
ÂÂ Combinations are not the same as permutations. The order of the items in a group is
ignored for combinations but not for permutations. For example, (1, 2, 3) and (3, 2, 1)
are the same combination but two unique permutations. If you want the number of
permutations rather than the number of combinations, use the PERMUT function.
Examples
=COMBIN(3, 2) returns 3, the number of unique groups you can create if you start with 3 items and
group them 2 at a time.
=COMBIN(3.2, 2.3) returns 3. Fractional parts are dropped.
=COMBIN(5, 2) and =COMBIN(5, 3) both return 10.

Related Topics
For related functions and additional information, see:
“PERMUT” on page 281
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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EVEN

The EVEN function rounds a number away from zero to the next even number.
EVEN(num-to-round)
ÂÂ num-to-round:  The number to be rounded. num-to-round is a number value.

Usage Notes
ÂÂ To round to an odd number, use the ODD function.
Examples
=EVEN(1) returns 2.
=EVEN(2) returns 2.
=EVEN(2.5) returns 4.
=EVEN(-2.5) returns -4.
=EVEN(0) returns 0.

Related Topics
For related functions and additional information, see:
“CEILING” on page 170
“FLOOR” on page 176
“INT” on page 178
“MROUND” on page 183
“ODD” on page 185
“ROUND” on page 191
“ROUNDDOWN” on page 192
“ROUNDUP” on page 193
“TRUNC” on page 204
“More on Rounding” on page 355
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 8    Numeric Functions

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EXP

The EXP function returns e (the base of natural logarithms) raised to the specified
power.
EXP(exponent)
ÂÂ exponent:  The power to which you want to raise e. exponent is a number value.

Usage Notes
ÂÂ EXP and LN are mathematically inverses over the domain where LN is defined, but
because of floating-point rounding, EXP(LN(x)) may not give exactly x.
Example
=EXP(1) returns 2.71828182845905, an approximation of e.

Related Topics
For related functions and additional information, see:
“LN” on page 179
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

FACT

The FACT function returns the factorial of a number.
FACT(fact-num)
ÂÂ fact-num:  A number. fact-num is a number value and must be greater than or equal

to 0. Any decimal (fractional) part of fact-num is ignored.
Examples
=FACT(5) returns 120, or 1 * 2 * 3 * 4 * 5.
=FACT(0) returns 1.
=FACT(4.5) returns 24. The fraction is dropped and 4 factorial is computed.
=FACT(-1) returns an error; the number must be nonnegative.

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Related Topics
For related functions and additional information, see:
“FACTDOUBLE” on page 175
“MULTINOMIAL” on page 184
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

FACTDOUBLE

The FACTDOUBLE function returns the double factorial of a number.
FACTDOUBLE(fact-num)
ÂÂ fact-num:  A number. fact-num is a number value and must be greater than or equal

to –1. Values in the range –1 to 1 return 1. Any decimal (fractional) part of fact-num is
ignored.
Usage Notes
ÂÂ For an even integer, the double factorial is the product of all even integers less than
or equal to the given integer and greater than or equal to 2. For an odd integer, the
double factorial is the product of all odd integers less than or equal to the given
integer and greater than or equal to 1.
Examples
=FACTDOUBLE(4) returns 8, the product of 2 and 4.
=FACTDOUBLE(4.7) returns 8, the product of 2 and 4. The decimal portion is ignored.
=FACTDOUBLE (10) returns 3840, the product of 2, 4, 6, 8, and 10.
=FACTDOUBLE(1) returns 1, as all numbers between –1 and 1 return 1.
=FACTDOUBLE(-1) returns 1, as all numbers between –1 and 1 return 1.
=FACTDOUBLE (7) returns 105, the product of 1, 3, 5, and 7.

Related Topics
For related functions and additional information, see:
“FACT” on page 174
“MULTINOMIAL” on page 184

Chapter 8    Numeric Functions

175

“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

FLOOR

The FLOOR function rounds a number toward zero to the nearest multiple of the
specified factor.
FLOOR(num-to-round, factor)
ÂÂ num-to-round:  The number to be rounded. num-to-round is a number value.
ÂÂ factor:  The number to use to determine the closet multiple. factor is a number

value. It must have the same sign as num-to-round.
Examples
=FLOOR(0.25, 1) returns 0.
=FLOOR(1.25, 1) returns 1.
=FLOOR(5, 2) returns 4.
=FLOOR(73, 10) returns 70.
=FLOOR(-0.25, -1) returns 0.
=FLOOR(9, 2.5) returns 7.5.

Related Topics
For related functions and additional information, see:
“CEILING” on page 170
“EVEN” on page 173
“INT” on page 178
“MROUND” on page 183
“ODD” on page 185
“ROUND” on page 191
“ROUNDDOWN” on page 192
“ROUNDUP” on page 193

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“TRUNC” on page 204
“More on Rounding” on page 355
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

GCD

The GCD function returns the greatest common divisor of the specified numbers.
GCD(num-value, num-value…)
ÂÂ num-value:  A number. num-value is a number value. If there is a decimal portion it

is ignored.
ÂÂ num-value…: Optionally include one or more additional numbers.

Usage Notes
ÂÂ Sometimes called the greatest common factor, the greatest common divisor is the
largest integer that divides into each of the numbers with no remainder.
Examples
=GCD(8, 10) returns 2.
=GCD(99, 102, 105) returns 3.
=GCD(34, 51) returns 17.

Related Topics
For related functions and additional information, see:
“LCM” on page 179
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 8    Numeric Functions

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INT

The INT function returns the nearest integer that is less than or equal to the number.
INT(num-to-round)
ÂÂ num-to-round:  The number to be rounded. num-to-round is a number value.
Examples
=INT(1.49) returns 1.
=INT(1.50) returns 1.
=INT(1.23456) returns 1.
=INT(1111.222) returns 1111.
=INT(-2.2) returns -3.
=INT(-2.8) returns -3.

Related Topics
For related functions and additional information, see:
“CEILING” on page 170
“EVEN” on page 173
“FLOOR” on page 176
“MROUND” on page 183
“ODD” on page 185
“ROUND” on page 191
“ROUNDDOWN” on page 192
“ROUNDUP” on page 193
“TRUNC” on page 204
“More on Rounding” on page 355
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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LCM

The LCM function returns the least common multiple of the specified numbers.
LCM(num-value, num-value…)
ÂÂ num-value:  A number. num-value is a number value.
ÂÂ num-value…: Optionally include one or more additional numbers.

Usage Notes
ÂÂ Sometimes called the lowest or smallest common multiple, the least common
multiple is the smallest integer that is a multiple of the specified numbers.
Examples
=LCM(2, 3) returns 6.
=LCM(34, 68) returns 68.
=LCM(30, 40, 60) returns 120.
=LCM(30.25, 40.333, 60.5) returns 120 (the fractional parts are ignored).
=LCM(2, -3) displays an error (negative numbers are not allowed).

Related Topics
For related functions and additional information, see:
“GCD” on page 177
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

LN

The LN function returns the natural logarithm of a number, the power to which e must
be raised to result in the number.
LN(pos-num)
ÂÂ pos-num:  A positive number. pos-num is a number value and must be greater than 0.

Usage Notes
ÂÂ EXP and LN are mathematically inverses over the domain where LN is defined, but
because of floating-point rounding, =LN(EXP(x)) may not give exactly x.

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179

Example
=LN(2.71828) returns approximately 1, the power to which e must be raised to produce 2.71828.

Related Topics
For related functions and additional information, see:
“EXP” on page 174
“LOG” on page 180
“LOGINV” on page 268
“LOGNORMDIST” on page 269
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

LOG

The LOG function returns the logarithm of a number using a specified base.
LOG(pos-num, base)
ÂÂ pos-num:  A positive number. pos-num is a number value and must be greater than 0.
ÂÂ base:  An optional value specifying the base of the logarithm. base is a number

value and must be greater than 0. If base is 1, a division by zero will result and the
function will return an error. If base is omitted, it is assumed to be 10.
Examples
=LOG(8, 2) returns 3.
=LOG(100, 10) and LOG(100) both return 2.
=LOG(5.0625, 1.5) returns 4.

Related Topics
For related functions and additional information, see:
“LOG10” on page 181
“Listing of Numeric Functions” on page 167

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“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

LOG10

The LOG10 function returns the base-10 logarithm of a number.
LOG10(pos-num)
ÂÂ pos-num:  A positive number. pos-num is a number value and must be greater than 0.

Usage Notes
ÂÂ To find the logarithm for a base other than 10, use the LOG function.
Examples
=LOG10(1) returns 0.
=LOG10(10) returns 1.
=LOG10(100) returns 2.
=LOG10(1000) returns 3.

Related Topics
For related functions and additional information, see:
“LN” on page 179
“LOG” on page 180
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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181

MOD

The MOD function returns the remainder from a division.
MOD(dividend, divisor)
ÂÂ dividend:  A number to be divided by another number. dividend is a number value.
ÂÂ divisor:  A number to divide into another number. divisor is a number value. If 0, a

division by zero will result and the function will return an error.
Usage Notes
ÂÂ The sign of the result matches that of the divisor.
ÂÂ When computing MOD(a, b), MOD gives a number r such that a = bk + r, where r is

between 0 and b, and k is an integer.
ÂÂ MOD(a, b) is equivalent to a–b*INT(a/b).
Examples
=MOD(6, 3) returns 0.
=MOD(7, 3) returns 1.
=MOD(8, 3) returns 2.
=MOD(-8, 3) returns 1.
=MOD(4.5, 2) returns 0.5.
=MOD(7, 0.75) returns 0.25.

Related Topics
For related functions and additional information, see:
“QUOTIENT” on page 188
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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MROUND

The MROUND function rounds a number to the nearest multiple of a specified factor.
MROUND(num-to-round, factor)
ÂÂ num-to-round:  The number to be rounded. num-to-round is a number value.
ÂÂ factor:  The number to use to determine the closet multiple. factor is a number

value. It must have the same sign as num-to-round.
Examples
=MROUND(2, 3) returns 3.
=MROUND(4, 3) returns 3.
=MROUND(4.4999, 3) returns 3.
=MROUND(4.5, 3) returns 6.
=MROUND(-4.5, 3) returns an error.

Related Topics
For related functions and additional information, see:
“CEILING” on page 170
“EVEN” on page 173
“FLOOR” on page 176
“INT” on page 178
“ODD” on page 185
“ROUND” on page 191
“ROUNDDOWN” on page 192
“ROUNDUP” on page 193
“TRUNC” on page 204
“More on Rounding” on page 355
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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183

MULTINOMIAL

The MULTINOMIAL function returns the multinomial coefficient of the given numbers.
It accomplishes this by determining the ratio of the factorial of the sum of the given
numbers to the product of the factorials of the given numbers.
MULTINOMIAL(non-neg-num, non-neg-num…)
ÂÂ non-neg-num:  A number. non-neg-num is a number value and must be greater

than or equal to 0.
ÂÂ non-neg-num…: Optionally include one or more additional numbers.
Examples
=MULTINOMIAL(2) returns 1. The factorial of the 2 is 2. The product of 1 and 2 is 2. The ratio of 2:2 is 1.
=MULTINOMIAL(1, 2, 3) returns 60. The factorial of the sum of 1, 2, and 3 is 720. The product of the
factorials of 1, 2, and 3 is 12. The ratio of 720:12 is 60.
=MULTINOMIAL(4, 5, 6) returns 630630. The factorial of the sum of 4, 5, and 6 is 1.30767E+12. The
product of the factorials of 4, 5, and 6 is 2073600. The ratio of 1.30767E+12:2073600 is 630630.

Related Topics
For related functions and additional information, see:
“FACT” on page 174
“FACTDOUBLE” on page 175
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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ODD

The ODD function rounds a number away from zero to the next odd number.
ODD(num-to-round)
ÂÂ num-to-round:  The number to be rounded. num-to-round is a number value.

Usage Notes
ÂÂ To round to an even number, use the EVEN function.
Examples
=ODD(1) returns 1.
=ODD(2) returns 3.
=ODD(2.5) returns 3.
=ODD(-2.5) returns -3.
=ODD(0) returns 1.

Related Topics
For related functions and additional information, see:
“CEILING” on page 170
“EVEN” on page 173
“FLOOR” on page 176
“INT” on page 178
“MROUND” on page 183
“ROUND” on page 191
“ROUNDDOWN” on page 192
“ROUNDUP” on page 193
“TRUNC” on page 204
“More on Rounding” on page 355
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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PI

The PI function returns the approximate value of π (pi), the ratio of a circle’s
circumference to its diameter.
PI()
Usage Notes
ÂÂ The PI function does not have any arguments. However, you must include the
parentheses: =PI().
ÂÂ PI is accurate to 15 decimal places.
Examples
=PI() returns 3.14159265358979.
=SIN(PI()/2) returns 1, the sine of π/2 radians or 90 degrees.

Related Topics
For related functions and additional information, see:
“COS” on page 333
“SIN” on page 336
“TAN” on page 338
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

POWER

The POWER function returns a number raised to a power.
POWER(number, exponent)
ÂÂ number:  A number. number is a number value.
ÂÂ exponent:  The power to which to raise the given number. exponent is a number value.

Usage Notes
ÂÂ The POWER function produces the same result as the ^ operator:  =POWER(x, y)
returns the same result as =x^y.

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Examples
=POWER(2, 3) returns 8.
=POWER(2, 10) returns 1024.
=POWER(0.5, 3) returns 0.125.
=POWER(100, 0.5) returns 10.

Related Topics
For related functions and additional information, see:
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

PRODUCT

The PRODUCT function returns the product of one or more numbers.
PRODUCT(num-value, num-value…)
ÂÂ num-value:  A number. num-value is a number value.
ÂÂ num-value…: Optionally include one or more additional numbers.

Usage Notes
ÂÂ Empty cells included within the values are ignored and do not affect the result.
Examples
=PRODUCT(2, 4) returns 8.
=PRODUCT(0.5, 5, 4, 5) returns 50.

Related Topics
For related functions and additional information, see:
“SUM” on page 196
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15

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“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

QUOTIENT

The QUOTIENT function returns the integer quotient of two numbers.
QUOTIENT(dividend, divisor)
ÂÂ dividend:  A number to be divided by another number. dividend is a number value.
ÂÂ divisor:  A number to divide into another number. divisor is a number value. If 0, a

division by zero will result and the function will return an error.
Usage Notes
ÂÂ If either, but not both, the dividend or divisor is negative, the result will be negative.
If the sign of both the dividend and the divisor is the same, the result will be
positive.
ÂÂ Only the whole part of the quotient is returned. The fractional part (or remainder)

is ignored.
Examples
=QUOTIENT(5, 2) returns 2.
=QUOTIENT(5.99, 2) returns 2.
=QUOTIENT(-5, 2) returns -2.
=QUOTIENT(6, 2) returns 3.
=QUOTIENT(5, 6) returns 0.

Related Topics
For related functions and additional information, see:
“MOD” on page 182
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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RAND

The RAND function returns a random number that is greater than or equal to 0 and
less than 1.
RAND()
Usage Notes
ÂÂ The RAND function does not have any arguments. However, you must include the
parentheses: =RAND().
ÂÂ Any time you change a value in the table, a new random number greater than or

equal to 0 and less than 1 is generated.
Example
=RAND() returns, for example, 0.217538648284972, 0.6137690856, 0.0296026556752622, and
0.4684193600 for four recalculations.

Related Topics
For related functions and additional information, see:
“RANDBETWEEN” on page 189
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

RANDBETWEEN

The RANDBETWEEN function returns a random integer within the specified range.
RANDBETWEEN(lower, upper)
ÂÂ lower:  The lower limit or bound. lower is a number value.
ÂÂ upper:  The upper limit or bound. upper is a number value.

Usage Notes
ÂÂ Any time you change a value in the table, a new random number between the
lower and upper limits is generated.
Example
=RANDBETWEEN(1, 10) returns, for example, 8, 6, 2, 3, and 5 for five recalculations.

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Related Topics
For related functions and additional information, see:
“RAND” on page 189
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

ROMAN

The ROMAN function converts a number to Roman numerals.
ROMAN(arabic-num, roman-style)
ÂÂ arabic-num:  The Arabic numeral that you want to convert. arabic-num is a number

value in the range 0 to 3999.
ÂÂ roman-style:  An optional value that determines how strictly the classical rules for

forming Roman numerals are applied.
strict (0 or TRUE, or omitted):  Use the most strict classical rules. When a smaller
numeral precedes a larger to indicate subtraction, the smaller must be a power of
10 and can precede a number no more than 10 times its size. For example, 999 is
represented as CMXCIX, but not LMVLIV.
relax by one degree (1):  Relax the strict classical rule by one degree. When a
smaller number precedes a larger, the smaller need not be a power of 10 and the
relative size rule is extended by one numeral. For example, 999 can be represented
as LMVLIV, but not XMIX.
relax by two degrees (2):  Relax the classical rule by two degrees. When a smaller
number precedes a larger, the relative size rule is extended by two numerals. For
example, 999 can be represented as XMIX, but not VMIV.
relax by three degrees (3):  Relax the classical rule by three degrees. When a smaller
number precedes a larger, the relative size rule is extended by three numerals. For
example, 999 can be represented as VMIV, but not IM.
relax by four degrees (4 or FALSE):  Relax the classical rule by four degrees. When a
smaller number precedes a larger, the relative size rule is extended by four numerals.
For example, 999 can be represented as IM.

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Examples
=ROMAN(12) returns XII.
=ROMAN(999) returns CMXCIX.
=ROMAN(999, 1) returns LMVLIV.
=ROMAN(999, 2) returns XMIX.
=ROMAN(999, 3) returns VMIV.

Related Topics
For related functions and additional information, see:
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

ROUND

The ROUND function returns a number rounded to the specified number of places.
ROUND(num-to-round, digits)
ÂÂ num-to-round:  The number to be rounded. num-to-round is a number value.
ÂÂ digits:  The number of digits you want to retain, relative to the decimal point. digits

is a number value. A positive number represents digits (decimal places) to the right
of the decimal point to include. A negative number specifies digits to the left of the
decimal point to replace with zeros (the number of zeros at the end of the number).
Examples
=ROUND(1.49, 0) returns 1.
=ROUND(1.50, 0) returns 2.
=ROUND(1.23456, 3) returns 1.235.
=ROUND(1111.222, -2) returns 1100.
=ROUND(-2.2, 0) returns -2.
=ROUND(-2.8, 0) returns -3.

Related Topics
For related functions and additional information, see:
“CEILING” on page 170

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“EVEN” on page 173
“FLOOR” on page 176
“INT” on page 178
“MROUND” on page 183
“ODD” on page 185
“ROUNDDOWN” on page 192
“ROUNDUP” on page 193
“TRUNC” on page 204
“More on Rounding” on page 355
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

ROUNDDOWN

The ROUNDDOWN function returns a number rounded toward zero (rounded down)
to the specified number of places.
ROUNDDOWN(num-to-round, digits)
ÂÂ num-to-round:  The number to be rounded. num-to-round is a number value.
ÂÂ digits:  The number of digits you want to retain, relative to the decimal point. digits

is a number value. A positive number represents digits (decimal places) to the right
of the decimal point to include. A negative number specifies digits to the left of the
decimal point to replace with zeros (the number of zeros at the end of the number).
Examples
=ROUNDDOWN(1.49, 0) returns 1.
=ROUNDDOWN(1.50, 0) returns 1.
=ROUNDDOWN(1.23456, 3) returns 1.234.
=ROUNDDOWN(1111.222, -2) returns 1100.
=ROUNDDOWN(-2.2, 0) returns -2.
=ROUNDDOWN(-2.8, 0) returns -2.

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Related Topics
For related functions and additional information, see:
“CEILING” on page 170
“EVEN” on page 173
“FLOOR” on page 176
“INT” on page 178
“MROUND” on page 183
“ODD” on page 185
“ROUND” on page 191
“ROUNDUP” on page 193
“TRUNC” on page 204
“More on Rounding” on page 355
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

ROUNDUP

The ROUNDUP function returns a number rounded away from zero (rounded up) to
the specified number of places.
ROUNDUP(num-to-round, digits)
ÂÂ num-to-round:  The number to be rounded. num-to-round is a number value.
ÂÂ digits:  The number of digits you want to retain, relative to the decimal point. digits

is a number value. A positive number represents digits (decimal places) to the right
of the decimal point to include. A negative number specifies digits to the left of the
decimal point to replace with zeros (the number of zeros at the end of the number).

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Examples
=ROUNDUP(1.49, 0) returns 2.
=ROUNDUP(1.50, 0) returns 2.
=ROUNDUP(1.23456, 3) returns 1.235.
=ROUNDUP(1111.222, -2) returns 1200.
=ROUNDUP(-2.2, 0) returns -3.
=ROUNDUP(-2.8, 0) returns -3.

Related Topics
For related functions and additional information, see:
“CEILING” on page 170
“EVEN” on page 173
“FLOOR” on page 176
“INT” on page 178
“MROUND” on page 183
“ODD” on page 185
“ROUND” on page 191
“ROUNDDOWN” on page 192
“TRUNC” on page 204
“More on Rounding” on page 355
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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SIGN

The SIGN function returns 1 when the argument number is positive, –1 when it is
negative, and 0 when it is zero.
SIGN(num)
ÂÂ num:  A number. number is a number value.
Examples
=SIGN(2) returns 1.
=SIGN(0) returns 0.
=SIGN(-2) returns -1.
=SIGN(A4) returns -1, if cell A4 contains -2.

Related Topics
For related functions and additional information, see:
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

SQRT

The SQRT function returns the square root of a number.
SQRT(num)
ÂÂ num:  A number. number is a number value.
Examples
=SQRT(16) returns 4.
=SQRT(12.25) returns 3.5, the square root of 12.25.

Related Topics
For related functions and additional information, see:
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15

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“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

SQRTPI

The SQRTPI function returns the square root of a number after it has been multiplied
by π (pi).
SQRTPI(non-neg-number)
ÂÂ non-neg-number:  A nonnegative number. non-neg-num is a number value and

must be greater than or equal to 0.
Examples
=SQRTPI(5) returns 3.96332729760601.
=SQRTPI(8) returns 5.013256549262.

Related Topics
For related functions and additional information, see:
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

SUM

The SUM function returns the sum of a collection of numbers.
SUM(num-date-dur, num-date-dur…)
ÂÂ num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a

duration value.
ÂÂ num-date-dur…: Optionally include one or more additional values. If more than

one num-date-dur value is specified, they must all be of the same type.
Usage Notes
ÂÂ There is one case where all values do not have to be of the same type. If exactly one
date/time value is included, any number values are considered to be numbers of
days and all numbers and duration values are added to the date/time value.

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ÂÂ Date/time values can’t be added together, so only one date/time value (as discussed

above) is permitted.
ÂÂ The values can be in individual cells, ranges of cells, or included directly as

arguments to the function.
Examples
=SUM(A1:A4) adds the numbers in four cells.
=SUM(A1:D4) adds the numbers in a square array of sixteen cells.
=SUM(A1:A4, 100) adds the numbers in four cells plus 100.

Related Topics
For related functions and additional information, see:
“PRODUCT” on page 187
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

SUMIF

The SUMIF function returns the sum of a collection of numbers, including only
numbers that satisfy a specified condition.
SUMIF(test-values, condition, sum-values)
ÂÂ test-values:  The collection containing the values to be tested. test-values is a

collection containing any value type.
ÂÂ condition:  An expression that results in a logical TRUE or FALSE. condition is an

expression that can contain anything as long as the result from comparing condition
to a value in test-values can be expressed as a Boolean value of TRUE or FALSE.
ÂÂ sum-values:  An optional collection containing the numbers to be summed. sum-

values is a collection containing number, date/time, or duration values. It should
have the same dimensions as test-values.
Usage Notes
ÂÂ If sum-values is omitted, the default value is test-values.
ÂÂ Although test-values can contain any type of value, it should usually contain values

all of the same type.

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ÂÂ If sum-values is omitted, test-values would normally contain only number or duration

values.
Examples
Given the following table:

=SUMIF(A1:A8, “<5”) returns 10.
=SUMIF(A1:A8, “<5”, B1:B8) returns 100.
=SUMIF(D1:F3, “=c”, D5:F7) returns 27.
=SUMIF(B1:D1, 1) or SUMIF(B1:D1, SUM(1)) both total all the occurrences of 1 in the range.

Related Topics
For related functions and additional information, see:
“AVERAGEIF” on page 233
“AVERAGEIFS” on page 234
“COUNTIF” on page 247
“COUNTIFS” on page 248
“SUMIFS” on page 198
“Specifying Conditions and Using Wildcards” on page 360
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

SUMIFS

The SUMIFS function returns the sum of the cells in a collection where the test values
meet the given conditions.
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SUMIFS(sum-values, test-values, condition, test-values…, condition…)
ÂÂ sum-values:  A collection containing the values to be summed. sum-values is a

collection containing number, date/time, or duration values.
ÂÂ test-values:  A collection containing values to be tested. test-values is a collection

containing any type of value.
ÂÂ condition:  An expression that results in a logical TRUE or FALSE. condition is an

expression that can contain anything as long as the result from comparing condition
to a value in test-values can be expressed as a Boolean value of TRUE or FALSE.
ÂÂ test-values…: Optionally include one or more additional collections containing

values to be tested. Each test-values collection must be followed immediately with a
condition expression. This pattern of test-values, condition can be repeated as many
times as needed.
ÂÂ condition…: If an optional collection of test-values is included, an expression that

results in a logical TRUE or FALSE. There must be one condition following each testvalues collection; therefore, this function will always have an odd number of arguments.
Usage Notes
ÂÂ For each of the test and condition value pairs, the corresponding (same position
within range or array) cell or value is compared to the condition. If all of the conditions
are met, the corresponding cell or value in sum-values is included in the sum.
ÂÂ All arrays must be of the same size.
Examples
The following table shows part of a ledger of deliveries of a certain commodity. Each load is weighed,
rated either 1 or 2, and the date of the delivery is noted.

=SUMIFS(A2:A13,B2:B13,”=1”,C2:C13,”>=12/13/2010”,C2:C13,”<=12/17/2010”) returns 23, the number of
tons of the commodity delivered during the week of December 17 that were rated “1.”
=SUMIFS(A2:A13,B2:B13,”=2”,C2:C13,”>=12/13/2010”,C2:C13,”<=12/17/2010”) returns 34, the number of
tons of the commodity delivered during the same week that were rated “2.”

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Related Topics
For related functions and additional information, see:
“AVERAGEIF” on page 233
“AVERAGEIFS” on page 234
“COUNTIF” on page 247
“COUNTIFS” on page 248
“SUMIF” on page 197
“Specifying Conditions and Using Wildcards” on page 360
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

SUMPRODUCT

The SUMPRODUCT function returns the sum of the products of corresponding
numbers in one or more ranges.
SUMPRODUCT(range, range…)
ÂÂ range:  A range of cells. range is a reference to a single range of cells containing

values of any type. If string or Boolean values are included in range, they are ignored.
ÂÂ range…: Optionally include one or more additional ranges of cells. The ranges must

all have the same dimensions.
Usage Notes
ÂÂ The SUMPRODUCT function multiplies the corresponding numbers in each range
and then sums each of the products. If only one range is specified, SUMPRODUCT
returns the sum of the range.
Examples
=SUMPRODUCT(3, 4) returns 12.
=SUMPRODUCT({1, 2}, {3, 4}) = 3 + 8 = 11.

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Related Topics
For related functions and additional information, see:
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

SUMSQ

The SUMSQ function returns the sum of the squares of a collection of numbers.
SUMSQ(num-value, num-value…)
ÂÂ num-value:  A number. num-value is a number value.
ÂÂ num-value…: Optionally include one or more additional numbers.

Usage Notes
ÂÂ The numbers can be in individual cells, or ranges of cells, or be included directly as
arguments to the function.
Examples
=SUMSQ(3, 4) returns 25.
=SUMSQ(A1:A4) adds the squares of the list of four numbers.
=SUMSQ(A1:D4) adds the squares of the 16 numbers in a square array of cells.
=SUMSQ(A1:A4, 100) adds the squares of the numbers in four cells plus 100.
=SQRT(SUMSQ(3, 4)) returns 5, using the Pythagorean theorem to find the length of the hypotenuse
of a triangle with sides 3 and 4.

Related Topics
For related functions and additional information, see:
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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SUMX2MY2

The SUMX2MY2 function returns the sum of the difference of the squares of
corresponding values in two collections.
SUMX2MY2(set-1-values, set-2-values)
ÂÂ set-1-values:  The first collection of values. set-1-values is a collection containing

number values.
ÂÂ set-2-values:  The second collection of values. set-2-values is a collection containing

number values.
Example
Given the following table:

=SUMX2MY2(A1:A6,B1:B6) returns –158, the sum of the differences of the squares of the values in
column A and the squares of the values in column B. The formula for the first such difference is A12 –
B12.

Related Topics
For related functions and additional information, see:
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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SUMX2PY2

The SUMX2PY2 function returns the sum of the squares of corresponding values in
two collections.
SUMX2PY2(set-1-values, set-2-values)
ÂÂ set-1-values:  The first collection of values. set-1-values is a collection containing

number values.
ÂÂ set-2-values:  The second collection of values. set-2-values is a collection containing

number values.
Example
Given the following table:

=SUMX2PY2(A1:A6,B1:B6) returns 640, the sum of the squares of the values in column A and the
squares of the values in column B. The formula for the first such sum is A12+ B12.

Related Topics
For related functions and additional information, see:
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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SUMXMY2

The SUMXMY2 function returns the sum of the squares of the differences between
corresponding values in two collections.
SUMXMY2(set-1-values, set-2-values)
ÂÂ set-1-values:  The first collection of values. set-1-values is a collection containing

number values.
ÂÂ set-2-values:  The second collection of values. set-2-values is a collection containing

number values.
Example
Given the following table:

=SUMXMY2(A1:A6,B1:B6) returns 196, the sum of the squares of the values in column A and the
squares of the values in column B. The formula for the first such sum is (A1 – B1)2.

Related Topics
For related functions and additional information, see:
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

TRUNC

The TRUNC function truncates a number to the specified number of digits.
TRUNC(number, digits)
ÂÂ number:  A number. number is a number value.
ÂÂ digits:  An optional value specifying the number of digits you want to retain, relative

to the decimal point. digits is a number value. A positive number represents digits
(decimal places) to the right of the decimal point to include. A negative number
specifies digits to the left of the decimal point to replace with zeros (the number of
zeros at the end of the number).
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Usage Notes
ÂÂ If digits is omitted, it is assumed to be 0.
Examples
=TRUNC(1.49, 0) returns 1.
=TRUNC(1.50, 0) returns 1.
=TRUNC(1.23456, 3) returns 1.234.
=TRUNC(1111.222, -2) returns 1100.
=TRUNC(-2.2, 0) returns -2.
=TRUNC(-2.8, 0) returns -2.

Related Topics
For related functions and additional information, see:
“CEILING” on page 170
“EVEN” on page 173
“FLOOR” on page 176
“INT” on page 178
“MROUND” on page 183
“ODD” on page 185
“ROUND” on page 191
“ROUNDDOWN” on page 192
“ROUNDUP” on page 193
“More on Rounding” on page 355
“Listing of Numeric Functions” on page 167
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 8    Numeric Functions

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9

Reference Functions

The reference functions help you find data within tables and
retrieve data from cells.
Listing of Reference Functions

iWork provides these reference functions for use with tables.

206

Function

Description

“ADDRESS” (page 207)

The ADDRESS function constructs a cell address
string from separate row, column, and table
identifiers.

“AREAS” (page 209)

The AREAS function returns the number of
ranges the function references.

“CHOOSE” (page 209)

The CHOOSE function returns a value from a
collection of values based on a specified index
value.

“COLUMN” (page 210)

The COLUMN function returns the column
number of the column containing a specified cell.

“COLUMNS” (page 211)

The COLUMNS function returns the number of
columns included in a specified range of cells.

“HLOOKUP” (page 211)

The HLOOKUP function returns a value from a
range of rows by using the top row of values to
pick a column and a row number to pick a row
within that column.

“HYPERLINK” (page 213)

The HYPERLINK function creates a clickable link
that opens a webpage or new email message.

“INDEX” (page 214)

The INDEX function returns the value in the cell
located at the intersection of the specified row
and column within a range of cells.

“INDIRECT” (page 216)

The INDIRECT function returns the contents of a
cell or range referenced by an address specified
as a string.

Function

Description

“LOOKUP” (page 217)

The LOOKUP function finds a match for a given
search value in one range, and then returns the
value in the cell with the same relative position in
a second range.

“MATCH” (page 218)

The MATCH function returns the position of a
value within a range.

“OFFSET” (page 219)

The OFFSET function returns a range of cells that
is the specified number of rows and columns
away from the specified base cell.

“ROW” (page 221)

The ROW function returns the row number of the
row containing a specified cell.

“ROWS” (page 221)

The ROWS function returns the number of rows
included in a specified range of cells.

“TRANSPOSE” (page 222)

The transpose function returns a vertical range of
cells as a horizontal range of cells, or vice versa.

“VLOOKUP” (page 223)

The VLOOKUP function returns a value from a
range of columns by using the left column of
values to pick a row and a column number to
pick a column in that row.

ADDRESS

The ADDRESS function constructs a cell address string from separate row, column, and
table identifiers.
ADDRESS(row, column, addr-type, addr-style, table)
ÂÂ row:  The row number of the address. row is a number value that must be in the

range 1 to 65,535.
ÂÂ column:  The column number of the address. column is a number value that must

be in the range 1 to 256.
ÂÂ addr-type:  An optional value specifying whether the row and column numbers are

relative or absolute.
all absolute (1 or omitted):  Row and column references are absolute.
row absolute, column relative (2):  Row references are absolute and column
references are relative.
row relative, column absolute (3):  Row references are relative and column
references are absolute.
all relative (4):  Row and column references are relative.
ÂÂ addr-style:  An optional value specifying the address style.

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A1 (TRUE, 1, or omitted):  The address format should use letters for columns and
numbers for rows.
R1C1 (FALSE):  The address format isn’t supported, returning an error.
ÂÂ table:  An optional value specifying the name of the table. table is a string value.

If the table is on another sheet, you must also include the name of the sheet. If
omitted, table is assumed to be the current table on the current sheet (that is, the
table where the ADDRESS function resides).
Usage Notes
ÂÂ An address style of R1C1 is not supported and this modal argument is provided only
for compatibility with other spreadsheet programs.
Examples
=ADDRESS(3, 5) creates the address $E$3.
=ADDRESS(3, 5, 2) creates the address E$3.
=ADDRESS(3, 5, 3) creates the address $E3.
=ADDRESS(3, 5, 4) creates the address E3.
=ADDRESS(3, 3, ,, “Sheet 2 ::  Table 1”) creates the address Sheet 2 ::  Table 1 ::  $C$3.

Related Topics
For related functions and additional information, see:
“Listing of Reference Functions” on page 206
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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AREAS

The AREAS function returns the number of ranges the function references.
AREAS(areas)
ÂÂ areas:  The areas the function should count. areas is a list value. It is either a single

range or more than one range separated by commas and enclosed in an additional
set of parentheses; for example, AREAS((B1:B5, C10:C12)).
Examples
=AREAS(A1:F8) returns 1.
=AREAS(C2:C8 B6:E6) returns 1.
=AREAS((A1:F8, A10:F18)) returns 2.
=AREAS((A1:C1, A3:C3, A5:C5)) returns 3.

Related Topics
For related functions and additional information, see:
“Listing of Reference Functions” on page 206
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

CHOOSE

The CHOOSE function returns a value from a collection of values based on a specified
index value.
CHOOSE(index, value, value…)
ÂÂ index:  The index of the value to be returned. index is a number value and must be

greater than 0.
ÂÂ value:  A value. value can contain any value type.
ÂÂ value…: Optionally include one or more additional values.
Examples
=CHOOSE(4, “Monday”, “Tuesday”, “Wednesday”, “Thursday”, “Friday”, “Saturday”, “Sunday”) returns
Thursday, the fourth value in the list.
=CHOOSE(3, “1st”, “second”, 7, “last”) returns 7, the third value in the list.

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Related Topics
For related functions and additional information, see:
“Listing of Reference Functions” on page 206
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

COLUMN

The COLUMN function returns the column number of the column containing a
specified cell.
COLUMN(cell)
ÂÂ cell:  An optional reference to a single table cell. cell is a reference value to a single

cell that can contain any value, or be empty. If cell is omitted, as in =COLUMN(), the
function returns the column number of the cell that contains the formula.
Examples
=COLUMN(B7) returns 2, the absolute column number of column B.
=COLUMN() returns the column number of the cell that contains the function.

Related Topics
For related functions and additional information, see:
“INDEX” on page 214
“ROW” on page 221
“Listing of Reference Functions” on page 206
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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COLUMNS

The COLUMNS function returns the number of columns included in a specified range
of cells.
COLUMNS(range)
ÂÂ range:  A range of cells. range is a reference to a single range of cells, which may

contain values of any type.
Usage Notes
ÂÂ If you select an entire table row for range, COLUMNS returns the total number of
columns in the row, which changes when you resize the table.
Examples
=COLUMNS(B3:D10) returns 3, the number of columns in the range (columns B, C, and D).
=COLUMNS(5:5) returns the total number of columns in row 5.

Related Topics
For related functions and additional information, see:
“ROWS” on page 221
“Listing of Reference Functions” on page 206
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

HLOOKUP

The HLOOKUP function returns a value from a range of rows by using the top row of
values to pick a column and a row number to pick a row within that column.
HLOOKUP(search-for, rows-range, return-row, close-match)
ÂÂ search-for:  The value to find. search-for can contain any value type.
ÂÂ rows-range:  A range of cells. range is a reference to a single range of cells which

may contain values of any type.
ÂÂ return-row:  The row number from which to return the value. return-row is a number

value and must be greater than or equal to 1 and less than or equal to the number
of rows in the specified range.
ÂÂ close-match:  An optional value that specifies whether an exact match is required.

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close match (TRUE, 1, or omitted):  If there’s no exact match, select the column with
the largest top-row value that is less than the search value. Wildcards can’t be used
in search-for.
exact match (FALSE or 0):  If there’s no exact match, return an error. Wildcards can
be used in search-for.
Usage Notes
ÂÂ HLOOKUP compares a search value to the values in the top row of a specified range.
Unless an exact match is required, the column containing the largest top-row value
that is less than the search value is selected. Then, the value from the specified row
in that column is returned by the function. If an exact match is required and none of
the top-row values match the search value, the function returns an error.
Examples
Given the following table:

=HLOOKUP(20, A1:E4, 2) returns “E.”
=HLOOKUP(39, A1:E4, 2) returns “E.”
=HLOOKUP(”M”, A2:E4, 2) returns “dolor.”
=HLOOKUP(”C”, A2:E3, 2) returns “lorem.”
=HLOOKUP(”blandit”, A3:E4, 2) returns “5.”
=HLOOKUP(”C”, A2:E4, 3, TRUE) returns “1.”
=HLOOKUP(”C”, A2:E4, 3, FALSE) returns an error because the value can’t be found (there is no exact
match).

Related Topics
For related functions and additional information, see:
“LOOKUP” on page 217
“MATCH” on page 218
“VLOOKUP” on page 223
“Specifying Conditions and Using Wildcards” on page 360
“Listing of Reference Functions” on page 206
“Value Types” on page 36

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“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

HYPERLINK

The HYPERLINK function creates a clickable link that opens a webpage or new email
message.
HYPERLINK(url, link-text)
ÂÂ url:  A standard universal resource locator. url is a string value that should contain a

properly formatted universal resource locator string.
ÂÂ link-text:  An optional value that specifies the text that appears as a clickable link in

the cell. link-text is a string value. If omitted, url is used as the link-text.
Examples
=HYPERLINK(”http://www.apple.com”, “Apple”) creates a link with the text Apple that opens the
default web browser to the Apple homepage.
=HYPERLINK(”mailto:janedoe@example.com?subject=Quote Request”, “Get Quote”) creates a link
with the text Get Quote that opens the default email application and addresses a new message to
janedoe@example.com with the subject line Quote Request.

Related Topics
For related functions and additional information, see:
“Listing of Reference Functions” on page 206
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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213

INDEX

The INDEX function returns the value in the cell located at the intersection of the
specified row and column within a range of cells or an array.
INDEX(range, row-index, column-index, area-index)
ÂÂ range:  A range of cells. range may contain values of any type. range is either a single

range or more than one range separated by commas and enclosed in an additional
set of parentheses. For example, ((B1:B5, C10:C12)).
ÂÂ row-index:  The row number of the value to be returned. row-index is a number

value and must be greater than or equal to 0 and less than or equal to the number
of rows in range.
ÂÂ column-index:  An optional value specifying the column number of the value to be

returned. column-index is a number value and must be greater than or equal to 0
and less than or equal to the number of columns in range.
ÂÂ area-index:  An optional value specifying the area number of the value to be

returned. area-index is a number value and must be greater than or equal to 1 and
less than or equal to the number of areas in range. If omitted, 1 is used.
Usage Notes
ÂÂ INDEX can return the value at the specified intersection of a two-dimensional range
of values. For example, assume that cells B2:E7 contain the values. =INDEX(B2:D7, 2,
3) returns the value found at the intersection of the second row and third column
(the value in cell D3).
ÂÂ More than one area can be specified by enclosing the ranges in an additional pair

of parentheses. For example, =INDEX((B2:D5,B7:D10), 2, 3, 2) returns the value at the
intersection of the second column and the third row in the second area (the value in
cell D8).
ÂÂ INDEX can return a one-row or one-column array for another function. In this

form, either row-index or column-index is required, but the other argument may be
omitted. For example =SUM(INDEX(B2:D5, , 3)) returns the sum of the values in the
third column (cells D2 through D5). Similarly, =AVERAGE(INDEX(B2:D5, 2)) returns the
average of the values in the second row (cells B3 through D3).
ÂÂ INDEX can return (or “read”) the value from an array returned by an array

function (a function that returns an array of values, rather than a single value).
The FREQUENCY function returns an array of values, based on specified intervals.
=INDEX(FREQUENCY($A$1:$F$5, $B$8:$E$8), 1) would turn the first value in the array
returned by the given FREQUENCY function. Similarly =INDEX(FREQUENCY($A$1:$F$5,
$B$8:$E$8), 5) would return the fifth value in the array.
ÂÂ The location in the range or array is specified by indicating the number of rows

down and the number of columns to the right in relation to the cell in the upperleft corner of the range or array.

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ÂÂ Except when INDEX is specified as shown in the third case above, row-index can’t be

omitted, and if column-index is omitted, it is assumed to be 1.
Examples
Given the following table:

=INDEX(B2:D5,2,3) returns 22, the value in the second row and third column (cell D3).
=INDEX((B2:D5,B7:D10), 2, 3, 2) returns “f”, the value in the second row and third column of the second
area (cell D8).
=SUM(INDEX(B2:D5, , 3)) returns 90, the sum of the values in the third column (cells D2 through D5).
=AVERAGE(INDEX(B2:D5,2)) returns 12, the average of the values in the second row (cells B3 through D3).

Related Topics
For related functions and additional information, see:
“COLUMN” on page 210
“INDIRECT” on page 216
“OFFSET” on page 219
“ROW” on page 221
“Listing of Reference Functions” on page 206
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 9    Reference Functions

215

INDIRECT

The INDIRECT function returns the contents of a cell or range referenced by an address
specified as a string.
INDIRECT(addr-string, addr-style)
ÂÂ addr-string:  A string representing a cell address. addr-string is a string value.
ÂÂ addr-style:  An optional value specifying the address style.

A1 (TRUE, 1, or omitted):  The address format should use letters for columns and
numbers for rows.
R1C1 (FALSE):  The address format isn’t supported, returning an error.
Usage Notes
ÂÂ The given address can be a range reference, that is, “A1:C5”, not just a reference
to a single cell. If used this way, INDIRECT returns an array that can be used as
an argument to another function or directly read using the INDEX function. For
example, =SUM(INDIRECT(A1:C5, 1)) returns the sum of the values in the cells
referenced by the addresses in cells A1 through C5.
ÂÂ An address style of R1C1 is not supported and this modal argument is provided only

for compatibility with other spreadsheet programs.
Example
If cell A1 contains 99 and A20 contains A1:
=INDIRECT(A20) returns 99, the contents of cell A1.

Related Topics
For related functions and additional information, see:
“INDEX” on page 214
“Listing of Reference Functions” on page 206
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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LOOKUP

The LOOKUP function finds a match for a given search value in one range, and then
returns the value in the cell with the same relative position in a second range.
LOOKUP(search-for, search-where, result-values)
ÂÂ search-for:  The value to find. search-value can contain any value type.
ÂÂ search-where:  The collection containing the values to be searched. search-where is

a collection containing any value type.
ÂÂ result-values:  An optional collection containing the value to be returned based on

the search. result-values is a collection containing any value type.
Usage Notes
ÂÂ Both search-where and result-values are normally included and are specified as either
multiple columns or multiple rows, but not both (one dimensional). However, for
compatibility with other spreadsheet applications, search-where can be specified as
both multiple columns and multiple rows (two dimensional) and result-values can
be omitted.
ÂÂ If search-where is two dimensional and result-values is specified, the topmost row or

leftmost column, whichever contains more cells, is searched and the corresponding
value from result-values is returned.
ÂÂ If search-where is two dimensional and result-values is omitted, the corresponding

value in the last row (if the number of columns included in the range is larger) or
column (if the number of rows included in the range is larger) is returned.
Examples
Given the following table:

=LOOKUP(”C”, A1:F1, A2:F2) returns 30.
=LOOKUP(40, A2:F2, A1:F1) returns D.
=LOOKUP(”B”, A1:C1, D2:F2) returns 50.
=LOOKUP(”D”,A1:F2) returns 40, the value in the last row that corresponds to “D.”

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Related Topics
For related functions and additional information, see:
“HLOOKUP” on page 211
“MATCH” on page 218
“VLOOKUP” on page 223
“Listing of Reference Functions” on page 206
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

MATCH

The MATCH function returns the position of a value within a range.
MATCH(search-for, search-where, matching-method)
ÂÂ search-for:  The value to find. search-for can contain any value type.
ÂÂ search-where:  The collection containing the values to be searched. search-where is

a collection containing any value type.
ÂÂ matching-method:  An optional value specifying how value matching is performed.

find largest value (1 or omitted): Find the cell with the largest value less than or
equal to search-for. Wildcards can’t be used in search-for.
find value (0): Find the first cell with a value that exactly matches search-for.
Wildcards can be used in search-for.
find smallest value (–1): Find the cell with the smallest value greater than or equal
to search-for. Wildcards can’t be used in search-for.
Usage Notes
ÂÂ MATCH works only on a range that is part of a single row or column; you can’t use it
to search a two-dimensional collection.
ÂÂ Cell numbering starts with 1 at the top or left cell for vertical and horizontal ranges,

respectively. Searches are performed top-to-bottom or left-to-right.
ÂÂ When searching for text, case is ignored.

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Examples
Given the following table:

=MATCH(40, A1:A5) returns 4.
=MATCH(40, E1:E5) returns 1.
=MATCH(35, E1:E5, 1) returns 3 (30 is the largest value less than or equal to 35).
=MATCH(35, E1:E5, -1) returns 1 (40 is the smallest value greater than or equal to 35).
=MATCH(35, E1:E5, 0) displays an error (no exact match can be found).
=MATCH(”lorem”, C1:C5) returns 1 (“lorem” appears in the first cell of the range).
=MATCH(”*x”,C1:C5,0) returns 3 (“lorex”, which ends with an “x”, appears in the third cell of the range).

Related Topics
For related functions and additional information, see:
“LOOKUP” on page 217
“Specifying Conditions and Using Wildcards” on page 360
“Listing of Reference Functions” on page 206
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

OFFSET

The OFFSET function returns a range of cells that is the specified number of rows and
columns away from the specified base cell.
OFFSET(base, row-offset, column-offset, rows, columns)
ÂÂ base:  The address of the cell from which the offsets are measured. base is a

reference value.
ÂÂ row-offset: The number of rows from the base cell to the target cell. row-offset is a

number value. 0 means the target cell is in the same row as the base cell. A negative
number means the target is in a row above the base.
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ÂÂ column-offset: The number of columns from the base cell to the target cell. column-

offset is a number value. 0 means the target cell is in the same column as the base
cell. A negative number means the target is in a column to the left of the base.
ÂÂ rows:  An optional value specifying the number of rows to return starting with the

offset location.rows is a number value.
ÂÂ columns:  An optional value specifying the number of columns to return starting

with the offset location.columns is a number value.
Usage Notes
ÂÂ OFFSET can return an array for use with another function. For example, assume you
have entered into A1, A2, and A3, the base cell, the number of rows, and the number
of columns, respectively, that you wish to have summed. The sum could be found
using =SUM(OFFSET(INDIRECT(A1),0,0,A2,A3)).
Examples
=OFFSET(A1, 5, 5) returns the value in cell F6, the cell five columns to the right and five rows below
cell A1.
=OFFSET(G33, 0, -1) returns the value in the cell to the left of G33, the value in F33.
=SUM(OFFSET(A7, 2, 3, 5, 5)) returns the sum of the values in cells D9 through H13, the five rows and
five columns that begin two rows to the right of and three columns below cell A7.
Assume that you have entered 1 in cell D7, 2 in cell D8, 3 in cell D9, 4 in cell E7, 5 in cell E8, and 6 in
cell E9.
=OFFSET(D7,0,0,3,1) entered in cell B6 returns an error, since the 3 rows and 1 column returned (the
range D7:D9) does not have one single intersection with B6 (it has none).
=OFFSET(D7,0,0,3,1) entered in cell D4 returns an error, since the 3 rows and 1 column returned (the
range D7:D9) does not have one single intersection with B6 (it has three).
=OFFSET(D7,0,0,3,1) entered in cell B8 returns 2, since the 3 rows and 1 column returned (the range
D7:D9) has one single intersection with B8 (cell D8, which contains 2).
=OFFSET(D7:D9,0,1,3,1) entered in cell B7 returns 4, since the 3 rows and 1 column returned (the
range E7:E9) has one single intersection with B7 (cell E7, which contains 4).

Related Topics
For related functions and additional information, see:
“COLUMN” on page 210
“ROW” on page 221
“Listing of Reference Functions” on page 206
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41
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ROW

The ROW function returns the row number of the row containing a specified cell.
ROW(cell)
ÂÂ cell:  An optional reference to a single table cell. cell is a reference value to a single

cell that can contain any value, or be empty. If cell is omitted, as in =ROW(), the
function returns the row number of the cell that contains the formula.
Examples
=ROW(B7) returns 7, the number of row 7.
=ROW() returns the absolute row number of the cell containing the function.

Related Topics
For related functions and additional information, see:
“COLUMN” on page 210
“INDEX” on page 214
“Listing of Reference Functions” on page 206
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

ROWS

The ROWS function returns the number of rows included in a specified range of cells.
ROWS(range)
ÂÂ range:  A range of cells. range is a reference to a single range of cells, which may

contain values of any type.
Usage Notes
ÂÂ If you select an entire table column for range, ROWS returns the total number of
rows in the column, which changes when you resize the table.
Examples
=ROWS(A11:D20) returns 10, the number of rows from 11 through 20.
=ROWS(D:D) returns the total number of rows in column D.

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Related Topics
For related functions and additional information, see:
“COLUMNS” on page 211
“Listing of Reference Functions” on page 206
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

TRANSPOSE

The transpose function returns a vertical range of cells as a horizontal range of cells,
or vice versa.
TRANSPOSE(range-array)
ÂÂ range-array:  The collection containing the values to be transposed. range-array is a

collection containing any type of value.
Usage Notes
ÂÂ TRANSPOSE returns an array containing the transposed values. This array will
contain a number of rows equal to the number of columns in the original range and
a number of columns equal to the number of rows in the original range. The values
in this array can be determined (“read”) using the INDEX function.
Examples
Given the following table:
row/column

A

B

C

D

E

1

5

15

10

9

7

2

11

96

29

11

23

3

37

56

23

1

12

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=INDEX(TRANSPOSE($A$1:$E$3),1,1) returns 5, the value in row 1. column 1 of the transposed range
(was row 1, column A, of the original array).
=INDEX(TRANSPOSE($A$1:$E$3),1,2) returns 11, the value in row 1, column 2 of the transposed range
(was row 2, column A, of the original range).
=INDEX(TRANSPOSE($A$1:$E$3),1,3) returns 37, the value in row 1, column 3 of the transposed range
(was row 3, column A, of the original range).
=INDEX(TRANSPOSE($A$1:$E$3),2,1 returns 15, the value in row 2, column 1 of the transposed range
(was row 1, column 2, of the original range).
=INDEX(TRANSPOSE($A$1:$E$3),3,2) returns 29, the value in row 3, column 2 of the transposed range
(was row 2, column C, of the original range).
=INDEX(TRANSPOSE($A$1:$E$3),4,3) returns 1, the value in row 4, column 3 of the transposed range
(was row 3, column D, of the original range).

Related Topics
For related functions and additional information, see:
“Listing of Reference Functions” on page 206
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

VLOOKUP

The VLOOKUP function returns a value from a range of columns by using the left
column of values to pick a row and a column number to pick a column in that row.
VLOOKUP(search-for, columns-range, return-column, close-match)
ÂÂ search-for:  The value to find. search-value can contain any value type.
ÂÂ columns-range:  A range of cells. range is a reference to a single range of cells,

which may contain values of any type.
ÂÂ return-column:  A number that specifies the relative column number of the cell

from which to return the value. return-column is a number value. The leftmost
column in the range is column 1.
ÂÂ close-match:  An optional value that determines whether an exact match is required.

close match (TRUE, 1, or omitted):  If there’s no exact match, select the column with
the largest top-row value that is less than the search value. Wildcards can’t be used
in search-for.
exact match (FALSE or 0):  If there’s no exact match, return an error. Wildcards can
be used in search-for.
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Usage Notes
ÂÂ VLOOKUP compares a search value to the values in the leftmost column of a
specified range. Unless an exact match is required, the row containing the largest
left-column value that is less than the search value is selected. Then, the value from
the specified column in that row is returned by the function. If an exact match
is required and none of the leftmost-column values match the search value, the
function returns an error.
Examples
Given the following table:

=VLOOKUP(20, B2:E6, 2) returns E.
=VLOOKUP(21, B2:E6, 2) returns E.
=VLOOKUP(”M”, C2:E6, 2) returns dolor.
=VLOOKUP(”blandit”, D2:E6, 2) returns 5.
=VLOOKUP(21, B2:E6, 2, FALSE) returns an error because no value in the left column exactly matches 21.

Related Topics
For related functions and additional information, see:
“HLOOKUP” on page 211
“LOOKUP” on page 217
“MATCH” on page 218
“Specifying Conditions and Using Wildcards” on page 360
“Listing of Reference Functions” on page 206
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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10

Statistical Functions

The statistical functions help you manipulate and analyze
collections of data using a variety of measures and statistical
techniques.
Listing of Statistical Functions

iWork provides these statistical functions for use with tables.
Function

Description

“AVEDEV” (page 230)

The AVEDEV function returns the average of the
difference of a collection of numbers from their
average (arithmetic mean).

“AVERAGE” (page 231)

The AVERAGE function returns the average
(arithmetic mean) of a collection of numbers.

“AVERAGEA” (page 232)

The AVERAGEA function returns the average
(arithmetic mean) of a collection of values,
including text and Boolean values.

“AVERAGEIF” (page 233)

The AVERAGEIF function returns the average
(arithmetic mean) of the cells in a range that
meet a given condition.

“AVERAGEIFS” (page 234)

The AVERAGEIFS function returns the average
(arithmetic mean) of the cells in a collection that
meet all the given conditions.

“BETADIST” (page 236)

The BETADIST function returns the cumulative
beta distribution probability value.

		

225

226		

Function

Description

“BETAINV” (page 237)

The BETAINV function returns the inverse of the
given cumulative beta distribution probability
value.

“BINOMDIST” (page 238)

The BINOMDIST function returns the individual
term binomial distribution probability of the
specified form.

“CHIDIST” (page 239)

The CHIDIST function returns the one-tailed
probability of the chi-square distribution.

“CHIINV” (page 239)

The CHIINV function returns the inverse of
the one-tailed probability of the chi-square
distribution.

“CHITEST” (page 240)

The CHITEST function returns the value from the
chi-square distribution for the given data.

“CONFIDENCE” (page 242)

The CONFIDENCE function returns a value for
creating a statistical confidence interval for a
sample from a population with a known standard
deviation.

“CORREL” (page 242)

The CORREL function returns the correlation
between two collections using linear regression
analysis.

“COUNT” (page 244)

The COUNT function returns the number of
its arguments that contain numbers, numeric
expressions, or dates.

“COUNTA” (page 245)

The COUNTA function returns the number of its
arguments that are not empty.

“COUNTBLANK” (page 246)

The COUNTBLANK function returns the number
of cells in a range that are empty.

“COUNTIF” (page 247)

The COUNTIF function returns the number of
cells in a range that satisfy a given condition.

“COUNTIFS” (page 248)

The COUNTIFS function returns the number of
cells in one or more ranges that satisfy given
conditions (one condition per range).

“COVAR” (page 250)

The COVAR function returns the covariance of
two collections.

“CRITBINOM” (page 252)

The CRITBINOM function returns the smallest
value for which the cumulative binomial
distribution is greater than or equal to a given
value.

“DEVSQ” (page 253)

The DEVSQ function returns the sum of the
squares of deviations of a collection of numbers
from their average (arithmetic mean).

Chapter 10    Statistical Functions

Function

Description

“EXPONDIST” (page 253)

The EXPONDIST function returns the exponential
distribution of the specified form.

“FDIST” (page 254)

The FDIST function returns the F probability
distribution.

“FINV” (page 255)

The FINV function returns the inverse of the F
probability distribution.

“FORECAST” (page 256)

The FORECAST function returns the forecasted y
value for a given x value based on sample values
using linear regression analysis.

“FREQUENCY” (page 257)

The FREQUENCY function returns an array of how
often data values occur within a range of interval
values.

“GAMMADIST” (page 259)

The GAMMADIST function returns the gamma
distribution in the specified form.

“GAMMAINV” (page 260)

The GAMMAINV function returns the inverse
gamma cumulative distribution.

“GAMMALN” (page 260)

The GAMMALN function returns the natural
logarithm of the gamma function, G(x).

“GEOMEAN” (page 261)

The GEOMEAN function returns the geometric
mean.

“HARMEAN” (page 262)

The HARMEAN function returns the harmonic
mean.

“INTERCEPT” (page 262)

The INTERCEPT function returns the y-intercept
of the best-fit line for the collection using linear
regression analysis.

“LARGE” (page 264)

The LARGE function returns the nth-largest value
within a collection. The largest value is ranked
number 1.

“LINEST” (page 265)

The LINEST function returns an array of the
statistics for a straight line that best fits the given
data using the least squares method.

“LOGINV” (page 268)

The LOGINV function returns the inverse of the
log-normal cumulative distribution function of x.

“LOGNORMDIST” (page 269)

The LOGNORMDIST function returns the lognormal distribution.

“MAX” (page 270)

The MAX function returns the largest number in
a collection.

Chapter 10    Statistical Functions

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228		

Function

Description

“MAXA” (page 270)

The MAXA function returns the largest number in
a collection of values that may include text and
Boolean values.

“MEDIAN” (page 271)

The MEDIAN function returns the median value in
a collection of numbers. The median is the value
where half the numbers in the collection are less
than the median and half are greater.

“MIN” (page 272)

The MIN function returns the smallest number in
a collection.

“MINA” (page 273)

The MINA function returns the smallest number
in a collection of values that may include text and
Boolean values.

“MODE” (page 274)

The MODE function returns the most frequently
occurring value in a collection of numbers.

“NEGBINOMDIST” (page 275)

The NEGBINOMDIST function returns the
negative binomial distribution.

“NORMDIST” (page 276)

The NORMDIST function returns the normal
distribution of the specified function form.

“NORMINV” (page 277)

The NORMINV function returns the inverse of the
cumulative normal distribution.

“NORMSDIST” (page 277)

The NORMSDIST function returns the standard
normal distribution.

“NORMSINV” (page 278)

The NORMSINV function returns the inverse of
the cumulative standard normal distribution.

“PERCENTILE” (page 279)

The PERCENTILE function returns the value within
a collection that corresponds to a particular
percentile.

“PERCENTRANK” (page 280)

The PERCENTRANK function returns the rank of
a value in a collection as a percentage of the
collection.

“PERMUT” (page 281)

The PERMUT function returns the number of
permutations for a given number of objects that
can be selected from a total number of objects.

“POISSON” (page 282)

The POISSON function returns the probability
that a specific number of events will occur using
the Poisson distribution.

“PROB” (page 282)

The PROB function returns the probability of a
range of values if you know the probabilities of
the individual values.

Chapter 10    Statistical Functions

Function

Description

“QUARTILE” (page 284)

The QUARTILE function returns the value for the
specified quartile of a given collection.

“RANK” (page 285)

The RANK function returns the rank of a number
within a range of numbers.

“SLOPE” (page 287)

The SLOPE function returns the slope of the bestfit line for the collection using linear regression
analysis.

“SMALL” (page 288)

The SMALL function returns the nth-smallest
value within a range. The smallest value is ranked
number 1.

“STANDARDIZE” (page 289)

The STANDARDIZE function returns a normalized
value from a distribution characterized by a given
mean and standard deviation.

“STDEV” (page 290)

The STDEV function returns the standard
deviation, a measure of dispersion, of a collection
of values based on their sample (unbiased)
variance.

“STDEVA” (page 291)

The STDEVA function returns the standard
deviation, a measure of dispersion, of a collection
of values that may include text and Boolean
values, based on the sample (unbiased) variance.

“STDEVP” (page 293)

The STDEVP function returns the standard
deviation, a measure of dispersion, of a collection
of values based on their population (true)
variance.

“STDEVPA” (page 294)

The STDEVPA function returns the standard
deviation, a measure of dispersion, of a collection
of values that may include text and Boolean
values, based on the population (true) variance.

“TDIST” (page 296)

The TDIST function returns the probability from
the Student’s t-distribution.

“TINV” (page 297)

The TINV functions returns the t value (a function
of the probability and degrees of freedom) from
the Student’s t-distribution.

“TTEST” (page 297)

The TTEST function returns the probability
associated with a Student’s t-test, based on the
t-distribution function.

“VAR” (page 298)

The VAR function returns the sample (unbiased)
variance, a measure of dispersion, of a collection
of values.

Chapter 10    Statistical Functions

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Function

Description

“VARA” (page 300)

The VARA function returns the sample (unbiased)
variance, a measure of dispersion, of a collection
of values, including text and Boolean values.

“VARP” (page 302)

The VARP function returns the population (true)
variance, a measure of dispersion, of a collection
of values.

“VARPA” (page 303)

The VARPA function returns the sample (unbiased)
variance, a measure of dispersion, of a collection
of values, including text and Boolean values.

“ZTEST” (page 305)

The ZTEST function returns the one-tailed
probability value of the Z-test.

AVEDEV

The AVERAGE function returns the average (arithmetic mean) of a collection of numbers.
AVEDEV(num-date-dur, num-date-dur…)
ÂÂ num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a

duration value.
ÂÂ num-date-dur…: Optionally include one or more additional values. If more than

one num-date-dur value is specified, all must be of the same type.
Usage Notes
ÂÂ AVEDEV divides the sum of the numbers by the number of numbers to get the
average. The difference (absolute value) between the average and each number is
summed and divided by the number of numbers.
ÂÂ If num-date-dur contains date/time values, a duration value is returned.
Examples
=AVEDEV(2, 2, 2, 4, 4, 4) returns 1.
=AVEDEV(2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4) returns 0.6666667.

Related Topics
For related functions and additional information, see:
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41
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AVERAGE

The AVERAGE function returns the average (arithmetic mean) of a collection of
numbers.
AVERAGE(num-date-dur, num-date-dur…)
ÂÂ num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a

duration value.
ÂÂ num-date-dur…: Optionally include one or more additional values. If more than

one num-date-dur value is specified, all must be of the same type.
Usage Notes
ÂÂ AVERAGE divides the sum of the numbers by the number of numbers.
ÂÂ A string or Boolean value included in a referenced cell is ignored. If you wish to

include string and Boolean values in the average, use the AVERAGEA function.
ÂÂ A reference included as an argument to the function can be either to a single cell or

to a range of cells.
Examples
=AVERAGE(4, 4, 4, 6, 6, 6) returns 5.
=AVERAGE(2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4) returns 3.

Related Topics
For related functions and additional information, see:
“AVERAGEA” on page 232
“AVERAGEIF” on page 233
“AVERAGEIFS” on page 234
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 10    Statistical Functions

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AVERAGEA

The AVERAGEA function returns the average (arithmetic mean) of a collection of
values, including text and Boolean values.
AVERAGEA(value, value…)
ÂÂ value:  A value. value can contain any value type.
ÂÂ value…: Optionally include one or more additional values. All numeric values must

be of the same type. You cannot mix numbers, dates, and duration values.
Usage Notes
ÂÂ A string value included in a referenced cell is given a value of 0. A Boolean FALSE is
assigned a value of 0 and a Boolean TRUE is assigned a value of 1.
ÂÂ A reference included as an argument to the function can be either to a single cell or

to a range of cells.
ÂÂ For a collection containing only numbers, AVERAGEA returns the same result as the

AVERAGE function, which ignores cells that don’t contain numbers.
Examples
=AVERAGEA(A1:A4) returns 2.5 if cells A1 through A4 contain 4, a, 6, b. The text values are counted
as zeros in the sum of 10 and included in the count of values (4). Compare with =AVERAGE(A1:A4),
which ignores the text values completely for a sum of 10, a count of 2, and an average of 5.
=AVERAGEA(A1:A4) returns 4 if cells A1 through A4 contain 5, a, TRUE, 10. The text value counts zero
and TRUE counts 1 for a sum of 16 and a count of 4.
=AVERAGEA(A1:A4) returns 0.25 if cells A1 through A4 contain FALSE, FALSE, FALSE, TRUE. Each FALSE
counts zero and TRUE counts 1 for a sum of 1 and a count of 4.

Related Topics
For related functions and additional information, see:
“AVERAGE” on page 231
“AVERAGEIF” on page 233
“AVERAGEIFS” on page 234
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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AVERAGEIF

The AVERAGEIF function returns the average (arithmetic mean) of the cells in a range
that meet a given condition.
AVERAGEIF(test-values, condition, avg-values)
ÂÂ test-values:  A collection containing values to be tested. test-values is a collection

containing any type of value.
ÂÂ condition:  An expression that results in a logical TRUE or FALSE. condition is an

expression that can contain anything as long as the result from comparing condition
to a value in test-values can be expressed as a Boolean value of TRUE or FALSE.
ÂÂ avg-values:  An optional collection containing the values to be averaged. avg-values

is a reference to a single range of cells or an array, which may contain only numbers,
numeric expressions, or Boolean values.
Usage Notes
ÂÂ Each value is compared to condition. If the value meets the conditional test, the
corresponding value in avg-values is included in the average.
ÂÂ avg-values and test-values (if specified) must be the same size.
ÂÂ If avg-values is omitted, test-values is used for avg-values.
ÂÂ If avg-values is omitted or is the same as test-values, test-values can contain only

numbers, numeric expressions, or Boolean values.
Examples
Given the following table:

=AVERAGEIF(A2:A13, “<40”, D2:D13) returns approximately 57429, the average income of people under
the age of forty.
=AVERAGEIF(B2:B13, “=F”, D2:D13) returns 62200, the average income of females (indicated by an “F” in
column B).
=AVERAGEIF(C2:C13, “S”, D2:D13) returns 55800, the average income of people who are single
(indicated by an “S” in column C).
=AVERAGEIF(A2:A13, “>=40”, D2:D13) returns 75200, the average income of people who are forty or older.
Chapter 10    Statistical Functions

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Related Topics
For related functions and additional information, see:
“AVERAGE” on page 231
“AVERAGEA” on page 232
“AVERAGEIFS” on page 234
“Specifying Conditions and Using Wildcards” on page 360
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

AVERAGEIFS

The AVERAGEIFS function returns the average (arithmetic mean) of the cells in a given
range where one or more ranges meet one or more related conditions.
AVERAGEIFS(avg-values, test-values, condition, test-values…, condition…)
ÂÂ avg-values:  A collection containing the values to be averaged. avg-values is a

reference to a single range of cells or an array, which may contain only numbers,
numeric expressions, or Boolean values.
ÂÂ test-values:  A collection containing values to be tested. test-values is a collection

containing any type of value.
ÂÂ condition:  An expression that results in a logical TRUE or FALSE. condition is an

expression that can contain anything as long as the result from comparing condition
to a value in test-values can be expressed as a Boolean value of TRUE or FALSE.
ÂÂ test-values…: Optionally include one or more additional collections containing

values to be tested. Each test-values collection must be followed immediately with a
condition expression. This pattern of test-values, condition can be repeated as many
times as needed.
ÂÂ condition…: If an optional collection of test-values is included, an expression that

results in a logical TRUE or FALSE. There must be one condition following each
test-values collection; therefore, this function will always have an odd number of
arguments.

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Usage Notes
ÂÂ For each of the test-values and condition pairs, the corresponding (same position

within range or array) value is compared to the conditional test. If all of the conditional
tests are met, the corresponding value in avg-values is included in the average.
ÂÂ avg-values and all test-values collections must be the same size.
Examples
Given the following table:

=AVERAGEIFS(D2:D13,A2:A13,”<40”,B2:B13,”=M”) returns 56000, the average income of males
(indicated by an “M” in column B) under the age of forty.
=AVERAGEIFS(D2:D13,A2:A13,”<40”,B2:B13,”=M”,C2:C13,”=S”) returns 57000, the average income of
males who are single (indicated by an “S” in column C) under the age of forty.
=AVERAGEIFS(D2:D13,A2:A13,”<40”,B2:B13,”=M”,C2:C13,”=M”) returns 55000, the average income of
males who are married (indicated by an “M” in column C) under the age of forty.
=AVERAGEIFS(D2:D13,A2:A13,”<40”,B2:B13,”=F”) returns approximately 59333, the average income of
females (indicated by an “F” in column B) who are under the age of forty.

Related Topics
For related functions and additional information, see:
“AVERAGE” on page 231
“AVERAGEA” on page 232
“AVERAGEIF” on page 233
“Specifying Conditions and Using Wildcards” on page 360
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15

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235

“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

BETADIST

The BETADIST function returns the cumulative beta distribution probability value.
BETADIST(x-value, alpha, beta, x-lower, x-upper)
ÂÂ x-value:  The x value at which you want to evaluate the function. x-value is a number

value and must be in the range 0 to 1.
ÂÂ alpha:  One of the shape parameters of the distribution. alpha is a number value

and must be greater than 0.
ÂÂ beta:  One of the shape parameters of the distribution. beta is a number value and

must be greater than 0.
ÂÂ x-lower:  An optional lower limit or bound for the specified x value or probability.

x-lower is a number value and must be less than or equal to the specified x value or
probability. If omitted, 0 is used.
ÂÂ x-upper:  An optional upper limit or bound for the specified x value or probability.

x-upper is a number value and must be greater than or equal to the specified x value
or probability. If omitted, 1 is used.
Examples
=BETADIST(0.5, 1, 2, 0.3, 2) returns 0.221453287197232.
=BETADIST(1, 1, 2, 0, 1) returns 1.
=BETADIST(0.1, 2, 2, 0, 2) returns 0.00725.

Related Topics
For related functions and additional information, see:
“BETAINV” on page 237
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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BETAINV

The BETAINV function returns the inverse of the given cumulative beta distribution
probability value.
BETAINV(probability, alpha, beta, x-lower, x-upper)
ÂÂ probability:  A probability associated with the distribution. probability is a number

value and must be greater than 0 and less than 1.
ÂÂ alpha:  One of the shape parameters of the distribution. alpha is a number value

and must be greater than 0.
ÂÂ beta:  One of the shape parameters of the distribution. beta is a number value and

must be greater than 0.
ÂÂ x-lower:  An optional lower limit or bound for the specified x value or probability.

x-lower is a number value and must be less than or equal to the specified x value or
probability. If omitted, 0 is used.
ÂÂ x-upper:  An optional upper limit or bound for the specified x value or probability.

x-upper is a number value and must be greater than or equal to the specified x value
or probability. If omitted, 1 is used.
Examples
=BETAINV(0.5, 1, 2, 0.3, 2) returns 0.797918471982869.
=BETAINV(0.99, 1, 2, 0, 1) returns 0.9.
=BETAINV(0.1, 2, 2, 0, 2) returns 0.391600211318183.

Related Topics
For related functions and additional information, see:
“BETADIST” on page 236
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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BINOMDIST

The BINOMDIST function returns the individual term binomial distribution probability
of the specified form.
BINOMDIST(success-num, trials, prob-success, form-type)
ÂÂ success-num:  The number of successful trials or tests. success-num is a number

value that must be greater than or equal to 1 and less than or equal to trials.
ÂÂ trials:  The total number of trials or tests. trials is a number value that must be

greater than or equal to 0.
ÂÂ prob-success:  The probability of success for each trial or test. prob-success is a

number value that must be greater than or equal to 0 and less than or equal to 1.
ÂÂ form-type:  A value that indicates which form of the exponential function to provide.

cumulative form (TRUE or 1):  Return the value of the cumulative distribution
function form (that the specified number or fewer successes or events will occur).
probability mass form (FALSE or 0):  Return the value of the probability mass
function form (that there are exactly the specified number of successes or events).
Usage Notes
ÂÂ The BINOMDIST is appropriate for problems with a fixed number of independent
trials that have a constant probability of success and where the outcomes of a trial
are only success or failure.
Examples
=BINOMDIST(3, 98, 0.04, 1) returns 0.445507210083272 (cumulative distribution form).
=BINOMDIST(3, 98, 0.04, 0) returns 0.201402522366024 (probability mass form).

Related Topics
For related functions and additional information, see:
“CRITBINOM” on page 252
“NEGBINOMDIST” on page 275
“PERMUT” on page 281
“PROB” on page 282
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41
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CHIDIST

The CHIDIST function returns the one-tailed probability of the chi-square distribution.
CHIDIST(non-neg-x-value, degrees-freedom)
ÂÂ non-neg-x-value:  The value at which you want to evaluate the function. non-neg-x-

value is a number value that must be greater than or equal to 0.
ÂÂ degrees-freedom:  Degrees of freedom. degrees-freedom is a number value and

must be greater than or equal to 1.
Examples
=CHIDIST(5, 2) returns 0.0820849986238988.
=CHIDIST(10, 10) returns 0.440493285065212.
=CHIDIST(5, 1) returns 0.0253473186774683.

Related Topics
For related functions and additional information, see:
“CHIINV” on page 239
“CHITEST” on page 240
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

CHIINV

The CHIINV function returns the inverse of the one-tailed probability of the chi-square
distribution.
CHIINV(probability, degrees-freedom)
ÂÂ probability:  A probability associated with the distribution. probability is a number

value and must be greater than 0 and less than 1.
ÂÂ degrees-freedom:  Degrees of freedom. degrees-freedom is a number value and

must be greater than or equal to 1.

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Examples
=CHIINV(0.5, 2) returns 1.38629436111989.
=CHIINV(0.1, 10) returns 15.9871791721053.
=CHIINV(0.5, 1) returns 0.454936423119572.

Related Topics
For related functions and additional information, see:
“CHIDIST” on page 239
“CHITEST” on page 240
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

CHITEST

The CHITEST function returns the value from the chi-square distribution for the given
data.
CHITEST(actual-values, expected-values)
ÂÂ actual-values:  The collection containing the actual values. actual-values is a

collection containing number values.
ÂÂ expected-values:  The collection containing the expected values. expected-values is

a collection containing number values.
Usage Notes
ÂÂ The degrees of freedom relating to the value returned is the number of rows in
actual-values minus 1.
ÂÂ Each expected value is computed by multiplying the sum of the row by the sum of

the column and dividing by the grand total.

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Example
Given the following table:

=CHITEST(A2:B6,A9:B13) returns 5.91020074984668E-236.
Each expected value is computed by multiplying the sum of the row by the sum of the
column and dividing by the grand total. The formula for the first expected value (cell A9) is
=SUM(A$2:B$2)*SUM($A2:$A6)/SUM($A$2:$B$6). This formula can be extended to cell B9 and then
A9:B9 extended to A13:B13 to complete the expected values. The resulting formula for the final
expected value (cell B13) is =SUM(B$2:C$2)*SUM($A6:$A11)/SUM($A$2:$B$6).

Related Topics
For related functions and additional information, see:
“CHIDIST” on page 239
“CHIINV” on page 239
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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CONFIDENCE

The CONFIDENCE function returns a value for creating a statistical confidence interval
for a sample from a population with a known standard deviation.
CONFIDENCE(alpha, stdev, sample-size)
ÂÂ alpha:  The probability that the true population value lies outside the interval.

alpha is a number value and must be greater than or equal to 1. Subtracting the
confidence interval from 1 yields the alpha.
ÂÂ stdev:  The standard deviation of the population. stdev is a number value and must

be greater than 0.
ÂÂ sample-size:  The size of the sample. sample-size is a number value and must be

greater than 0.
Usage Notes
ÂÂ The confidence estimate assumes that values in the sample are normally distributed.
Examples
=CONFIDENCE(0.05, 1, 10) returns 0.62. If the mean of the sample values is 100, then with 95%
confidence the population mean falls in the range 99.38–100.62.
=CONFIDENCE(0.1, 1, 10) returns 0.52. If the mean of the sample values is 100, then with 90%
confidence the population mean falls in the range 99.48–100.52.
=CONFIDENCE(0.05, 1, 20) returns 0.44.
=CONFIDENCE(0.05, 1, 30) returns 0.36.
=CONFIDENCE(0.05, 1, 40) returns 0.31.

Related Topics
For related functions and additional information, see:
“STDEV” on page 290
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

CORREL

The CORREL function returns the correlation between two collections using linear
regression analysis.

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CORREL(y-values, x-values)
ÂÂ y-values:  The collection containing the y (dependent) values. y-values is a collection

that can contain number, date/time, or duration values. All values must be of the
same type.
ÂÂ x-values:  The collection containing the x (independent) values. x-values is a

collection that can contain number, date/time, or duration values. All values must be
of the same type.
Usage Notes
ÂÂ y-values and x-values must have the same dimensions.
ÂÂ If text or Boolean values are included in the collections, they are ignored.
Example
In this example, the CORREL function is used to determine how closely related the price of heating oil
(column A) is to the temperature that this hypothetical homeowner has set on the thermostat.

=CORREL(A2:A11, B2:B11) evaluates to approximately -0.9076, indicating a close correlation (as prices
rose, the thermostat was lowered).

Related Topics
For related functions and additional information, see:
“COVAR” on page 250
“Survey Results Example” on page 362
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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COUNT

The COUNT function returns the number of its arguments that contain numbers,
numeric expressions, or dates.
COUNT(value, value…)
ÂÂ value:  A value. value can contain any value type.
ÂÂ value…: Optionally include one or more additional values.

Usage Notes
ÂÂ To count any cell that contains any type of value (that is, any cell that is not empty),
use the COUNTA function.
Examples
The table in this example is used to illustrate all variations of the COUNT function. The information is
not meaningful, but does illustrate what type of arguments each variation of COUNT includes in the
function result.

=COUNT(A1:E1) returns 5, as all arguments are numeric.
=COUNT(A2:E2) returns 0, as none of the arguments are numeric.
=COUNT(A3:E3) returns 3, as the least two cells are not numeric.
=COUNT(A4:E4) returns 0, as the arguments are logical TRUE or FALSE, which are not counted as
numeric.
=COUNT(A5:E5) returns 2, as three cells are empty.
=COUNT(2, 3, A5:E5, SUM(A1:E1), “A”, “b”) returns 5, as the arguments 2 and 3 are numbers, there are
2 numbers in the range A5:E5, the SUM function returns 1 number, and the last two arguments are
text, not numeric (altogether 5 numeric arguments).

Related Topics
For related functions and additional information, see:
“COUNTA” on page 245
“COUNTBLANK” on page 246
“COUNTIF” on page 247
“COUNTIFS” on page 248
“Survey Results Example” on page 362

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“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

COUNTA

The COUNTA function returns the number of its arguments that are not empty.
COUNTA(value, value…)
ÂÂ value:  A value. value can contain any value type.
ÂÂ value…: Optionally include one or more additional values.

Usage Notes
ÂÂ To count only cells or arguments that contain numbers or dates, use the COUNT
function.
Examples
The table in this example is used to illustrate all variations of the COUNT function, including COUNTA.
The information is not meaningful, but does illustrate what type of arguments each variation of
COUNT includes in the function result.

=COUNTA(A1:E1) returns 5, as all cells contain an argument (all numeric).
=COUNTA(A2:E2) returns 5, as all cells contain an argument (all text).
=COUNTA(A3:E3) returns 5, as all cells contain an argument (mix of text and numeric).
=COUNTA(A4:E4) returns 5, as all cells contain an argument (TRUE or FALSE).
=COUNTA(A5:E5) returns 2, as three cells are empty.
=COUNTA(2, 3, A5:E5, SUM(A1:E1), “A”, “b”) returns 7, as the arguments 2 and 3 are numbers, there are
2 cells that are not empty in the range A5:E5, the SUM function returns 1 number, and “A” and “b” are
text expressions (altogether 7 arguments).

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Related Topics
For related functions and additional information, see:
“COUNT” on page 244
“COUNTBLANK” on page 246
“COUNTIF” on page 247
“COUNTIFS” on page 248
“Survey Results Example” on page 362
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

COUNTBLANK

The COUNTBLANK function returns the number of cells in a range that are empty.
COUNTBLANK(range)
ÂÂ range:  A range of cells. range is a reference to a single range of cells, which may

contain values of any type.
Examples
The table in this example is used to illustrate all variations of the COUNT function, including
COUNTBLANK. The information is not meaningful, but does illustrate what type of arguments each
variation of COUNT includes in the function result.

=COUNTBLANK(A1:E1) returns 0, as there are no blank cells in the range.
=COUNTBLANK(A2:E2) returns 0, as there are no blank cells in the range.
=COUNTBLANK(A5:E5) returns 3, as there are three blank cells in the range.
=COUNTBLANK(A6:E6) returns 5, as there are only blank cells in the range.
=COUNTBLANK(A1:E6) returns 8, as there are a total of 8 blank cells in the range.
=COUNTBLANK(A1:E1, A5:E5) returns an error, as COUNTBLANK accepts only one range as an argument.

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Related Topics
For related functions and additional information, see:
“COUNT” on page 244
“COUNTA” on page 245
“COUNTIF” on page 247
“COUNTIFS” on page 248
“Survey Results Example” on page 362
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

COUNTIF

The COUNTIF function returns the number of cells in a range that satisfy a given
condition.
COUNTIF(test-array, condition)
ÂÂ test-array:  The collection containing the values to be tested. test-array is a collection

that can contain any value type.
ÂÂ condition:  An expression that results in a logical TRUE or FALSE. condition is an

expression that can contain anything as long as the result from comparing condition
to a value in test-array can be expressed as a Boolean value of TRUE or FALSE.
Usage Notes
ÂÂ Each test-array value is compared to condition. If the value meets the conditional
test, it is included in the count.

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Examples
The table in this example is used to illustrate all variations of the COUNT function, including COUNTIF.
The information is not meaningful, but does illustrate what type of arguments each variation of
COUNT includes in the function result.

=COUNTIF(A1:E1, “>0”) returns 5, as all cells in the range have a value greater than zero.
=COUNTIF(A3:E3, “>=100”) returns 3, as all three numbers are greater than 100 and the two text
values are ignored in the comparison.
=COUNTIF(A1:E5, “=amet”) returns 2, as the test string “amet” appears twice in the range.
=COUNTIF(A1:E5, “=*t”) returns 4, as a string ending in the letter “t” appears four times in the range.

Related Topics
For related functions and additional information, see:
“COUNT” on page 244
“COUNTA” on page 245
“COUNTBLANK” on page 246
“COUNTIFS” on page 248
“Specifying Conditions and Using Wildcards” on page 360
“Survey Results Example” on page 362
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

COUNTIFS

The COUNTIFS function returns the number of cells in one or more ranges that satisfy
given conditions (one condition per range).

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COUNTIFS(test-values, condition, test-values…, condition…)
ÂÂ test-values:  A collection containing values to be tested. test-values is a collection

containing any type of value.
ÂÂ condition:  An expression that results in a logical TRUE or FALSE. condition is an

expression that can contain anything as long as the result from comparing condition
to a value in test-values can be expressed as a Boolean value of TRUE or FALSE.
ÂÂ test-values…: Optionally include one or more additional collections containing

values to be tested. Each test-values collection must be followed immediately with a
condition expression. This pattern of test-values, condition can be repeated as many
times as needed.
ÂÂ condition…: If an optional collection of test-values is included, an expression that

results in a logical TRUE or FALSE. There must be one condition following each
test-values collection; therefore, this function will always have an odd number of
arguments.
Usage Notes
ÂÂ Each value in test-values is compared to the corresponding condition. If the
corresponding values in each collection meet the corresponding conditional tests,
the count is increased by 1.
Examples
Given the following table:

=COUNTIFS(A2:A13,”<40”,B2:B13,”=M”) returns 4, the number of males (indicated by an “M” in column
B) under the age of forty.
=COUNTIFS(A2:A13,”<40”,B2:B13,”=M”,C2:C13,”=S”) returns 2, the number of males who are single
(indicated by an “S” in column C) and under the age of forty.
=COUNTIFS(A2:A13,”<40”,B2:B13,”=M”,C2:C13,”=M”) returns 2, the number of males who are married
(indicated by an “M” in column C) and under the age of forty.
=COUNTIFS(A2:A13,”<40”,B2:B13,”=F”) returns 3, the number of females (indicated by an “F” in column
B) who are under the age of forty.

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Related Topics
For related functions and additional information, see:
“COUNT” on page 244
“COUNTA” on page 245
“COUNTBLANK” on page 246
“COUNTIF” on page 247
“Specifying Conditions and Using Wildcards” on page 360
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

COVAR

The COVAR function returns the covariance of two collections.
COVAR(sample-1-values, sample-2-values)
ÂÂ sample-1-values:  The collection containing the first collection of sample values.

sample-1-values is a collection containing number values.
ÂÂ sample-2-values:  The collection containing the second collection of sample values.

sample-2-values is a collection containing number values.
Usage Notes
ÂÂ The two arrays must have the same dimensions.
ÂÂ If text or Boolean values are included within the arrays, they are ignored.
ÂÂ If the two collections are identical, the covariance is the same as the population

variance.

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Example
In this example, the COVAR function is used to determine how closely related the price of heating oil
(column A) is to the temperature that this hypothetical homeowner has set on the thermostat.

=COVAR(A2:A11, B2:B11) evaluates to approximately -1.6202, indicating a correlation (as prices rose,
the thermostat was lowered).

Related Topics
For related functions and additional information, see:
“CORREL” on page 242
“Survey Results Example” on page 362
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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CRITBINOM

The CRITBINOM function returns the smallest value for which the cumulative binomial
distribution is greater than or equal to a given value.
CRITBINOM(trials, prob-success, alpha)
ÂÂ trials:  The total number of trials or tests. trials is a number value that must be

greater than or equal to 0.
ÂÂ prob-success:  The probability of success for each trial or test. prob-success is a

number value that must be greater than or equal to 0 and less than or equal to 1.
ÂÂ alpha:  The probability that the true population value lies outside the interval. alpha

is a number value and must be less than or equal to 1. Subtracting the confidence
interval from 1 yields the alpha.
Example
=CRITBINOM(97, 0.05, 0.05) returns 2, based on 97 trials, with each trial having a probability of success
of 5% and a 95% confidence interval (5% alpha).
=CRITBINOM(97, 0.25, 0.1) returns 19, based on 97 trials, with each trial having a probability of success
of 25% and a 90% confidence interval (10% alpha).
=CRITBINOM(97, 0.25, 0.05) returns 17, based on 97 trials, with each trial having a probability of
success of 25% and a 95% confidence interval (5% alpha).

Related Topics
For related functions and additional information, see:
“BINOMDIST” on page 238
“NEGBINOMDIST” on page 275
“PERMUT” on page 281
“PROB” on page 282
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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DEVSQ

The DEVSQ function returns the sum of the squares of deviations of a collection of
numbers from their average (arithmetic mean).
DEVSQ(num-value, num-value…)
ÂÂ num-value:  A number. num-value is a number value.
ÂÂ num-value…: Optionally include one or more additional numbers.

Usage Notes
ÂÂ DEVSQ divides the sum of the numbers by the number of numbers to get the
average (arithmetic mean). The difference (absolute value) between the average and
each number is squared and summed and the total is returned.
Example
=DEVSQ(1, 7, 19, 8, 3, 9) returns 196.833333333333.

Related Topics
For related functions and additional information, see:
“STDEV”
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

EXPONDIST

The EXPONDIST function returns the exponential distribution of the specified form.
EXPONDIST(non-neg-x-value, lambda, form-type)
ÂÂ non-neg-x-value:  The value at which you want to evaluate the function. non-neg-x-

value is a number value that must be greater than or equal to 0.
ÂÂ lambda:  The parameter value. lambda is a number value and must be greater than 0.
ÂÂ form-type:  A value that indicates which form of the exponential function to

provide.
cumulative form (TRUE or 1):  Return the value of the cumulative distribution
function form.
probability density form (FALSE or 0):  Return the value of the probability density
function form.
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Examples
=EXPONDIST(4, 2, 1) returns 0.999664537372097 (cumulative distribution form).
=EXPONDIST(4, 2, 0) returns 0.000670925255805024 (probability density form).

Related Topics
For related functions and additional information, see:
“LOGNORMDIST” on page 269
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

FDIST

The FDIST function returns the F probability distribution.
FDIST(non-neg-x-value, d-f-numerator, d-f-denominator)
ÂÂ non-neg-x-value:  The value at which you want to evaluate the function. non-neg-x-

value is a number value that must be greater than or equal to 0.
ÂÂ d-f-numerator:  The degrees of freedom to include as the numerator. d-f-numerator

is a number value and must be greater than or equal to 1. If there is a decimal
portion, it is ignored.
ÂÂ d-f-denominator:  The degrees of freedom to include as the denominator. d-f-

denominator is a number value and must be greater than or equal to 1. If there is a
decimal portion, it is ignored.
Usage Notes
ÂÂ The F distribution is also known as Snedecor’s F distribution or the Fisher-Snedecor
distribution.
Examples
=FDIST(0.77, 1, 2) returns 0.472763488223567.
=FDIST(0.77, 1, 1) returns 0.541479597634413.
=FDIST(0.77, 2, 1) returns 0.627455805138159.

Related Topics
For related functions and additional information, see:

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“FINV” on page 255
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

FINV

The FINV function returns the inverse of the F probability distribution.
FINV(prob, d-f-numerator, d-f-denominator)
ÂÂ prob:  A probability associated with the distribution. prob is a number value and

must be greater than 0 and less than or equal to 1.
ÂÂ d-f-numerator:  The degrees of freedom to include as the numerator. d-f-numerator

is a number value and must be greater than or equal to 1. If there is a decimal
portion, it is ignored.
ÂÂ d-f-denominator:  The degrees of freedom to include as the denominator. d-f-

denominator is a number value and must be greater than or equal to 1. If there is a
decimal portion, it is ignored.
Examples
=FINV(0.77, 1, 2) returns 0.111709428782599.
=FINV(0.77, 1, 1) returns 0.142784612191674.
=FINV(0.77, 2, 1) returns 0.34331253162422.

Related Topics
For related functions and additional information, see:
“FDIST” on page 254
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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FORECAST

The FORECAST function returns the forecasted y value for a given x based on sample
values using linear regression analysis.
FORECAST(x-num-date-dur, y-values, x-values)
ÂÂ x-num-date-dur:  The x value for which the function should return a forecasted y

value. x-num-date-dur is a number value, a date/time value, or a duration value.
ÂÂ y-values:  The collection containing the y (dependent) values. y-values is a collection

that can contain number, date/time, or duration values. All values must be of the
same type.
ÂÂ x-values:  The collection containing the x (independent) values. x-values is a

collection that can contain number, date/time, or duration values. All values must be
of the same type.
Usage Notes
ÂÂ All arguments must be of the same type.
ÂÂ The two arrays must be of the same size.
ÂÂ If, for example, you had data on the driving speed of a vehicle and its fuel efficiency

at each speed, fuel efficiency would be the dependent variable (y) and driving speed
would be the independent variable (x).
ÂÂ You can use the SLOPE and INTERCEPT functions to find the equation used to

calculate forecast values.
Example
Given the following table:

=FORECAST(9, A3:F3, A2:F2) returns 19.

Related Topics
For related functions and additional information, see:
“CORREL” on page 242
“COVAR” on page 250
“INTERCEPT” on page 262
“SLOPE” on page 287
“Listing of Statistical Functions” on page 225

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“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

FREQUENCY

The FREQUENCY function returns an array of how often data values occur within a
range of interval values.
FREQUENCY(data-values, interval-values)
ÂÂ data-values:  A collection containing the values to be evaluated. data-values is a

collection containing number or date/time values. All values should be of the same
type.
ÂÂ interval-values:  A collection containing the interval values. interval-values is a

collection containing number or date/time values. All values should be of the same
type as the values in the data-values collection.
Usage Notes
ÂÂ FREQUENCY determines the number of values in data-values that fall within each
interval. The interval array is easiest to understand if it is arranged in ascending
order. The first frequency will be the count of those values that are less than or
equal to the lowest interval value. All other frequency values, except the last, will be
the count of those values that are greater than the immediately lower interval value
and less than or equal to the current interval value. The final frequency value will be
the count of those data values that are greater than the largest interval value.
ÂÂ The values returned by the function are contained in an array. One method of

reading the values in the array is to use the INDEX function. You can wrap the
FREQUENCY function within the INDEX function: =INDEX(FREQUENCY(data-values,
interval-values), x) where x is the desired interval. Remember that there will be one
more interval than there are interval-values.

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Example
Assume the following table contains the test scores of 30 students who recently took an exam you
administered. Assume further that that the minimum passing grade is 65 and that the lowest score
for other grades are as given. In order to facilitate building the formulas, an “F” is represented by 1
and an “A” by 5.

=INDEX(FREQUENCY($A$1:$F$5, $B$8:$E$8), B9) returns 5, the number of students who received an
“F” (score of 65 or less). This formula can be entered in cell B10 and then extended across to cell F10.
The resulting values returned for grades of “D” to “A” are 3, 8, 8, and 6, respectively.

Related Topics
For related functions and additional information, see:
“INDEX” on page 214
“PERCENTILE” on page 279
“PERCENTRANK” on page 280
“QUARTILE” on page 284
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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GAMMADIST

The GAMMADIST function returns the gamma distribution in the specified form.
GAMMADIST(non-neg-x-value, alpha, beta, form-type)
ÂÂ non-neg-x-value:  The value at which you want to evaluate the function. non-neg-x-

value is a number value that must be greater than or equal to 0.
ÂÂ alpha:  One of the shape parameters of the distribution. alpha is a number value

and must be greater than 0.
ÂÂ beta:  One of the shape parameters of the distribution. beta is a number value and

must be greater than 0.
ÂÂ form-type:  A value that indicates which form of the exponential function to provide.

cumulative form (TRUE or 1):  Return the value of the cumulative distribution
function form.
probability density form (FALSE or 0):  Return the value of the probability density
function form.
Examples
=GAMMADIST(0.8, 1, 2, 1) returns 0.329679953964361 (the cumulative distribution form).
=GAMMADIST(0.8, 1, 2, 0) returns 0.33516002301782 (the probability density form).

Related Topics
For related functions and additional information, see:
“GAMMAINV” on page 260
“GAMMALN” on page 260
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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GAMMAINV

The GAMMAINV function returns the inverse gamma cumulative distribution.
GAMMAINV(probability, alpha, beta)
ÂÂ probability:  A probability associated with the distribution. probability is a number

value and must be greater than 0 and less than 1.
ÂÂ alpha:  One of the shape parameters of the distribution. alpha is a number value

and must be greater than 0.
ÂÂ beta:  One of the shape parameters of the distribution. beta is a number value and

must be greater than 0.
Examples
=GAMMAINV(0.8, 1, 2) returns 3.2188758248682.
=GAMMAINV(0.8, 2, 1) returns 2.99430834700212.

Related Topics
For related functions and additional information, see:
“GAMMADIST” on page 259
“GAMMALN” on page 260
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

GAMMALN

The GAMMALN function returns the natural logarithm of the gamma function, G(x).
GAMMALN(pos-x-value)
ÂÂ pos-x-value:  The positive x value at which you want to evaluate the function. pos-x-

value is a number value and must be greater than 0.
Examples
=GAMMALN(0.92) returns 0.051658003497744.
=GAMMALN(0.29) returns 1.13144836880416.

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Related Topics
For related functions and additional information, see:
“GAMMADIST” on page 259
“GAMMAINV” on page 260
“LN” on page 179
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

GEOMEAN

The GEOMEAN function returns the geometric mean.
GEOMEAN(pos-num, pos-num…)
ÂÂ pos-num:  A positive number. pos-num is a number value and must be greater

than 0.
ÂÂ pos-num…: Optionally include one or more additional positive numbers.

Usage Notes
ÂÂ GEOMEAN multiples the arguments to arrive at a product and then takes the root of
the product that is equal to the number of arguments.
Example
=GEOMEAN(5, 7, 3, 2, 6, 22) returns 5.50130264578853.

Related Topics
For related functions and additional information, see:
“AVERAGE” on page 231
“HARMEAN” on page 262
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15

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“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

HARMEAN

The HARMEAN function returns the harmonic mean.
HARMEAN(pos-num, pos-num…)
ÂÂ pos-num:  A positive number. a-pos-num is a number value and must be greater

than 0.
ÂÂ pos-num…: Optionally include one or more additional positive numbers.

Usage Notes
ÂÂ The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals.
Example
=HARMEAN(5, 7, 3, 2, 6, 22) returns 4.32179607109448.

Related Topics
For related functions and additional information, see:
“AVERAGE” on page 231
“GEOMEAN” on page 261
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

INTERCEPT

The INTERCEPT function returns the y-intercept of the best-fit line for the collection
using linear regression analysis.
INTERCEPT(y-values, x-numbers)
ÂÂ y-values:  The collection containing the y (dependent) values. y-values is a collection

that can contain number, date/time, or duration values. All values must be of the
same type.

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ÂÂ x-numbers:  The collection containing the x (independent) values. x-numbers is a

collection containing number values.
Usage Notes
ÂÂ The two arrays must be of the same size.
ÂÂ To find the slope of the best-fit line, use the SLOPE function.
Example
In this example, the INTERCEPT function is used to determine the y-intercept of the best-fit line
for the temperature that this hypothetical homeowner has set on the thermostat (the dependent
variable), based on the price of heating oil (the independent variable).

=INTERCEPT(B2:B11, A2:A11) evaluates to approximately 78, above the highest hypothetical value as
the best-fit line sloping downward (as prices rose, the thermostat was lowered).

Related Topics
For related functions and additional information, see:
“SLOPE” on page 287
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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LARGE

The LARGE function returns the nth-largest value within a collection. The largest value
is ranked number 1.
LARGE(num-date-dur-set, ranking)
ÂÂ num-date-dur-set:  A collection of values. num-date-dur-set is a collection

containing number, date, or duration values. All values must be of the same type.
ÂÂ ranking:  A number representing the size ranking of the value you want to retrieve.

ranking is a number value and must be in the range of 1 to the number of values in
the collection.
Usage Notes
ÂÂ A ranking of 1 retrieves the largest number in the collection, 2 the second-largest,
and so on. Values included in the array that are of the same size are ranked together,
but impact the outcome.
Examples
Assume the following table contains the cumulative test scores for this semester for your 20 students.
(We have organized the data this way for the example; it would likely originally have been in 20
separate rows.)

=LARGE(A1:E4, 1) returns 100, the largest cumulative test score (cell B2).
=LARGE(A1:E4, 2) returns 92, the second-largest cumulative test score (either cell B2 or cell C2).
=LARGE(A1:E4, 3) returns 92, also the third-largest cumulative test score as it appears twice (cells B2
and C2).
=LARGE(A1:E4, 6) returns 86, the sixth-largest cumulative test score (order is 100 , 92, 92, 91, 90, then 86).

Related Topics
For related functions and additional information, see:
“RANK” on page 285
“SMALL” on page 288
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15

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“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

LINEST

The LINEST function returns an array of the statistics for a straight line that best fits the
given data using the “least squares” method.
LINEST(known-y-values, known-x-values, nonzero-y-intercept, more-stats)
ÂÂ known-y-values:  The collection containing the known y values. known-y-values is

a collection containing number values. If there is only one collection of known x
values, known-y-values can be any size. If there is more than one collection of known
x values, known-y-values can be either one column containing the values or one row
containing the values, but not both.
ÂÂ known-x-values:  An optional collection containing the known x values. known-

x-values is a collection containing number values. If omitted, it will be assumed to
be the set {1, 2, 3…} of the same size as known-y-values. If there is only one set of
known x values, known-x-values, if specified, should be the same size as known-yvalues. If there is more than one set of known x values, each row/column of knownx-values is considered to be one set and the size of each row/column must be the
same as the size of the row/column of known-y-values.
ÂÂ nonzero-y-intercept:  An optional value specifying how the y intercept (constant b)

should be calculated.
normal (1, TRUE, or omitted):  The value of the y intercept (constant b) should be
calculated normally.
force 0 value (0, FALSE):  The value of the y intercept (constant b) should be forced
to be 0.
ÂÂ more-stats:  An optional value specifying whether additional statistical information

should be returned.
no additional stats (0, FALSE, or omitted):  Do not return additional regression
statistics in the returned array.
additional stats (1, TRUE):  Return additional regression statistics in the returned
array.
Usage Notes
ÂÂ The values returned by the function are contained in an array. One method of
reading the values in the array is to use the INDEX function. You can wrap the
LINEST function within the INDEX function: =INDEX(LINEST(known-y-values, knownx-values, const-b, stats), y, x) where y and x are the column and row index of the
desired value.

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If additional statistics are not returned (stats is FALSE), the array returned is one row
deep. The number of columns is equal to the the number of sets of known-x-values
plus 1. It contains the line slopes (one value for each row/column of x values) in
reverse order (the first value relates to the last row/column of x values) and then the
value for b, the intercept.
If additional statistics are returned (stats is TRUE), the array contains five rows. See
“Additional Statistics” on page 267 for the contents of the array.
Examples
Assume the following table contains the test scores of 30 students who recently took an exam you
administered. Assume further that the minimum passing grade is 65 and that the lowest score for
other grades are as given. In order to facilitate building the formulas, an “F” is represented by 1 and
an “A” by 5.

=INDEX(LINEST(A2:A6, C2:C6, 1, 0), 1) returns 0.752707581227437, which is the best-fit line slope.
=INDEX(LINEST(A2:A6, C2:C6, 1, 0), 2) returns 0.0342960288808646, which is b, the intercept.

Related Topics
For related functions and additional information, see:
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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Additional Statistics

This section discusses the additional statistics that can be returned by the LINEST
function.
LINEST can include additional statistical information in the array returned by the
function. For purposes of the following discussion, assume that there are five sets of
known x values, in addition to the known y values. Assume further that the known
x values are in five table rows or five table columns. Based on these assumptions,
the array returned by LINEST would be as follows (where the number following an x
indicates which set of x values the item refers to):
Row/Column

1

2

3

4

5

6

1

slope x5

slope x4

slope x3

slope x2

slope x1

b (y intercept)

2

std-err x1

std-err x2

std-err x3

std-err x4

std-err x5

std-err b

3

coefficient-det

std-err y

4

F-stat

degrees-offreedom

5

reg-ss

reside-ss

Argument definitions
slope x:  The slope of the line related to this set of known x values. The values are
returned in reverse order; that is, if there are five known x value sets, the value for the
fifth set is first in the returned array.
b:  The y intercept for the known x values.
std-err x:  The standard error for the coefficient associated with this set of known x
values. The values are returned in order; that is, if there are five known x value sets, the
value for the first set is returned first in the array. This is the opposite of the way the
slope values are returned.
std-err b:  The standard error associated with the y-intercept value (b).
coefficient-det: The coefficient of determination. This statistic compares estimated and
actual y values. If it is 1, there is no difference between the estimated y value and the
actual y value. This is known as perfect correlation. If the coefficient of determination is
0, there is no correlation and the given regression equation is not helpful in predicting
a y value.
std-err y:  The standard error associated with the y value estimate.
F-stat:  The F observed value. The F observed value can be used to help determine
whether the observed relationship between the dependent and independent
variables occurs by chance.
degrees-of-freedom:  The degrees of freedom. Use the degrees of freedom statistic to
help determine a confidence level.

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reg-ss:  The regression sum of squares.
reside-ss:  The residual sum of squares.
Usage Notes
ÂÂ It does not matter whether the known x values and known y values are in rows or
columns. In either case, the returned array is ordered by rows as illustrated in the
table.
ÂÂ The example assumed five sets of known x values. If there were more or less than

five, the number of columns in the returned array would change accordingly (it is
always equal to the number of sets of known x values plus 1), but the number of
rows would remain constant.
ÂÂ If additional statistics are not specified in the arguments to LINEST, the returned

array is equal to the first row only.

LOGINV

The LOGINV function returns the inverse of the log-normal cumulative distribution
function of x.
LOGINV(probability, mean, stdev)
ÂÂ probability:  A probability associated with the distribution. probability is a number

value and must be greater than 0 and less than 1.
ÂÂ mean:  The mean of the natural logarithm, that is, ln(x). mean is a number value and

is the average (arithmetic mean) of ln(x); the natural logarithm of x.

ÂÂ stdev:  The standard deviation of the population. stdev is a number value and must

be greater than 0.
Usage Notes
ÂÂ LOGINV is appropriate where the logarithm of x is normally distributed.
Example
=LOGINV(0.78, 1.7, 2.2) returns 29.9289150377259.

Related Topics
For related functions and additional information, see:
“LN” on page 179
“LOGNORMDIST” on page 269
“Listing of Statistical Functions” on page 225
“Value Types” on page 36

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“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

LOGNORMDIST

The LOGNORMDIST function returns the log-normal distribution.
LOGNORMDIST(pos-x-value, mean, stdev)
ÂÂ pos-x-value:  The positive x value at which you want to evaluate the function. pos-x-

value is a number value that must be greater than 0.
ÂÂ mean:  The mean of the natural logarithm, that is, ln(x). mean is a number value and

is the average (arithmetic mean) of ln(x); the natural logarithm of x.

ÂÂ stdev:  The standard deviation of the population. stdev is a number value and must

be greater than 0.
Example
=LOGNORMDIST(0.78, 1.7, 2.2) returns 0.187899237956868.

Related Topics
For related functions and additional information, see:
“LN” on page 179
“LOGINV” on page 268
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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MAX

The MAX function returns the largest number in a collection.
MAX(value, value…)
ÂÂ value:  A value. value can contain any value type.
ÂÂ value…: Optionally include one or more additional values.

Usage Notes
ÂÂ If value does not evaluate to a date or number, it is not included in the result.
ÂÂ To determine the largest of any type of value in a collection, use the MAXA function.
Examples
=MAX(5, 5, 5, 5, 6) returns 6.
=MAX(1, 2, 3, 4, 5) returns 5.

Related Topics
For related functions and additional information, see:
“LARGE” on page 264
“MAXA” on page 270
“MIN” on page 272
“SMALL” on page 288
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

MAXA

The MAXA function returns the largest number in a collection of values that may
include text and Boolean values.
MAXA(value, value…)
ÂÂ value:  A value. value can contain any value type.
ÂÂ value…: Optionally include one or more additional values. All numeric values must

be of the same type. You cannot mix numbers, dates, and duration values.

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Usage Notes
ÂÂ Text values and logical FALSE are given a value of 0 and logical TRUE is given a value
of 1.
ÂÂ To determine the largest value of a collection that contains only numbers or dates,

use the MAX function.
Examples
=MAXA(1, 2, 3, 4) returns 4.
=MAXA(A1:C1), where A1:C1 contains -1, -10, hello, returns 0.

Related Topics
For related functions and additional information, see:
“MAX” on page 270
“MINA” on page 273
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

MEDIAN

The MEDIAN function returns the median value in a collection of numbers. The median
is the value where half the numbers in the set are less than the median and half are
greater.
MEDIAN(num-date-dur, num-date-dur…)
ÂÂ num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a

duration value.
ÂÂ num-date-dur…: Optionally include one or more additional values. If more than

one num-date-dur value is specified, all must be of the same type.
Usage Notes
ÂÂ If there is an even number of values in the set, the MEDIAN function returns the
average of the two middle values.

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Examples
=MEDIAN(1, 2, 3, 4, 5) returns 3.
=MEDIAN(1, 2, 3, 4, 5, 6) returns 3.5.
=MEDIAN(5, 5, 5, 5, 6) returns 5.

Related Topics
For related functions and additional information, see:
“AVERAGE” on page 231
“MODE” on page 274
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

MIN

The MIN function returns the smallest number in a collection.
MIN(value, value…)
ÂÂ value:  A value. value can contain any value type.
ÂÂ value…: Optionally include one or more additional values.

Usage Notes
ÂÂ If value does not evaluate to a date or number, it is not included in the result.
ÂÂ To determine the smallest of any type of value in a collection, use the MINA

function.
Examples
=MIN(5, 5, 5, 5, 6) returns 5.
=MIN(1, 2, 3, 4, 5) returns 1.

Related Topics
For related functions and additional information, see:
“LARGE” on page 264
“MAX” on page 270

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“MINA” on page 273
“SMALL” on page 288
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

MINA

The MINA function returns the smallest number in a collection of values that may
include text and Boolean values.
MINA(value, value…)
ÂÂ value:  A value. value can contain any value type.
ÂÂ value…: Optionally include one or more additional values. All numeric values must

be of the same type. You cannot mix numbers, dates, and duration values.
Usage Notes
ÂÂ Text values and logical FALSE are given a value of 0 and logical TRUE is given a value
of 1.
ÂÂ To determine the smallest value of a collection that contains only numbers or dates,

use the MIN function.
Examples
=MINA(1, 2, 3, 4) returns 1.
=MINA(A1:C1), where A1:C1 contains -1, -10, hello, returns -10.
=MINA(A1:C1), where A1:C1 contains 1, 10, hello, returns 0.

Related Topics
For related functions and additional information, see:
“MAXA” on page 270
“MIN” on page 272
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
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“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

MODE

The MODE function returns the most frequently occurring value in a collection of
numbers.
MODE(num-date-dur, num-date-dur…)
ÂÂ num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a

duration value.
ÂÂ num-date-dur…: Optionally include one or more additional values. If more than

one num-date-dur value is specified, all must be of the same type.
Usage Notes
ÂÂ If more than one number occurs the maximum multiple times in the arguments,
MODE returns the first such number.
ÂÂ If no value occurs more than once, the function returns an error.
Examples
=MODE(5, 5, 5, 5, 6) returns 5.
=MODE(1, 2, 3, 4, 5) returns an error.
=MODE(2, 2, 4, 6, 6) returns 2.
=MODE(6, 6, 4, 2, 2) returns 6.

Related Topics
For related functions and additional information, see:
“AVERAGE” on page 231
“MEDIAN” on page 271
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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NEGBINOMDIST

The NEGBINOMDIST function returns the negative binomial distribution.
NEGBINOMDIST(f-num, s-num, prob-success)
ÂÂ f-num:  The number of failures. f-num is a number value and must be greater than

or equal to 0.
ÂÂ s-num:  The number of successful trials or tests. s-num is a number value that must

be greater than or equal to 1.
ÂÂ prob-success:  The probability of success for each trial or test. prob-success is a

number value that must be greater than 0 and less than 1.
Usage Notes
ÂÂ NEGBINOMDIST returns the probability that there will be a specified number of
failures, f-num, before the specified number of successes, s-num. The constant
probability of a success is prob-success.
Example
=NEGBINOMDIST(3, 68, 0.95) returns 0.20913174716192.

Related Topics
For related functions and additional information, see:
“BINOMDIST” on page 238
“CRITBINOM” on page 252
“PERMUT” on page 281
“PROB” on page 282
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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NORMDIST

The NORMDIST function returns the normal distribution of the specified function form.
NORMDIST(num, average, stdev, form-type)
ÂÂ num:  The number to be evaluated. num is a number value.
ÂÂ average:  The average of the distribution. average is a number value representing

the known average (arithmetic mean) rate at which events occur.
ÂÂ stdev:  The standard deviation of the population. stdev is a number value and must

be greater than 0.
ÂÂ form-type:  A value that indicates which form of the exponential function to

provide.
cumulative form (TRUE or 1):  Return the value of the cumulative distribution
function form.
probability density form (FALSE or 0):  Return the value of the probability density
function form.
Usage Notes
ÂÂ If average is 0, stdev is 1, and form-type is TRUE, NORMDIST returns the same value as
the cumulative standard normal distribution returned by NORMSDIST.
Examples
=NORMDIST(22, 15, 2.5, 1) returns 0.997444869669572, the cumulative distribution form.
=NORMDIST(22, 15, 2.5, 0) returns 0.00316618063319199, the probability density form.

Related Topics
For related functions and additional information, see:
“NORMINV” on page 277
“NORMSDIST” on page 277
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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NORMINV

The NORMINV function returns the inverse of the cumulative normal distribution.
NORMINV(probability, average, stdev)
ÂÂ probability:  A probability associated with the distribution. probability is a number

value and must be greater than 0 and less than 1.
ÂÂ average:  The average of the distribution. average is a number value representing

the known average (arithmetic mean) rate at which events occur.
ÂÂ stdev:  The standard deviation of the population. stdev is a number value and must

be greater than 0.
Usage Notes
ÂÂ If average is 0 and stdev is 1, NORMINV returns the same value as the inverse of the
cumulative standard normal distribution returned by NORMSINV.
Example
=NORMINV(0.89, 15, 2.5) returns 18.0663203000915.

Related Topics
For related functions and additional information, see:
“NORMDIST” on page 276
“NORMSINV” on page 278
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

NORMSDIST

The NORMSDIST function returns the standard normal distribution.
NORMSDIST(num)
ÂÂ num:  A number. num is a number value.

Usage Notes
ÂÂ A standard normal distribution has an average (arithmetic mean) of 0 and a
standard deviation of 1.

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Example
=NORMSDIST(4.3) returns 0.999991460094529.

Related Topics
For related functions and additional information, see:
“NORMDIST” on page 276
“NORMSINV” on page 278
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

NORMSINV

The NORMSINV function returns the inverse of the cumulative standard normal
distribution.
NORMSINV(probability)
ÂÂ probability:  A probability associated with the distribution. probability is a number

value and must be greater than 0 and less than 1.
Usage Notes
ÂÂ A standard normal distribution has an average (arithmetic mean) of 0 and a
standard deviation of 1.
Example
=NORMSINV(0.89) returns 1.22652812003661.

Related Topics
For related functions and additional information, see:
“NORMINV” on page 277
“NORMSDIST” on page 277
“Listing of Statistical Functions” on page 225
“Value Types” on page 36

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“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

PERCENTILE

The PERCENTILE function returns the value within a collection that corresponds to a
particular percentile.
PERCENTILE(num-date-dur-set, percentile-value)
ÂÂ num-date-dur-set:  A collection of values. num-date-dur-set is a collection

containing number, date, or duration values. All values must be of the same type.
ÂÂ percentile-value:  The percentile value you want to find, in the range 0 to 1.

percentile-value is a number value and is either entered as a decimal (for example,
0.25) or delimited with a percent sign (for example, 25%). It must be greater than or
equal to 0 and less than or equal to 1.
Usage Notes
ÂÂ Values included in the array of the same size are ranked together, but impact the
outcome.
Examples
Assume the following table contains the cumulative test scores for this semester for your 20 students.
(We have organized the data this way for the example; it would likely originally have been in 20
separate rows.)

=PERCENTILE(A1:E4, 0.90) returns 92, the minimum cumulative test score to be in the top 10% of the
class (90th percentile).
=PERCENTILE(A1:E4, 2/3) returns 85, the minimum cumulative test score to be in the top one-third of
the class (2/3 or approximately 67th percentile).
=PERCENTILE(A1:E4, 0.50) returns 83, the minimum cumulative test score to be in the top half of the
class (the 50th percentile).

Related Topics
For related functions and additional information, see:
“FREQUENCY” on page 257
“PERCENTRANK” on page 280
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“QUARTILE” on page 284
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

PERCENTRANK

The PERCENTRANK function returns the rank of a value in a collection as a percentage
of the collection.
PERCENTRANK(num-date-dur-set, num-date-dur, significance)
ÂÂ num-date-dur-set:  A collection of values. num-date-dur-set is a collection

containing number, date, or duration values. All values must be of the same type.
ÂÂ num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a

duration value.
ÂÂ significance: An optional value specifying the number of digits to the right of the

decimal point. significance is a number value that must be greater than or equal to 1.
If omitted, a default value of 3 is used (x.xxx%).
Usage Notes
ÂÂ PERCENTRANK can be used to evaluate the relative standing of a value within
a collection. It is calculated by determining where in the collection a specified
number falls. For example, if in a given collection, there are ten values smaller than a
specified number and ten values that are larger, the PERCENTRANK of the specified
number is 50%.
Example
=PERCENTRANK({5, 6, 9, 3, 7, 11, 8, 2, 14}, 10) returns 0.813, as there are seven values smaller than 10
and only two that are larger.

Related Topics
For related functions and additional information, see:
“FREQUENCY” on page 257
“PERCENTILE” on page 279
“Listing of Statistical Functions” on page 225

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“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

PERMUT

The PERMUT function returns the number of permutations for a given number of
objects that can be selected from a total number of objects.
PERMUT(num-objects, num-elements)
ÂÂ num-objects:  The total number of objects. num-objects is a number value and must

be greater than or equal to 0.
ÂÂ num-elements:  The number of objects to be selected from the total number of

objects in each permutation. num-elements is a number value and must be greater
than or equal to 0.
Examples
=PERMUT(25, 5) returns 6375600.
=PERMUT(10, 3) returns 720.
=PERMUT(5, 2) returns 20.

Related Topics
For related functions and additional information, see:
“BINOMDIST” on page 238
“CRITBINOM” on page 252
“NEGBINOMDIST” on page 275
“PROB” on page 282
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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POISSON

The POISSON function returns the probability that a specific number of events will
occur using the Poisson distribution.
POISSON(events, average, form-type)
ÂÂ events:  The number of events (arrivals) for which you want to calculate the

probability. events is a number value.
ÂÂ average:  The average of the distribution. average is a number value representing

the known average (arithmetic mean) rate at which events occur.
ÂÂ form-type:  A value that indicates which form of the exponential function to

provide.
cumulative form (TRUE or 1):  Return the value of the cumulative distribution
function form (that the specified number or fewer successes or events will occur).
probability mass form (FALSE or 0):  Return the value of the probability mass
function form (that there are exactly the specified number of successes or events).
Example
For a mean of 10 and an arrival rate of 8:
=POISSON(8, 10, FALSE) returns 0.112599.

Related Topics
For related functions and additional information, see:
“EXPONDIST” on page 253
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

PROB

The PROB function returns the probability of a range of values if you know the
probabilities of the individual values.
PROB(num-set, probability-values, lower, upper)
ÂÂ num-set:  A collection of numbers. num-set is a collection containing number values.

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ÂÂ probability-values:  The collection containing the probability values. probability-

values is a collection containing number values. The sum of the probabilities must
add up to 1. Any string values are ignored.
ÂÂ lower:  The lower limit or bound. lower is a number value.
ÂÂ upper:  An optional upper limit or bound. upper is a number value and must be

greater than or equal to lower.
Usage Notes
ÂÂ The PROB function sums the probabilities associated with all values in the collection
greater than or equal to the specified lower limit value and less than or equal to the
specified upper limit value. If upper is omitted, PROB returns the probability of the
single number equal to the specified lower limit.
ÂÂ The two arrays must be of the same size. If text is contained in an array, it will be

ignored.
Examples
Assume you are thinking of a number from 1 to 10 to have someone guess. Most people would say
the probability that you would be thinking of a particular number is 0.1 (10%), as listed in column
C, since there are ten possible choices. However, studies have shown that people do not choose
numbers randomly.
Assume that a study has shown that people like you are more likely to select certain numbers than
others. These revised probabilities are in column E.

=PROB(A1:A10, C1:C10, 4, 6) returns 0.30, the probability that the value is 4, 5, or 6, assuming choices
are completely random.
=PROB(A1:A10, E1:E10, 7) returns 0.28, the probability that the value is 4, 5, or 6, based on the research
that numbers are not chosen randomly.
=PROB(A1:A10, E1:E10, 4, 6) returns 0.20, the probability that the value is 7, based on the research that
numbers are not chosen randomly.
=PROB(A1:A10, C1:C10, 6, 10) returns 0.50, the probability that the value is greater than 5 (6 to 10),
assuming choices are completely random.

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Related Topics
For related functions and additional information, see:
“BINOMDIST” on page 238
“CRITBINOM” on page 252
“NEGBINOMDIST” on page 275
“PERMUT” on page 281
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

QUARTILE

The QUARTILE function returns the value for the specified quartile of a given data
collection.
QUARTILE(num-set, quartile-num)
ÂÂ num-set:  A collection of numbers. num-set is a collection containing number values.
ÂÂ quartile-num:  Specifies the desired quartile.

smallest (0):  Returns the smallest value.
first (1): Returns the first quartile (25th percentile).
second (2):  Returns the second quartile (50th percentile).
third (3):  Returns the third quartile (75th percentile).
largest (4):  Returns the largest value.
Usage Notes
ÂÂ MIN, MEDIAN, and MAX return the same value as QUARTILE when quartile-num is
equal to 0, 2, and 4, respectively.

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Examples
=QUARTILE({5, 6, 9, 3, 7, 11, 8, 2, 14}, 0) returns 2, the smallest value.
=QUARTILE({5, 6, 9, 3, 7, 11, 8, 2, 14}, 1) returns 5, the 25th percentile or first quartile.
=QUARTILE({5, 6, 9, 3, 7, 11, 8, 2, 14}, 2) returns 7, the 50th percentile or second quartile.
=QUARTILE({5, 6, 9, 3, 7, 11, 8, 2, 14}, 3) returns 9, the 75th percentile or third quartile.
=QUARTILE({5, 6, 9, 3, 7, 11, 8, 2, 14}, 0) returns 14, the largest value.

Related Topics
For related functions and additional information, see:
“FREQUENCY” on page 257
“MAX” on page 270
“MEDIAN” on page 271
“MIN” on page 272
“PERCENTILE” on page 279
“PERCENTRANK” on page 280
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

RANK

The RANK function returns the rank of a number within a range of numbers.
RANK(num-date-dur, num-date-dur-set, largest-is-high)
ÂÂ num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a

duration value.
ÂÂ num-date-dur-set:  A collection of values. num-date-dur-set is a collection

containing number, date, or duration values. All values must be of the same type.

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ÂÂ largest-is-high:  An optional value specifying whether the smallest or the largest

value in the collection is ranked 1.
largest is low (0, FALSE, or omitted):  Assign the largest value in the collection the
rank 1.
largest is high (1, or TRUE):  Assign the smallest value in the collection the rank 1.
Usage Notes
ÂÂ Values included in the collection that are the same are ranked together, but impact
the outcome.
ÂÂ If the specified value does not match any of the values in the collection, an error is

returned.
Examples
Assume the following table contains the cumulative test scores for this semester for your 20 students.
(We have organized the data this way for the example; it would likely originally have been in 20
separate rows.)

=RANK(30, A1:E4, 1) returns 1, as 30 is the smallest cumulative test score and we chose to rank the
smallest first.
=RANK(92, A1:E4, 0) returns 2, as 92 is the second-largest cumulative test score and we chose to rank
largest first.
=RANK(91, A1:E4, 1) returns 4, as there is a “tie” for second place. The order is 100, 92, 92, then 91 and
the rank is 1, 2, 2, and then 4.

Related Topics
For related functions and additional information, see:
“LARGE” on page 264
“SMALL” on page 288
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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SLOPE

The SLOPE function returns the slope of the best-fit line for the collection using linear
regression analysis.
SLOPE(y-values, x-values)
ÂÂ y-values:  The collection containing the y (dependent) values. y-values is a collection

that can contain number, date/time, or duration values. All values must be of the
same type.
ÂÂ x-values:  The collection containing the x (independent) values. x-values is a

collection that can contain number, date/time, or duration values. All values must be
of the same type.
Usage Notes
ÂÂ The two collections must be of the same size or the function returns an error.
ÂÂ If, for example, you had data on the driving speed of a vehicle and its fuel efficiency

at each speed, fuel efficiency would be the dependent variable and driving speed
would be the independent variable.
ÂÂ To find the y-intercept of the best-fit line, use the INTERCEPT function.
Example
In this example, the SLOPE function is used to determine the slope of the best-fit line for the
temperature that this hypothetical homeowner has set on the thermostat (the dependent variable),
based on the price of heating oil (the independent variable).

=SLOPE(B2:B11, A2:A11) evaluates to approximately -3.2337, indicating a best-fit line sloping
downward (as prices rose, the thermostat was lowered).

Related Topics
For related functions and additional information, see:
“INTERCEPT” on page 262
“Listing of Statistical Functions” on page 225
“Value Types” on page 36

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“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

SMALL

The SMALL function returns the nth-smallest value within a range. The smallest value is
ranked number 1.
SMALL(num-date-dur-set, ranking)
ÂÂ num-date-dur-set:  A collection of values. num-date-dur-set is a collection

containing number, date, or duration values. All values must be of the same type.
ÂÂ ranking:  A number representing the size ranking of the value you want to retrieve.

ranking is a number value and must be in the range of 1 to the number of values in
the collection.
Usage Notes
ÂÂ A ranking of 1 retrieves the smallest number in the collection, 2 the second-smallest,
and so on. Values included in the collection that are of the same size are ranked
together, but impact the outcome.
Examples
Assume the following table contains the cumulative test scores for this semester for your 20 students.
(We have organized the data this way for the example; it would likely originally have been in 20
separate rows.)

=SMALL(A1:E4, 1) returns 30, the smallest cumulative test score (cell A1).
=SMALL(A1:E4, 2) returns 51, the second-smallest cumulative test score (cell E1).
=SMALL(A1:E4, 6) returns 75, the sixth-smallest cumulative test score (order is 30, 51, 68, 70, 75, then
75 again, so 75 is both the fifth- and sixth-smallest cumulative test score).

Related Topics
For related functions and additional information, see:
“LARGE” on page 264
“RANK” on page 285
“Listing of Statistical Functions” on page 225
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“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

STANDARDIZE

The STANDARDIZE function returns a normalized value from a distribution
characterized by a given mean and standard deviation.
STANDARDIZE(num, average, stdev)
ÂÂ num:  The number to be evaluated. num is a number value.
ÂÂ average:  The average of the distribution. average is a number value representing

the known average (arithmetic mean) rate at which events occur.
ÂÂ stdev:  The standard deviation of the population. stdev is a number value and must

be greater than 0.
Example
=STANDARDIZE(6, 15, 2.1) returns –4.28571428571429.

Related Topics
For related functions and additional information, see:
“NORMDIST” on page 276
“NORMINV” on page 277
“NORMSDIST” on page 277
“NORMSINV” on page 278
“ZTEST” on page 305
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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STDEV

The STDEV function returns the standard deviation, a measure of dispersion, of a
collection of values based on their sample (unbiased) variance.
STDEV(num-date-dur, num-date-dur…)
ÂÂ num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a

duration value.
ÂÂ num-date-dur…: One or more additional values (a minimum of two values are

required). All num-date-dur values must be of the same type.
Usage Notes
ÂÂ It is appropriate to use STDEV when the specified values represent only a sample of
a larger population. If the values you are analyzing represent the entire collection or
population, use the STDEVP function.
ÂÂ If you want to include text or Boolean values in the computation, use the STDEVA

function.
ÂÂ The standard deviation is the square root of the variance returned by the VAR

function.
Example
Assume you have administered five tests to a group of students. You have arbitrarily selected
five students to represent the total population of students (note that this is an example only; this
would not likely be statistically valid). Using the sample data, you could use the STDEV function to
determine which test had the widest dispersion of test scores.
The results of the STDEV functions are approximately 22.8035, 24.5357, 9.5026, 8.0747, and 3.3466. So
test 2 had the highest dispersion, followed closely by test 1. The other three tests had low dispersion.
Test 1

Test 2

Test 3

Test 4

Test 5

Student 1

75

82

90

78

84

Student 2

100

90

95

88

90

Student 3

40

80

78

90

85

Student 4

80

35

95

98

92

Student 5

90

98

75

97

88

=STDEV(B2:B6)

=STDEV(C2:C6)

=STDEV(D2:D6)

=STDEV(E2:E6)

=STDEV(F2:F6)

Related Topics
For related functions and additional information, see:
“STDEVA” on page 291
“STDEVP” on page 293

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“STDEVPA” on page 294
“VAR” on page 298
“VARA” on page 300
“VARP” on page 302
“VARPA” on page 303
“Survey Results Example” on page 362
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

STDEVA

The STDEVA function returns the standard deviation, a measure of dispersion, of a
collection of values that may include text and Boolean values, based on the sample
(unbiased) variance.
STDEVA(value, value…)
ÂÂ value:  A value. value can contain any value type. All numeric values must be of the

same type. You cannot mix numbers, dates, and duration values.
ÂÂ value…: One or more additional values (a minimum of two values are required).

All numeric values must be of the same type. You cannot mix numbers, dates, and
duration values.
Usage Notes
ÂÂ It is appropriate to use STDEVA when the specified values represent only a sample
of a larger population. If the values you are analyzing represent the entire collection
or population, use the STDEVPA function.
ÂÂ STDEVA assigns a value of 0 to any text value, 0 to the Boolean value FALSE, and 1

to the Boolean value TRUE and includes them in the computation. Empty cells are
ignored. If you do not want to include text or Boolean values in the computation,
use the STDEV function.
ÂÂ The standard deviation is the square root of the variance returned by the VARA function.

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Example
Assume you have installed a temperature sensor in Cupertino, California. The sensor records each
day’s high and low temperatures. In addition, you have kept a record of each day you turned on the
air conditioner in your condo. The data from the first few days is shown in the following table and is
used as a sample for the population of high and low temperatures (note that this is an example only;
this would not be statistically valid).

=STDEVA(B2:B13) returns 24.8271, the dispersion as measured by STDEVA, of the sample of daily high
temperatures.
It exceeds the actual range of high temperatures of 15 degrees because the “unavailable” temperature
is given a value of zero.

Related Topics
For related functions and additional information, see:
“STDEV” on page 290
“STDEVP” on page 293
“STDEVPA” on page 294
“VAR” on page 298
“VARA” on page 300
“VARP” on page 302
“VARPA” on page 303
“Survey Results Example” on page 362
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15

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“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

STDEVP

The STDEVP function returns the standard deviation, a measure of dispersion, of a
collection of values based on their population (true) variance.
STDEVP(num-date-dur, num-date-dur…)
ÂÂ num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a

duration value.
ÂÂ num-date-dur…: Optionally include one or more additional values. If more than

one num-date-dur value is specified, all must be of the same type.
Usage Notes
ÂÂ It is appropriate to use STDEVP when the specified values represent the entire
collection or population. If the values you are analyzing represent only a sample of a
larger population, use the STDEV function.
ÂÂ If you want to include text or Boolean values in the computation, use the STDEVPA

function.
ÂÂ The standard deviation is the square root of the variance returned by the VARP

function.
Example
Assume you have administered five tests to a group of students. You have a very small class and
this represents the total population of your students. Using this population data, you could use the
STDEVP function to determine which test had the widest dispersion of test scores.
The results of the STDEVP functions are approximately 20.3961, 21.9454, 8.49994, 7.2222, and 2.9933.
So test 2 had the highest dispersion, followed closely by test 1. The other three tests had low
dispersion.
Test 1

Test 2

Test 3

Test 4

Test 5

Student 1

75

82

90

78

84

Student 2

100

90

95

88

90

Student 3

40

80

78

90

85

Student 4

80

35

95

98

92

Student 5

75

82

90

78

84

=STDEVP(B2:B6)

=STDEVP(C2:C6)

=STDEVP(D2:D6)

=STDEVP(E2:E6)

=STDEVP(F2:F6)

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Related Topics
For related functions and additional information, see:
“STDEV” on page 290
“STDEVA” on page 291
“STDEVPA” on page 294
“VAR” on page 298
“VARA” on page 300
“VARP” on page 302
“VARPA” on page 303
“Survey Results Example” on page 362
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

STDEVPA

The STDEVPA function returns the standard deviation, a measure of dispersion, of a
collection of values that may include text and Boolean values, based on the population
(true) variance.
STDEVPA(value, value…)
ÂÂ value:  A value. value can contain any value type.
ÂÂ value…: Optionally include one or more additional values. All numeric values must

be of the same type. You cannot mix numbers, dates, and duration values.
Usage Notes
ÂÂ It is appropriate to use STDEVPA when the specified values represent the entire
collection or population. If the values you are analyzing represent only a sample of a
larger population, use the STDEVA function.
ÂÂ STDEVPA assigns a value of 0 to any text value, 0 to the Boolean value FALSE, and 1

to the Boolean value TRUE and includes them in the computation. Empty cells are
ignored. If you do not want to include text or Boolean values in the computation,
use the STDEVP function.

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ÂÂ The standard deviation is the square root of the variance returned by the VARPA

function.
Example
Assume you have installed a temperature sensor in Cupertino, California. The sensor records each
day’s high and low temperatures. In addition, you have kept a record of each day you turned on the
air conditioner in your condo. The sensor failed after the first few days so the following table is the
population of high and low temperatures.

=STDEVPA(B2:B13) returns 23.7702, the dispersion as measured by STDEVPA, of the sample of daily
high temperatures.
It exceeds the actual range of high temperatures of 15 degrees because the “unavailable” temperature
is given a value of zero.

Related Topics
For related functions and additional information, see:
“STDEV” on page 290
“STDEVA” on page 291
“STDEVP” on page 293
“VAR” on page 298
“VARA” on page 300
“VARP” on page 302
“VARPA” on page 303
“Survey Results Example” on page 362
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
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“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

TDIST

The TDIST function returns the probability from the student’s t-distribution.
TDIST(non-neg-x-value, degrees-freedom, tails)
ÂÂ non-neg-x-value:  The value at which you want to evaluate the function. non-neg-x-

value is a number value that must be greater than or equal to 0.
ÂÂ degrees-freedom:  Degrees of freedom. degrees-freedom is a number value and

must be greater than or equal to 1.
ÂÂ tails:  The number of tails to return.

one tail (1):  Return the value for a one-tailed distribution.
two tails (2):  Return the value for a two-tailed distribution.
Examples
=TDIST(4, 2, 1) returns 0.0285954792089682, for the one-tailed distribution.
=TDIST(4, 2, 2) returns 0.0571909584179364, for the two-tailed distribution.

Related Topics
For related functions and additional information, see:
“TINV” on page 297
“TTEST” on page 297
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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TINV

The TINV function returns the t value (a function of the probability and degrees of
freedom) from the student’s t-distribution.
TINV(probability, degrees-freedom)
ÂÂ probability:  A probability associated with the distribution. probability is a number

value and must be greater than 0 and less than 1.
ÂÂ degrees-freedom:  Degrees of freedom. degrees-freedom is a number value and

must be greater than or equal to 1.
Example
=TINV(0.88, 2) returns 0.170940864689457.

Related Topics
For related functions and additional information, see:
“TDIST” on page 296
“TTEST” on page 297
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

TTEST

The TTEST function returns the probability associated with a student’s t-test, based on
the t-distribution function.
TTEST(sample-1-values, sample-2-values, tails, test-type)
ÂÂ sample-1-values:  The collection containing the first collection of sample values.

sample-1-values is a collection containing numbers.
ÂÂ sample-2-values:  The collection containing the second collection of sample values.

sample-2-values is a collection containing number values.
ÂÂ tails:  The number of tails to return.

one tail (1):  Returns the value for a one-tailed distribution.
two tails (2):  Returns the value for a two-tailed distribution.
ÂÂ test-type:  The type of t-test to perform.

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paired (1):  Perform a paired test.
two-sample equal (2):  Perform a two-sample equal variance (homoscedastic) test.
two-sample unequal (3):  Perform a two-sample unequal variance (heteroscedastic)
test.
Examples
=TTEST({57, 75, 66, 98, 92, 80}, {87, 65, 45, 95, 88, 79}, 1, 1) returns 0.418946725989974, for the one-tailed,
paired test.
=TTEST({57, 75, 66, 98, 92, 80}, {87, 65, 45, 95, 88, 79}, 2, 1) returns 0.837893451979947 for the two-tailed,
paired test.
=TTEST({57, 75, 66, 98, 92, 80}, {87, 65, 45, 95, 88, 79}, 1, 2) returns 0.440983897602811 for the one-tailed,
two sample equal test.
=TTEST({57, 75, 66, 98, 92, 80}, {87, 65, 45, 95, 88, 79}, 2, 2) returns 0.881967795205622 for the two-tailed,
two sample equal test.
=TTEST({57, 75, 66, 98, 92, 80}, {87, 65, 45, 95, 88, 79}, 1, 3) returns 0.441031763311189 for the one-tailed,
two sample unequal test.

Related Topics
For related functions and additional information, see:
“TDIST” on page 296
“TINV” on page 297
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

VAR

The VAR function returns the sample (unbiased) variance, a measure of dispersion, of a
collection of values.
VAR(num-date, num-date…)
ÂÂ num-date:  A value. num-date is a number value or a date/time value.
ÂÂ num-date…: Optionally include one or more additional values. If more than one

num-date-dur value is specified, they must all be of the same type.

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Usage Notes
ÂÂ The VAR function finds the sample (unbiased) variance by dividing the sum of the
squares of the deviations of the data points by one less than the number of values.
ÂÂ It is appropriate to use VAR when the specified values represent only a sample of a

larger population. If the values you are analyzing represent the entire collection or
population, use the VARP function.
ÂÂ If you want to include text or Boolean values in the computation, use the VARA function.
ÂÂ The square root of the variance returned by the VAR function is returned by the

STDEV function.
Examples
Assume you have administered five tests to a group of students. You have arbitrarily selected five
students to represent the total population of students (note that this is an example only; this would
not likely be statistically valid). Using the sample data, you could use the VAR function to determine
which test had the widest dispersion of test scores.
The results of the VAR functions are approximately 520.00, 602.00, 90.30, 65.20, and 11.20. So test 2
had the highest dispersion, followed closely by test 1. The other three tests had low dispersion.
Test 1

Test 2

Test 3

Test 4

Test 5

Student 1

75

82

90

78

84

Student 2

100

90

95

88

90

Student 3

40

80

78

90

85

Student 4

80

35

95

98

92

Student 5

75

82

90

78

84

=VAR(B2:B6)

=VAR(C2:C6)

=VAR(D2:D6)

=VAR(E2:E6)

=VAR(F2:F6)

Related Topics
For related functions and additional information, see:
“STDEV” on page 290
“STDEVA” on page 291
“STDEVP” on page 293
“STDEVPA” on page 294
“VARA” on page 300
“VARP” on page 302
“VARPA” on page 303
“Survey Results Example” on page 362

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“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

VARA

The VARA function returns the sample (unbiased) variance, a measure of dispersion, of
a collection of values, including text and Boolean values.
VARA(value, value…)
ÂÂ value:  A value. value can contain any value type.
ÂÂ value…: Optionally include one or more additional values. All numeric values must

be of the same type. You cannot mix numbers, dates, and duration values.
Usage Notes
ÂÂ The VARA function finds the sample (unbiased) variance by dividing the sum of the
squares of the deviations of the data points by one less than the number of values.
ÂÂ It is appropriate to use VARA when the specified values represent only a sample of

a larger population. If the values you are analyzing represent the entire collection or
population, use the VARPA function.
ÂÂ VARA assigns a value of 0 to any text value, 0 to the Boolean value FALSE, and 1

to the Boolean value TRUE and includes them in the computation. Empty cells are
ignored. If you do not want to include text or Boolean values in the computation,
use the VAR function.
ÂÂ The square root of the variance returned by the VARA function is returned by the

STDEVA function.

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Example
Assume you have installed a temperature sensor in Cupertino, California. The sensor records each
day’s high and low temperatures. In addition, you have kept a record of each day you turned on the
air conditioner in your condo. The data from the first few days is shown in the following table and is
used as a sample for the population of high and low temperatures (note that this is an example only;
this would not be statistically valid).

=VARA(B2:B13) returns 616.3864, the dispersion as measured by VARA, of the sample of daily high
temperatures.

Related Topics
For related functions and additional information, see:
“STDEV” on page 290
“STDEVA” on page 291
“STDEVP” on page 293
“STDEVPA” on page 294
“VAR” on page 298
“VARP” on page 302
“VARPA” on page 303
“Survey Results Example” on page 362
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41
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VARP

The VARP function returns the population (true) variance, a measure of dispersion, of a
collection of values.
VARP(num-date, num-date…)
ÂÂ num-date:  A value. num-date is a number value or a date/time value.
ÂÂ num-date…: Optionally include one or more additional values. If more than one

num-date value is specified, all must be of the same type.
Usage Notes
ÂÂ The VARP function finds the population, or true, variance (as opposed to the sample,
or unbiased, variance) by dividing the sum of the squares of the deviations of the
data points by the number of values.
ÂÂ It is appropriate to use VARP when the specified values represent the entire

collection or population. If the values you are analyzing represent only a sample of a
larger population, use the VAR function.
ÂÂ If you want to include text or Boolean values in the computation, use the VARPA

function.
ÂÂ The square root of the variance returned by the VARP function is returned by the

STDEVP function.
Example
Assume you have administered five tests to a group of students. You have a very small class and this
represents the total population of your students. Using this population data, you could use the VARP
function to determine which test had the widest dispersion of test scores.
The results of the VARP functions are approximately 416.00, 481.60, 72.24, 52.16, and 8.96. So test 2 had
the highest dispersion, followed closely by test 1. The other three tests had low dispersion.
Test 1

Test 2

Test 3

Test 4

Test 5

Student 1

75

82

90

78

84

Student 2

100

90

95

88

90

Student 3

40

80

78

90

85

Student 4

80

35

95

98

92

Student 5

75

82

90

78

84

=VARP(B2:B6)

=VARP(C2:C6)

=VARP(D2:D6)

=VARP(E2:E6)

=VARP(F2:F6)

Related Topics
For related functions and additional information, see:
“STDEV” on page 290
“STDEVA” on page 291

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“STDEVP” on page 293
“STDEVPA” on page 294
“VAR” on page 298
“VARA” on page 300
“VARPA” on page 303
“Survey Results Example” on page 362
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

VARPA

The VARPA function returns the sample (unbiased) variance, a measure of dispersion, of
a collection of values, including text and Boolean values.
VARPA(value, value…)
ÂÂ value:  A value. value can contain any value type.
ÂÂ value…: Optionally include one or more additional values. All numeric values must

be of the same type. You cannot mix numbers, dates, and duration values.
Usage Notes
ÂÂ The VARPA function finds the population, or true, variance (as opposed to the
sample, or unbiased, variance) by dividing the sum of the squares of the deviations
of the data points.
ÂÂ It is appropriate to use VARPA when the specified values represent the entire

collection or population. If the values you are analyzing represent only a sample of a
larger population, use the VARA function.
ÂÂ VARPA assigns a value of 0 to any text value, 0 to the Boolean value FALSE, and 1

to the Boolean value TRUE and includes them in the computation. Empty cells are
ignored. If you do not want to include text or Boolean values in the computation,
use the VAR function.
ÂÂ The square root of the variance returned by the VARPA function is returned by the

STDEVPA function.

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Example
Assume you have installed a temperature sensor in Cupertino, California. The sensor records each
day’s high and low temperatures. In addition, you have kept a record of each day you turned on the
air conditioner in your condo. The sensor failed after the first few days so the following table is the
population of high and low temperatures.

=VARPA(B2:B13) returns 565.0208, the dispersion as measured by VARPA, of the sample of daily high
temperatures.

Related Topics
For related functions and additional information, see:
“STDEV” on page 290
“STDEVA” on page 291
“STDEVP” on page 293
“STDEVPA” on page 294
“VAR” on page 298
“VARA” on page 300
“VARP” on page 302
“Survey Results Example” on page 362
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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ZTEST

The ZTEST function returns the one-tailed probability value of the Z-test.
ZTEST(num-date-dur-set, num-date-dur, stdev)
ÂÂ num-date-dur-set:  A collection of values. num-date-dur-set is a collection

containing number, date, or duration values. All values must be of the same type.
ÂÂ num-date-dur:  A value. num-date-dur is a number value, a date/time value, or a

duration value.num-date-dur is the value to test.
ÂÂ stdev:  An optional value for the standard deviation of the population. stdev is a

number value and must be greater than 0.
Usage Notes
ÂÂ The Z-test is a statistical test which determines if the difference between a sample
mean and the population mean is large enough to be statistically significant. The
Z-test is used primarily with standardized testing.
ÂÂ If stdev is omitted, the assumed sample standard deviation is used.
Example
=ZTEST({57, 75, 66, 98, 92, 80}, 70, 9) returns 0.0147281928162857.

Related Topics
For related functions and additional information, see:
“STANDARDIZE” on page 289
“Listing of Statistical Functions” on page 225
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 10    Statistical Functions

305

11

Text Functions

The text functions help you work with strings of characters.
Listing of Text Functions

iWork provides these text functions for use with tables.

306

Function

Description

“CHAR” (page 308)

The CHAR function returns the character that
corresponds to a decimal Unicode character
code.

“CLEAN” (page 308)

The CLEAN function removes most common
nonprinting characters (Unicode character codes
0–31) from text.

“CODE” (page 309)

The CODE function returns the decimal Unicode
number of the first character in a specified string.

“CONCATENATE” (page 310)

The CONCATENATE function joins (concatenates)
strings.

“DOLLAR” (page 311)

The DOLLAR function returns a string formatted
as a dollar amount from a given number.

“EXACT” (page 312)

The EXACT function returns TRUE if the argument
strings are identical in case and content.

“FIND” (page 312)

The FIND function returns the starting position of
one string within another.

“FIXED” (page 313)

The FIXED function rounds a number to the
specified number of decimal places and then
returns the result as a string value.

“LEFT” (page 314)

The LEFT function returns a string consisting of
the specified number of characters from the left
end of a given string.

Function

Description

“LEN” (page 315)

The LEN function returns the number of
characters in a string.

“LOWER” (page 316)

The LOWER function returns a string that is
entirely lowercase, regardless of the case of the
characters in the specified string.

“MID” (page 316)

The MID function returns a string consisting of
the given number of characters from a string
starting at the specified position.

“PROPER” (page 317)

The PROPER function returns a string where
the first letter of each word is uppercase and all
remaining characters are lowercase, regardless of
the case of the characters in the specified string.

“REPLACE” (page 318)

The REPLACE function returns a string where a
specified number of characters of a given string
have been replaced with a new string.

“REPT” (page 319)

The REPT function returns a string that contains
a given string repeated a specified number of
times.

“RIGHT” (page 319)

The RIGHT function returns a string consisting of
the given number of characters from the right
end of a specified string.

“SEARCH” (page 320)

The SEARCH function returns the starting
position of one string within another, ignoring
case and allowing wildcards.

“SUBSTITUTE” (page 322)

The SUBSTITUTE function returns a string where
the specified characters of a given string have
been replaced with a new string.

“T” (page 323)

The T function returns the text contained in a
cell. This function is included for compatibility
with tables imported from other spreadsheet
applications.

“TRIM” (page 323)

The TRIM function returns a string based on a
given string, after removing extra spaces.

“UPPER” (page 324)

The UPPER function returns a string that is
entirely uppercase, regardless of the case of the
characters in the specified string.

“VALUE” (page 325)

The VALUE function returns a number value even
if the argument is formatted as text.

Chapter 11    Text Functions

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CHAR

The CHAR function returns the character that corresponds to a decimal Unicode
character code.
CHAR(code-number)
ÂÂ code-number:  A number for which you want to return the corresponding Unicode

character. code-number is a number value and must be greater than or equal to 32,
less than or equal to 65,535, and not equal to 127. If there is a decimal portion, it is
ignored. Note that character 32 is the space character.
Usage Notes
ÂÂ Not all Unicode numbers are associated with a printable character.
ÂÂ You can use the Special Characters window, which is available on the Edit menu, to

view entire sets of characters and their codes.
ÂÂ The CODE function returns the numeric code for a specific character.
Examples
=CHAR(98.6) returns “b”, which is represented by the code 98. The decimal portion of the number is
ignored.
=CODE(”b”) returns 98.

Related Topics
For related functions and additional information, see:
“CODE” on page 309
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

CLEAN

The CLEAN function removes most common nonprinting characters (Unicode
character codes 0–31) from text.
CLEAN(text)
ÂÂ text:  The text from which you want to remove nonprinting characters. text can

contain any value type.

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Usage Notes
ÂÂ This can be helpful if text you paste from another application contains unwanted
question marks, spaces, boxes, or other unexpected characters.
ÂÂ There are some less common nonprinting characters that are not removed by

CLEAN (character codes 127, 129, 141, 143, 144, and 157). To remove these, you can use
the SUBSTITUTE function to replace them with a code in the range 0–31 before you
use the CLEAN function.
ÂÂ You can use the TRIM function to remove extra spaces in text.
Example
Suppose you copy what you believe to be the text “a b c d e f” from another application and paste
it into cell A1, but instead see “a b c ? ?d e f”. You can try using CLEAN to remove the unexpected
characters:
=CLEAN(A1) returns “a b c d e f”.

Related Topics
For related functions and additional information, see:
“SUBSTITUTE” on page 322
“TRIM” on page 323
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

CODE

The CODE function returns the decimal Unicode number of the first character in a
specified string.
CODE(code-string)
ÂÂ code-string:  The string from which to return the Unicode value. code-string is a

string value. Only the first character is used.
Usage Notes
ÂÂ You can use the Special Characters window, which is available on the Edit menu, to
view entire sets of characters and their codes.

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ÂÂ You can use the CHAR function to do the opposite of the CODE function:  convert a

numeric code into a text character.
Examples
=CODE(”A”) returns 65, the character code for uppercase “A”.
=CODE(”abc”) returns 97 for lowercase “a”.
=CHAR(97) returns “a”.
=CODE(A3) returns 102 for lowercase “f”.
=CODE(”三二一”) returns 19,977, the decimal Unicode value of the first character.

Related Topics
For related functions and additional information, see:
“CHAR” on page 308
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

CONCATENATE

The CONCATENATE function joins (concatenates) strings.
CONCATENATE(string, string…)
ÂÂ string:  A string. string is a string value.
ÂÂ string…: Optionally include one or more additional strings.

Usage Notes
ÂÂ As an alternative to the CONCATENATE function, you can use the & string operator
to concatenate strings.
Examples
If cell A1 contains Lorem and cell B1 contains Ipsum, =CONCATENATE(B1, “, “, A1) returns “Ipsum,
Lorem”.
=CONCATENATE(”a”, “b”, “c”) returns “abc”.
=”a”&”b”&”c” returns “abc”.

Related Topics
For related functions and additional information, see:
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“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

DOLLAR

The DOLLAR function returns a string formatted as a dollar amount from a given
number.
DOLLAR(num, places)
ÂÂ num:  The number to be used. num is a number value.
ÂÂ places:  An optional argument specifying the number of places to the right, or left,

of the decimal point at which rounding should occur. places is a number value.
When rounding to the specified number of places, standard arithmetical rounding is
used; if the most significant digit being dropped is 5 or greater, the result is rounded
up. A negative number indicates rounding should occur to the left of the decimal
(for example, round to hundreds or thousands).
Examples
=DOLLAR(2323.124) returns $2,323.12.
=DOLLAR(2323.125) returns $2,323.13.
=DOLLAR(99.554, 0) returns $100.
=DOLLAR(12, 3) returns $12.000.
=DOLLAR(-12, 3) returns ($12.000), with parentheses indicating a negative amount.
=DOLLAR(123, -1) returns $120.

Related Topics
For related functions and additional information, see:
“FIXED” on page 313
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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EXACT

The EXACT function returns TRUE if the argument strings are identical in case and
content.
EXACT(string-1, string-2)
ÂÂ string-1:  The first string. string-1 is a string value.
ÂÂ string-2:  The second string. string-2 is a string value.
Examples
=EXACT(”toledo”, “toledo”) returns TRUE, since all the characters and their cases are identical.
=EXACT(”Toledo”, “toledo”) returns FALSE, since the case of the two strings is not identical.

Related Topics
For related functions and additional information, see:
“FIND” on page 312
“SEARCH” on page 320
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

FIND

The FIND function returns the starting position of one string within another.
FIND(search-string, source-string, start-pos)
ÂÂ search-string:  The string to find. search-string is a string value.
ÂÂ source-string:  A string. source-string is a string value.
ÂÂ start-pos:  An optional argument that specifies the position within the specified

string at which the action should begin. start-pos is a number value that must be
greater than or equal to 1 and less than or equal to the number of characters in
source-string.
Notes
ÂÂ The search is case sensitive and spaces are counted. Wildcards are not allowed. To
use wildcards or to ignore case in your search, use the SEARCH function.

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ÂÂ Specifying start-pos permits you to begin the search for search-string within, rather

than at the beginning of, source-string. This is particularly useful if source-string may
contain multiple instances of search-string and you wish to determine the starting
position of other than the first instance. If start-pos is omitted, it is assumed to be 1.
Examples
=FIND(”e”, “where on earth”) returns 3 (”e” is the third character in the string “where on earth”).
=FIND(”e”, “where on earth”, 8) returns 10 (”e” in earth is the first “e” found starting from character 8, the
“n” in “on”).

Related Topics
For related functions and additional information, see:
“EXACT” on page 312
“SEARCH” on page 320
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

FIXED

The FIXED function rounds a number to the specified number of decimal places and
then returns the result as a string value.
FIXED(num, places, no-commas)
ÂÂ num:  The number to be used. num is a number value.
ÂÂ places:  An optional argument indicating the number of places to the right, or left,

of the decimal point at which rounding should occur. places is a number value.
When rounding to the specified number of places, round-half-up is used. If the most
significant digit being dropped is 5 or greater, the result is rounded up. A negative
number indicates rounding should occur to the left of the decimal (for example,
round to hundreds or thousands).
ÂÂ no-commas:  An optional argument indicating whether to use position separators in

the whole portion of the resulting number.
use commas (FALSE, 0, or omitted):  Include position separators in the result.
no commas (TRUE or 1):  Don’t include position separators in the result.

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Examples
=FIXED(6789.123, 2) returns “6,789.12.”
=FIXED(6789.123, 1, 1) returns “6789.1.”
=FIXED(6789.123, -2) returns “6,800.”
=FIXED(12.4, 0) returns “12.”
=FIXED(12.5, 0) returns “13.”
=FIXED(4, -1) returns “0.”
=FIXED(5, -1) returns “10.”

Related Topics
For related functions and additional information, see:
“DOLLAR” on page 311
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

LEFT

The LEFT function returns a string consisting of the specified number of characters
from the left end of a given string.
LEFT(source-string, string-length)
ÂÂ source-string:  A string. source-string is a string value.
ÂÂ string-length:  An optional argument specifying the desired length of the returned

string. string-length is a number value and must be greater than or equal to 1.
Usage Notes
ÂÂ If string-length is greater than or equal to the length of source-string, the string
returned is equal to source-string.
Examples
=LEFT(”one two three”, 2) returns “on”.
=LEFT(”abc”) returns “a”.

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Related Topics
For related functions and additional information, see:
“MID” on page 316
“RIGHT” on page 319
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

LEN

The LEN function returns the number of characters in a string.
LEN(source-string)
ÂÂ source-string:  A string. source-string is a string value.

Usage Notes
ÂÂ The count includes all spaces, numbers, and special characters.
Examples
=LEN(”12345”) returns 5.
=LEN(” abc def “) returns 9, the sum of the six letters plus the leading, trailing, and separating spaces.

Related Topics
For related functions and additional information, see:
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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315

LOWER

The LOWER function returns a string that is entirely lowercase, regardless of the case of
the characters in the specified string.
LOWER(source-string)
ÂÂ source-string:  A string. source-string is a string value.
Examples
=LOWER(”UPPER”) returns “upper”.
=LOWER(”Lower”) returns “lower”.
=LOWER(”MiXeD”) returns “mixed”.

Related Topics
For related functions and additional information, see:
“PROPER” on page 317
“UPPER” on page 324
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

MID

The MID function returns a string consisting of the given number of characters from a
string starting at the specified position.
MID(source-string, start-pos, string-length)
ÂÂ source-string:  A string. source-string is a string value.
ÂÂ start-pos:  The position within the specified string at which the action should begin.

start-pos is a number value that must be greater than or equal to 1 and less than or
equal to the number of characters in source-string.
ÂÂ string-length:  The desired length of the returned string. string-length is a number

value and must be greater than or equal to 1.
Usage Notes
ÂÂ If string-length is greater than or equal to the length of source-string, the string
returned is equal to source-string, beginning at start-pos.

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Examples
=MID(”lorem ipsum dolor sit amet”, 7, 5) returns “ipsum”.
=MID(”1234567890”, 4, 3) returns “456”.
=MID(”shorten”, 5, 20) returns “ten”.

Related Topics
For related functions and additional information, see:
“LEFT” on page 314
“RIGHT” on page 319
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

PROPER

The PROPER function returns a string where the first letter of each word is uppercase
and all remaining characters are lowercase, regardless of the case of the characters in
the specified string.
PROPER(source-string)
ÂÂ source-string:  A string. source-string is a string value.

Usage Notes
ÂÂ Any character following a nonalphabetic character, except apostrophe (‘), is
treated as the first letter in a word. So, for example, any letter following a hyphen is
capitalized.
Examples
=PROPER(”lorem ipsum”) returns “Lorem Ipsum”.
=PROPER(”lorem’s ip-sum”) returns “Lorem’s Ip-Sum”.
=PROPER(”1a23 b456”) returns “1A23 B456”.

Related Topics
For related functions and additional information, see:
“LOWER” on page 316

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“UPPER” on page 324
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

REPLACE

The REPLACE function returns a string where a specified number of characters of a
given string have been replaced with a new string.
REPLACE(source-string, start-pos, replace-length, new-string)
ÂÂ source-string:  A string. source-string is a string value.
ÂÂ start-pos:  The position within the specified string at which the action should begin.

start-pos is a number value that must be greater than or equal to 1. If start-pos is
greater than the number of characters in source-string, new-string is added to the
end of source-string.
ÂÂ replace-length:  The number of characters to be replaced. replace-length is a number

value that must be greater than or equal to 1. If replace-length is greater than or equal
to the length of source-string, the returned string is equal to new-string.
ÂÂ new-string:  The text used as a replacement for the section of the given string that

is replaced. new-string is a string value. It does not have to be the same length as
the text replaced.
Example
=REPLACE(”received applicant’s forms”, 10, 9, “Frank”) returns “received Frank’s forms”.

Related Topics
For related functions and additional information, see:
“SUBSTITUTE” on page 322
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41
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REPT

The REPT function returns a string that contains a given string repeated a specified
number of times.
REPT(source-string, repeat-number)
ÂÂ source-string:  A string. source-string is a string value.
ÂÂ repeat-number:  The number of times the given string should be repeated. repeat-

number is a number value that must be greater than or equal to 0.
Examples
=REPT(”*”, 5) returns “*****”.
=REPT(”ha”, 3) returns “hahaha”.

Related Topics
For related functions and additional information, see:
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

RIGHT

The RIGHT function returns a string consisting of the specified number of characters
from the right end of a given string.
RIGHT(source-string, string-length)
ÂÂ source-string:  A string. source-string is a string value.
ÂÂ string-length:  An optional argument specifying the desired length of the returned

string. string-length is a number value and must be greater than or equal to 1.
Usage Notes
ÂÂ If string-length is greater than or equal to the length of source-string, the string
returned is equal to source-string.
Examples
=RIGHT(”one two three”, 2) returns “ee”.
=RIGHT(”abc”) returns “c”.

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Related Topics
For related functions and additional information, see:
“LEFT” on page 314
“MID” on page 316
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

SEARCH

The SEARCH function returns the starting position of one string within another,
ignoring case and allowing wildcards.
SEARCH(search-string, source-string, start-pos)
ÂÂ search-string:  The string to find. search-string is a string value.
ÂÂ source-string:  A string. source-string is a string value.
ÂÂ start-pos:  An optional argument that specifies the position within the specified

string at which the action should begin. start-pos is a number value that must be
greater than or equal to 1 and less than or equal to the number of characters in
source-string.
Usage Notes
ÂÂ Wildcards are permitted in search-string. In search-string, use an * (asterisk) to match
multiple characters or a ? (question mark) to match any single character in sourcestring.
ÂÂ Specifying start-pos permits you to begin the search for search-string within, rather

than at the beginning of, source-string. This is particularly useful if source-string may
contain multiple instances of search-string and you wish to determine the starting
position of other than the first instance. If start-pos is omitted, it is assumed to be 1.
ÂÂ To have case considered in your search, use the FIND function.

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Examples
=SEARCH(”ra”, “abracadabra”) returns 3; the first occurrence of the string “ra” starts at the third
character in “abracadabra”.
=SEARCH(”ra”, “abracadabra”, 5) returns 10, the position of the first occurrence of string “ra” when you
start looking at position 5.
=SEARCH(“*card”, “Wildcard”) returns 1, since the asterisk at the beginning of the search string
matches all the characters before “card”.
=SEARCH(“*cad”, “Wildcard”) returns an error, since the string “cad” does not exist.
=SEARCH(“?card”, “Wildcard”) returns 4, since the question mark matches the one character
immediately preceding “card”.
=SEARCH(“c*d”, “Wildcard”) returns 5, since the asterisk matches all the characters between the “c” and
“d”.
=SEARCH(“~?”, “Wildcard? No.”) returns 9, since the tilde means to interpret the next character (the
question mark) literally, not as a wildcard, and the question mark is the 9th character.

Related Topics
For related functions and additional information, see:
“EXACT” on page 312
“FIND” on page 312
“Specifying Conditions and Using Wildcards” on page 360
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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SUBSTITUTE

The SUBSTITUTE function returns a string where the specified characters of a given
string have been replaced with a new string.
SUBSTITUTE(source-string, existing-string, new-string, occurrence)
ÂÂ source-string:  A string. source-string is a string value.
ÂÂ existing-string:  The string within the given string that is to be replaced. existing-

string is a string value.
ÂÂ new-string:  The text used as a replacement for the section of the given string that

is replaced. new-string is a string value. It does not have to be the same length as
the text replaced.
ÂÂ occurrence:  An optional value specifying the occurrence that should be replaced.

occurrence is a number value and must be greater than or equal to 1, or omitted.
If greater than the number of times existing-string appears within source-string, no
replacement will occur. If omitted, all occurrences of existing-string within sourcestring will be replaced by new-string.
Usage Notes
ÂÂ You can replace individual characters, whole words, or strings of characters within
words.
Examples
=SUBSTITUTE(”a b c d e f”, “b”, “B”) returns “a B c d e f”.
=SUBSTITUTE(”a a b b b c”, “a”, “A”, 2) returns “a A b b b c”.
=SUBSTITUTE(”a a b b b c”, “b”, “B”) returns “a a B B B c”.
=SUBSTITUTE(”aaabbccc”, “bc”, “BC”, 2) returns “aaabbccc”.

Related Topics
For related functions and additional information, see:
“REPLACE” on page 318
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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T

The T function returns the text contained in a cell. This function is included for
compatibility with tables imported from other spreadsheet applications.
T(cell)
ÂÂ cell:  A reference to a single table cell. cell is a reference value to a single cell that

can contain any value, or be empty.
Usage Notes
ÂÂ If the cell doesn’t contain a string, T returns an empty string.
Examples
If cell A1 contains “text” and cell B1 is empty:
=T(A1) returns “text”
=T(B1) returns nothing.

Related Topics
For related functions and additional information, see:
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

TRIM

The TRIM function returns a string based on a given string, after removing extra spaces.
TRIM(source-string)
ÂÂ source-string:  A string. source-string is a string value.

Usage Notes
ÂÂ TRIM removes all spaces before the first character, all spaces after the last character,
and all duplicate spaces between characters, leaving only single spaces between
words.
Example
=TRIM(” spaces spaces spaces “) returns “spaces spaces spaces” (the leading and trailing space were
removed).

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Related Topics
For related functions and additional information, see:
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

UPPER

The UPPER function returns a string that is entirely uppercase, regardless of the case of
the characters in the specified string.
UPPER(source-string)
ÂÂ source-string:  A string. source-string is a string value.
Examples
=UPPER(”a b c”) returns “A B C”.
=UPPER(”First”) returns “FIRST”.

Related Topics
For related functions and additional information, see:
“LOWER” on page 316
“PROPER” on page 317
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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VALUE

The VALUE function returns a number value even if the argument is formatted as
text. This function is included for compatibility with tables imported from other
spreadsheet applications.
VALUE(source-string)
ÂÂ source-string:  A string. source-string is a string value.

Usage Notes
ÂÂ You’ll never need to use the VALUE function in a new table, as numbers in text are
automatically converted for you.
ÂÂ Only the formatted text is converted. For example, if the string $100.001 is typed into

a cell, the default format will display only two decimals ($100.00). If VALUE refers to
this cell, it will return 100, the value of the formatted text, not 100.001.
ÂÂ If the argument can’t be returned as a number value (does not contain a number),

the function returns an error.
Examples
=VALUE(”22”) returns the number 22.
=VALUE(RIGHT(”The year 1953”, 2)) returns the number 53.

Related Topics
For related functions and additional information, see:
“Listing of Text Functions” on page 306
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 11    Text Functions

325

Trigonometric Functions

12

The trigonometric functions help you work with angles and
their components.
Listing of Trigonometric Functions

iWork provides these trigonometric functions for use with tables.

326

Function

Description

“ACOS” (page 327)

The ACOS function returns the inverse cosine
(arccosine) of a number.

“ACOSH” (page 328)

The ACOSH function returns the inverse
hyperbolic cosine (hyperbolic arccosine) of a
number.

“ASIN” (page 329)

The ASIN function returns the arcsine (the inverse
sine) of a number.

“ASINH” (page 329)

The ASINH function returns the inverse
hyperbolic sine of a number.

“ATAN” (page 330)

The ATAN function returns the inverse tangent
(arctangent) of a number.

“ATAN2” (page 331)

The ATAN2 function returns the angle, relative to
the positive x-axis, of the line passing through
the origin and the specified point.

“ATANH” (page 332)

The ATANH function returns the inverse
hyperbolic tangent of a number.

“COS” (page 333)

The COS function returns the cosine of an angle
that is expressed in radians.

“COSH” (page 334)

The COSH function returns the hyperbolic cosine
of a number.

Function

Description

“DEGREES” (page 334)

The DEGREES function returns the number of
degrees in an angle expressed in radians.

“RADIANS” (page 335)

The RADIANS function returns the number of
radians in an angle expressed in degrees.

“SIN” (page 336)

The SIN function returns the sine of an angle that
is expressed in radians.

“SINH” (page 337)

The SINH function returns the hyperbolic sine of
the specified number.

“TAN” (page 338)

The TAN function returns the tangent of an angle
that is expressed in radians.

“TANH” (page 339)

The TANH function returns the hyperbolic
tangent of the specified number.

ACOS

The ACOS function returns the inverse cosine (arccosine) of a number.
ACOS(num)
ÂÂ num:  A number. num is a number value in the range –1 to 1.

Usage Notes
ÂÂ The ACOS function takes a cosine value and returns a corresponding angle. The
resulting angle is expressed in radians, in the range 0 to π (pi). To see the resulting
angle in degrees instead of radians, wrap this function in the DEGREES function;
that is, =DEGREES(ACOS(num)).
Examples
=ACOS(SQRT(2)/2) returns 0.785398163397448, which is approximately π/4.
=ACOS(0.54030230586814) returns 1.
=DEGREES(ACOS(.5)) returns 60, the degree measure of an angle that has a cosine of 0.5.

Related Topics
For related functions and additional information, see:
“ACOSH” on page 328
“COS” on page 333
“COSH” on page 334
“DEGREES” on page 334
“Listing of Trigonometric Functions” on page 326
Chapter 12    Trigonometric Functions

327

“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

ACOSH

The ACOSH function returns the inverse hyperbolic cosine (hyperbolic arccosine) of a
number.
ACOSH(num)
ÂÂ num:  A number. num is a number value that must be greater than or equal to 1.
Examples
=ACOSH(10.0676619957778) returns 3.
=ACOSH(COSH(5)) returns 5.

Related Topics
For related functions and additional information, see:
“ACOS” on page 327
“COS” on page 333
“COSH” on page 334
“Listing of Trigonometric Functions” on page 326
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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ASIN

The ASIN function returns the arcsine (the inverse sine) of a number.
ASIN(num)
ÂÂ num:  A number. num is a number value that must be greater than or equal to 1.

Usage Notes
ÂÂ The ASIN function takes a sine and returns the corresponding angle. The result
is expressed in radians, in the range –pi/2 to +pi/2. To see the resulting angle in
degrees instead of radians, wrap this function in the DEGREES function; that is,
=DEGREES(ASIN(num)).
Examples
=ASIN(0.841470985) returns 1, the radian measure (approximately 57.3 degrees) of the angle that has
a sine of 0.8411470984807897.
=DEGREES(ASIN(0.5)) returns 30, the degree measure of the angle that has a sine of 0.5.

Related Topics
For related functions and additional information, see:
“ASINH” on page 329
“DEGREES” on page 334
“SIN” on page 336
“SINH” on page 337
“Listing of Trigonometric Functions” on page 326
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

ASINH

The ASINH function returns the inverse hyperbolic sine of a number.
ASINH(num)
ÂÂ num:  A number. num is a number value.

Chapter 12    Trigonometric Functions

329

Examples
=ASINH(27.2899171971277) returns 4.
=ASINH(SINH(1)) returns 1.

Related Topics
For related functions and additional information, see:
“ASIN” on page 329
“SIN” on page 336
“SINH” on page 337
“Listing of Trigonometric Functions” on page 326
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

ATAN

The ATAN function returns the inverse tangent (arctangent) of a number.
ATAN(num)
ÂÂ num:  A number. num is a number value.

Usage Notes
ÂÂ The ATAN function takes a tangent and returns the corresponding angle,
expressed in radians in the range –pi/2 to +pi/2. To see the resulting angle in
degrees instead of radians, wrap this function in the DEGREES function; that is,
=DEGREES(ATAN(num)).
Examples
=ATAN(1) returns the angle measure 0.785398163 radians (45 degrees), which has a tangent of 1.
=DEGREES(ATAN(1)) returns 45.

Related Topics
For related functions and additional information, see:
“ATAN2” on page 331
“ATANH” on page 332

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“DEGREES” on page 334
“TAN” on page 338
“TANH” on page 339
“Listing of Trigonometric Functions” on page 326
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

ATAN2

The ATAN2 function returns the angle, relative to the positive x-axis, of the line passing
through the origin and the specified point.
ATAN2(x-point, y-point)
ÂÂ x-point:  The x-coordinate of the point the line passes through. x-point is a number

value.
ÂÂ y-point:  The y-coordinate of the point the line passes through. y-point is a number

value.
Usage Notes
ÂÂ The angle is expressed in radians, in the range –pi through +pi. To see the resulting
angle in degrees instead of radians, wrap this function in the DEGREES function; that
is, =DEGREES(ATAN2(x-point, y-point)).
Examples
=ATAN2(1, 1) returns 0.78539816 radians (45 degrees), the angle of a line segment from the origin to
point (1, 1).
=DEGREES(ATAN2(5, 5)) returns 45.

Related Topics
For related functions and additional information, see:
“ATAN” on page 330
“ATANH” on page 332
“DEGREES” on page 334
“TAN” on page 338

Chapter 12    Trigonometric Functions

331

“TANH” on page 339
“Listing of Trigonometric Functions” on page 326
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

ATANH

The ATANH function returns the inverse hyperbolic tangent of a number.
ATANH(num)
ÂÂ num:  A number. num is a number value that must be greater than –1 and less than 1.
Examples
=ATANH(0.995054753686731) returns 3.
=ATANH(TANH(2)) returns 2.

Related Topics
For related functions and additional information, see:
“ATAN” on page 330
“ATAN2” on page 331
“TAN” on page 338
“TANH” on page 339
“Listing of Trigonometric Functions” on page 326
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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COS

The COS function returns the cosine of an angle that is expressed in radians.
COS(radian-angle)
ÂÂ radian-angle:  An angle, expressed in radians. radian-angle is a number value.

Although it can be any value, it would normally be in the range –π to +π (–pi to +pi).
Usage Notes
ÂÂ To return an angle in degrees, use the DEGREES function (to convert radians to
degrees) with this function; that is, =DEGREES(COS(radian-angle)).
Examples
=COS(1) returns 0.540302306, the cosine of 1 radian (approximately 57.3 degrees).
=COS(RADIANS(60)) returns 0.5, the cosine of 60 degrees.
=COS(PI()/3) returns 0.5, π/3 radians (60 degrees).
=COS(PI()) returns –1, the cosine of π radians (180 degrees).

Related Topics
For related functions and additional information, see:
“ACOS” on page 327
“ACOSH” on page 328
“COSH” on page 334
“DEGREES” on page 334
“SIN” on page 336
“TAN” on page 338
“Listing of Trigonometric Functions” on page 326
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

Chapter 12    Trigonometric Functions

333

COSH

The COSH function returns the hyperbolic cosine of a number.
COSH(num)
ÂÂ num:  A number. num is a number value.
Examples
=COSH(0) returns 1.
=COSH(1) returns 1.543.
=COSH(5) returns 74.21.
=COSH(10) returns 11,013.233.

Related Topics
For related functions and additional information, see:
“ACOS” on page 327
“ACOSH” on page 328
“COS” on page 333
“Listing of Trigonometric Functions” on page 326
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

DEGREES

The DEGREES function returns the number of degrees in an angle expressed in radians.
DEGREES(radian-angle)
ÂÂ radian-angle:  An angle, expressed in radians. radian-angle is a number value.

Although it can be any value, it would normally be in the range –2π to 2π (–2 pi to
+2 pi).
Examples
=DEGREES(PI()) returns 180 (π radians = 180 degrees).
=DEGREES(1) returns 57.2957795130823, which is approximately the number of degrees per radian.

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Related Topics
For related functions and additional information, see:
“ACOS” on page 327
“ASIN” on page 329
“ATAN” on page 330
“ATAN2” on page 331
“COS” on page 333
“SIN” on page 336
“TAN” on page 338
“Listing of Trigonometric Functions” on page 326
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

RADIANS

The RADIANS function returns the number of radians in an angle expressed in degrees.
RADIANS(degree-angle)
ÂÂ degree-angle:  An angle, expressed in degrees. degree-angle is a number value.

Although it can be any value, it would normally be in the range –360 to +360.
Usage Notes
ÂÂ This function is useful if you wish to use an angle expressed in degrees with
any of the standard geometric functions, as they expect an angle expressed in
radians. Wrap the argument, expressed in degrees, in this function; for example,
=COS(RADIANS(degree-angle).
Examples
=RADIANS(90) returns 1.5708 (90 degrees is approximately 1.5708 radians).
=RADIANS(57.2957795130823) returns 1 (1 radian is approximately 57.296 degrees).

Related Topics
For related functions and additional information, see:

Chapter 12    Trigonometric Functions

335

“ACOS” on page 327
“ASIN” on page 329
“ATAN” on page 330
“ATAN2” on page 331
“COS” on page 333
“SIN” on page 336
“TAN” on page 338
“Listing of Trigonometric Functions” on page 326
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

SIN

The SIN function returns the sine of an angle that is expressed in radians.
SIN(radian-angle)
ÂÂ radian-angle:  An angle, expressed in radians. radian-angle is a number value.

Although it can be any value, it would normally be in the range –π to π (–pi to +pi).

Usage Notes
ÂÂ To return an angle in degrees, use the DEGREES function (to convert radians to
degrees) with this function; that is, =DEGREES(SIN(radian-angle)).
Examples
=SIN(1) returns 0.841470985, the sine of 1 radian (approximately 57.3 degrees).
=SIN(RADIANS(30)) returns 0.5, the sine of 30 degrees.
=SIN(PI()/2) returns 1, the sine of π/2 radians (90 degrees).

Related Topics
For related functions and additional information, see:
“ASIN” on page 329
“ASINH” on page 329

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“COS” on page 333
“DEGREES” on page 334
“SINH” on page 337
“TAN” on page 338
“Listing of Trigonometric Functions” on page 326
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

SINH

The SINH function returns the hyperbolic sine of the specified number.
SINH(num)
ÂÂ num:  A number. num is a number value.
Examples
=SINH(0) returns 0.
=SINH(1) returns 1.175.
=SINH(5) returns 74.203.
=SINH(10) returns 11013.233.

Related Topics
For related functions and additional information, see:
“ASIN” on page 329
“ASINH” on page 329
“SIN” on page 336
“Listing of Trigonometric Functions” on page 326
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41
Chapter 12    Trigonometric Functions

337

TAN

The TAN function returns the tangent of an angle that is expressed in radians.
TAN(radian-angle)
ÂÂ radian-angle:  An angle, expressed in radians. radian-angle is a number value.

Although it can be any value, it would normally be in the range –pi to +pi.
Usage Notes
ÂÂ The tangent is the ratio of the sine to the cosine.
ÂÂ To return an angle in degrees, use the DEGREES function (to convert radians to

degrees) with this function; that is, =DEGREES(TAN(radian-angle)).
Examples
=TAN(1) returns 1.557407725, the tangent of 1 radian (approximately 57.3 degrees).
=TAN(RADIANS(45)) returns 1, the tangent of a 45-degree angle.
=TAN(3*PI()/4) returns -1.

Related Topics
For related functions and additional information, see:
“ATAN” on page 330
“ATAN2” on page 331
“ATANH” on page 332
“COS” on page 333
“DEGREES” on page 334
“SIN” on page 336
“TANH” on page 339
“Listing of Trigonometric Functions” on page 326
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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TANH

The TANH function returns the hyperbolic tangent of the specified number.
TANH(num)
ÂÂ num:  A number. num is a number value.
Examples
=TANH(0) returns 0.
=TANH(1) returns 0.762.
=TANH(5) returns 0.999909.
=TANH(10) returns 0.999999996.

Related Topics
For related functions and additional information, see:
“ATAN” on page 330
“ATAN2” on page 331
“ATANH” on page 332
“TAN” on page 338
“Listing of Trigonometric Functions” on page 326
“Value Types” on page 36
“The Elements of Formulas” on page 15
“Using the Keyboard and Mouse to Create and Edit Formulas” on page 26
“Pasting from Examples in Help” on page 41

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339

Additional Examples and Topics

13

The in-depth examples and additional topics in this chapter
illustrate working with some of the more complex functions.
Additional Examples and Topics Included

The following table tells you where to find in-depth examples and additional topics
that illustrate working with some of the more complex functions with real-world
examples.

340

If you wish to see an example or learn more
about

See this section

The definitions and specification of arguments
used in financial functions

“Common Arguments Used in Financial
Functions” on page 341

The time value of money (TVM) functions

“Choosing Which Time Value of Money Function
to Use” on page 348

TVM functions dealing with fixed periodic cash
flows and fixed interest rates

“Regular Cash Flows and Time Intervals” on
page 348

TVM functions that can deal with uneven
(variable periodic) cash flows

“Irregular Cash Flows and Time Intervals” on
page 350

The function that may be most helpful in
answering a common financial question

“Which Function Should You Use to Solve
Common Financial Questions?” on page 351

Using financial functions to create a loan
amortization table

“Example of a Loan Amortization Table” on
page 353

The various functions that round numbers

“More on Rounding” on page 355

Using logical and information functions together
to build a more powerful formula

“Using Logical and Information Functions
Together” on page 358

Understanding conditions and how to use
wildcards with conditions

“Specifying Conditions and Using Wildcards” on
page 360

Using statistical functions to analyze the results
of a survey

“Survey Results Example” on page 362

Common Arguments Used in Financial Functions

Many arguments are common among related financial functions. This section provides
information regarding these arguments. Date arguments (issue, maturity, and settle)
are not included. Arguments that are used by only a single financial function are also
not included.
annual-rate
Bonds and other fixed-rate, interest-bearing debt securities have a stated coupon or annual interest
rate used to determine periodic interest payments. annual-rate is used to represent the annual
interest rate, whether it is called a coupon rate or an annual interest rate.
coupon-rate is specified as a decimal number representing the annual coupon rate. In some
functions, coupon-rate can be 0 (if the security does not pay periodic interest), but coupon-rate
cannot be negative.
Assume that you own a security with a face value of $1,000,000 and that pays annual interest of 4.5%
based on the face value. coupon-rate would be 0.045. frequency of payment does not matter.
annual-yield
Bonds and other interest-bearing and discount debt securities have a yield that is calculated using
the coupon interest rate and the current price of the bond.
annual-yield is specified as a decimal number representing the security’s annual yield, which is
commonly stated as a percentage. annual-yield must be greater than 0.
Assume that you are considering the purchase of a particular bond. As the price of a bond goes
down, its yield goes up. Conversely, if the price of the bond rises, its yield decreases. Your broker
checks the pricing screens and tells you that the bond you are considering has a coupon rate of
3.25% and an annual yield of 4.5%, based on its current price (the bond is trading at a discount).
annual-yield would be 0.045.
cash-flow
Annuities, loans, and investments have cash flows. One cash flow is the initial amount paid or
received, if any. Other cash flows are other receipts or payments at a specific point in time.
cash-flow is specified as a number, usually formatted as currency. Amounts received are specified as
positive numbers and amounts paid are specified as negative numbers.
Assume that there is a townhouse that you plan to purchase, rent out for a period of time, and then
resell. The initial cash purchase payment (which might consist of a down payment and closing costs),
loan payments, repairs and maintenance, advertising, and similar costs, would be payments (negative
cash flows). Rents received from tenants, tax benefits received through a reduction of other taxes,
and the amount received upon sale would be receipts (positive cash flows).
cost
The initial cost of the asset to be depreciated is generally the purchase price, including taxes, delivery,
and setup. Certain tax benefits may be deducted from the cost.
cost is specified as number, usually formatted as currency. cost must be greater than 0.
Assume that you purchase a new digital photocopy machine for your office. The purchase price of
the photocopy machine was $2,625 with tax. The vendor charged $100 to deliver and set it up. The
photocopy machine is expected to be used for 4 years, at which time it is expected to have a resale
value of $400. cost would be $2,725.

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341

cum-when-due
See discussion at when-due. The only difference is that functions that use cum-when-due require the
argument to be specified and do not assume a value if it is omitted.
days-basis
There are several different conventions used when counting the number of days in a month and
number of days in a year to determine interest on a loan or investment. days-basis is used to indicate
how days are counted for a specific investment or loan. days-basis is often defined by market practice
and may be related to a particular type of investment. Or days-basis may be specified in documents
related to a loan.
days-basis is a modal argument. It is specified as the number 0, 1, 2, 3, or 4.
ÂÂ

ÂÂ

ÂÂ
ÂÂ
ÂÂ

A value of 0 specifies that for purposes of computing interest, each full month will contain 30 days
and each full year will contain 360 days, using the NASD method for dates falling on the 31st of
a month. This is commonly known as the 30/360 convention. 0 (30/360 convention) is the default
value.
In the NASD method, if the day value in the starting date (for example, the settlement date) is 31,
it is treated as if it was 30. If the day value is the last day of February, it is not adjusted, so in this
case February has less than 30 days. If the day value for the ending date (for example, the maturity
date) is 31 and the day value in the starting date is earlier than the 30th of the same month, the
ending date is considered to be the first day of the following month. Otherwise it is considered to
be the 30th of the same month resulting in 0 days.
A value of 1 specifies that the actual number of days will be used for each full month and the
actual number of days will be used for each year. This is commonly known as the actual/actual
convention.
A value of 2 specifies that the actual number of days will be used for each full month and each full
year will contain 360 days. This is commonly known as the actual/360 convention.
A value of 3 specifies that the actual number of days will be used for each full month and each full
year will contain 365 days. This is commonly known as the actual/365 convention.
A value of 4 specifies that each full month will contain 30 days and each full year will contain 360
days, using the European method for dates falling on the 31st of a month. This is commonly known
as the 30E/360 convention.
In the European method, the 31st of a month is always considered to be the 30th of the same
month. February is always considered to have 30 days, so if the last day of February is the 28th, it is
considered to be the 30th.

Assume that you wish to determine the interest on a bond issued by a U.S. corporation. Most such
bonds use the 30/360 method of determining interest so days-basis would be 0, the default value.
Or assume that you wish to determine the interest on a United States Treasury Bond. These bonds
usually pay interest based on the actual days in each month and the actual days in each year, so
days-basis would be 1.
depr-factor
In certain formulas, the rate of the accelerated depreciation rate (in excess of straight-line
depreciation) can be specified. depr-factor is used to specify the desired rate of annual depreciation.
depr-factor is specified as a decimal number or as a percentage (using the percent sign).
Assume that you have purchased a new computer. After discussion with your tax accountant, you
find that it is permissible to depreciate the computer on an accelerated basis. You decide to use a
depreciation rate of 150% of straight-line depreciation, so depr-factor would be 1.5.

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depr-period
Certain functions return the amount of depreciation for a specified period. depr-period is used to
specify the period.
depr-period is specified as a number representing the desired depreciation period using the same
time frame (for example, monthly, quarterly, or annually) as life.
Assume that you purchase a new digital photocopy machine for your office. The purchase price of
the photocopy machine was $2,625 with tax. The vendor charged $100 to deliver and set it up. The
photocopy machine is expected to be used for 4 years, at which time it is expected to have a resale
value of $400. If you wished to determine the depreciation for the third year, depr-period would be 3.
effective-int-rate
Annuities and investments have an effective interest rate, which is calculated using the nominal
(stated or coupon) rate and the number of interest payments per year.
effective-int-rate is specified as a decimal number and must be greater than 0.
Assume that you own a security with a face value of $1,000,000 that pays annual interest of 4.5%
based on the face value, on a quarterly basis, which is an effective rate of approximately 4.58%.
effective-int-rate would be 0.0458. See also the description of nominal-rate and num-periods-year.
end-per
Certain functions return principal or interest for a series of specified payments. end-per is used to
indicate the last payment to be included in the value returned. See also the discussion of start-per.
end-per is specified as a number and must be greater than 0.
Assume that you are purchasing a home. The mortgage broker offers you a loan with an initial
balance of $200,000, a term of 10 years, an annual interest rate of 6.0%, fixed monthly payments of
$1070.45, and a balance to be refinanced at maturity of $100,000. If you wished to know the total
amount of interest paid in the third year, start-per would be 25 and end-per would be 36.
estimate
An estimate of the expected outcome is used by some financial functions.
estimate is specified as a decimal number. For example, 13% is specified as 0.13. estimate can be
negative, if a loss is expected. If estimate is not specified, 0.10 is used as the default value.
If you do not have an idea as to the expected outcome and the default value does not result in
a solution, initially try a larger positive estimate. If this does not result in an outcome, try a small
negative estimate.
frequency
An investment may pay interest on a periodic basis. frequency is used to indicate how often interest
is paid.
frequency is the number 1, 2, or 4.
A value of 1 indicates that the investment pays interest annually (once a year).
A value of 2 indicates that the investment pays interest semiannually (twice per year).
ÂÂ A value of 4 indicates that the investment pays interest quarterly (four times per year).
ÂÂ
ÂÂ

Assume that you are evaluating a corporate bond that pays interest quarterly. frequency would be 4.
Or assume you are evaluating a government bond that pays interest semiannually. frequency would
be 2.

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343

future-value
A future value is a cash flow received or paid at the end of the investment or loan period or the cash
value remaining after the final payment.
future-value is specified as a number, usually formatted as currency. Since future-value is a cash flow,
amounts received are specified as positive numbers and amounts paid are specified as negative
numbers.
Assume that there is a townhouse that you plan to purchase, rent out for a period of time, and then
resell. The estimated future sales price could be a future-value and would be positive. Or assume that
you lease a car and that the lease contains a provision allowing you to buy the car for a specified
price at the end of the lease term. The amount of that payment could be a future-value and would
be negative. Or assume that you have a mortgage loan that at the end of 10 years has a balloon
payment due. The balloon payment could be a future-value and would be negative.
invest-amount
The initial amount invested in a bond is specified using invest-amount.
invest-amount is specified as a number, usually formatted as currency. invest-amount must be greater
than 0.
Assume that you purchase a bond for $800. invest-amount would be $800.
life
Assets are depreciated over a specific period, known as the depreciable life or the expected useful
life. Generally for accounting purposes the expected useful life of the asset would be used for
depreciation, whereas for other purposes (such as preparing a tax return) the depreciable life may be
specified by regulation or practice.
life is specified as a number. life must be greater than 0.
Assume that you purchase a new digital photocopy machine for your office. The purchase price of
the photocopy machine was $2,625 with tax. The vendor charged $100 to deliver and set it up. The
photocopy machine is expected to be used for 4 years, at which time it is expected to have a resale
value of $400. life is 4.
nominal-rate
Annuities and investments have a nominal interest rate, which is calculated using the effective
interest rate and the number of compounding periods per year.
nominal-rate is specified as a decimal number and must be greater than 0.
Assume that own a security with a face value of $1,000,000 that pays annual interest of 4.5% based
on the face value, on a quarterly basis, which is an effective rate of approximately 4.58%. nominal-rate
would be 0.045. See also the description of effective-int-rate and num-periods-year.
num-periods
The number of periods (num-periods) is the total periods of a repeating cash flow, or the length of a
loan, or the length of the investment period.
num-periods is specified as a number using the same time frame (for example, monthly, quarterly, or
annually) as related arguments used by the function.
Assume that you are purchasing a home. The mortgage broker offers you a loan with an initial
balance of $200,000, a term of 10 years, an annual interest rate of 6.0%, fixed monthly payments, and
a balance to be refinanced at maturity of $100,000. num-periods would be 120 (12 monthly payments
for 10 years). Or assume that you invest your savings in a certificate of deposit that has a term of
5 years and compounds interest quarterly. num-periods would be 20 (4 quarterly compounding
periods for 5 years).

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num-periods-year
The calculation of the effective and nominal interest rates is based on the number of interest
compounding periods per year. num-periods-year is used to specify the number of periods.
num-periods-year is specified as a number and must be greater than 0.
Assume that you have purchased a certificate of deposit that pays interest annually, compounded
quarterly. If you wanted to determine the effective interest rate, num-periods-year would be 4. See
also the description of effective-int-rate and nominal-rate.
par
The par value of a security is generally its face or maturity value.
par is specified as a number, usually formatted as currency.
par is often a number like 100, 1,000, or 1,000,000.
Assume that you are considering purchasing a corporate bond. The prospectus for the bond states
that each bond will be issued with a face and maturity value of $1,000. The $1,000 would be the par
value of the bond.
payment
A payment is a fixed, periodic cash flow received or paid over an investment or loan period.
payment is specified as a number, usually formatted as currency. Since payment is a cash flow,
amounts received are specified as positive numbers and amounts paid are specified as negative
numbers.
payment often includes both principal and interest elements, but does not usually include other
amounts.
Assume that there is a townhouse that you plan to purchase, rent out for a period of time, and then
resell. The amount of the monthly mortgage payment could be a payment and would be negative.
The rent payment received each month could also be a payment and would be positive.
period
Certain functions return a principal or interest value for a given period. period is used to indicate the
desired period.
period is specified as a number and must be greater than 0.
Assume that you are purchasing a home. The mortgage broker offers you a loan with an initial
balance of $200,000, a term of 10 years, an annual interest rate of 6.0%, fixed monthly payments of
$1070.45, and a balance to be refinanced at maturity of $100,000. If you wished to know the amount
of interest in the first payment of the third year, period would be 25, since payments are monthly.
periodic-discount-rate
The discount rate is the interest rate representing the desired yield used to value (or discount) a
series of cash flows.
periodic-discount-rate is specified as a decimal (for example, 0.08) or delimited with a percent sign (for
example, 8%). It is specified using the same time frame as the time frame used for the cash flows. For
example, if the cash flows are monthly and the desired annual discount rate is 8%, periodic-discountrate must be specified as 0.00667 or 0.667% (0.08 divided by 12).
Assume that you are evaluating the possible purchase of a business. As part of your evaluation, you
determine the expected monthly cash flows from the business along with the requested purchase
price and estimated future resale price. You decide, based on alternative investment opportunities
and risk, that you will not invest unless the net cash flows yield at least an 18% annual interest rate.
periodic-discount-rate would be 0.015 (0.18 / 12 as specified cash flows are monthly).

Chapter 13    Additional Examples and Topics

345

periodic-rate
In some cases, when working with a series of cash flows, or an investment, or a loan, it may be
necessary to know the interest rate each period. This is the periodic-rate.
periodic-rate is specified as a decimal number using the same time frame (for example, monthly,
quarterly, or annually) as other arguments (num-periods or payment).
Assume that you are purchasing a home. The mortgage broker offers you a loan with an initial
balance of $200,000, a term of 10 years, an annual interest rate of 6.0%, fixed monthly payments, and
a balance to be refinanced at maturity of $100,000. periodic-rate would be 0.005 (annual rate divided
by 12 to match up with the monthly payment). Or assume that you invest your savings in a certificate
of deposit that has a term of 5 years, has a nominal annual interest rate of 4.5%, and interest
compounds quarterly. periodic-rate would be 0.0125 (annual rate divided by 4 to match the quarterly
compounding periods).
present-value
A present value is a cash flow received or paid at the beginning of the investment or loan period.
present-value is specified as a number, usually formatted as currency. Since present-value is a cash
flow, amounts received are specified as positive numbers and amounts paid are specified as negative
numbers.
Assume that there is a townhouse that you plan to purchase, rent out for a period of time, and
then resell. The initial cash purchase payment (which might consist of a down payment and closing
costs) could be a present-value and would be negative. The initial principal amount of a loan on the
townhouse could also be a present-value and would be positive.
price
The purchase price is the amount paid to buy a bond or other interest-bearing or discount debt
security. The purchase price does not include accrued interest purchased with the security.
price is specified as a number representing the amount paid per $100 of face value (purchase price /
face value * 100). price must be greater than 0.
Assume that you own a security that has a face value of $1,000,000. If you paid $965,000 when you
purchased the security, excluding accrued interest if any, price would be 96.50 ($965,000 / $1,000,000
* 100).
redemption
Bonds and other interest-bearing and discount debt securities usually have a stated redemption
value. This is the amount that will be received when the debt security matures.
redemption is specified as a number representing the amount that will be received per $100 of face
value (redemption value / face value * 100). Often, redemption is 100, meaning that the security’s
redemption value is equal to its face value. value must be greater than 0.
Assume that you own a security that has a face value of $1,000,000 and for which you will receive
$1,000,000 at maturity. redemption would be 100 ($1,000,000 / $1,000,000 * 100), because the face
value and the redemption value are the same, a common case. Assume further though that the issuer
of this security offers to redeem the security before maturity and has offered $1,025,000 if redeemed
one year early. redemption would be 102.50 ($1,025,000 / $1,000,000 * 100).

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salvage
Assets often have value remaining at the end of the depreciable life or the expected useful life. This is
the salvage value.
salvage is specified as a number, usually formatted as currency. salvage can be 0, but cannot be
negative.
Assume that you purchase a new digital photocopy machine for your office. The purchase price of
the photocopy machine was $2,625 with tax. The vendor charged $100 to deliver and set it up. The
photocopy machine is expected to be used for 4 years, at which time it is expected to have a resale
value of $400. salvage is $400.
start-per
Certain functions return principal or interest for a series of specified payments. start-per is used to
indicate the first payment to be included in the value returned. See also the discussion of end-per.
start-per is specified as a number and must be greater than 0.
Assume that you are purchasing a home. The mortgage broker offers you a loan with an initial
balance of $200,000, a term of 10 years, an annual interest rate of 6.0%, fixed monthly payments of
$1070.45, and a balance to be refinanced at maturity of $100,000. If you wished to know the total
amount of interest paid in the third year, start-per would be 25 and end-per would be 36.
when-due
Payments can be generalized to occur at the beginning or end of a period. when-due is used to
indicate whether a payment occurs at the beginning or end of a period.
when-due is a modal argument. It can be the number 0 or 1.
A value of 0 specifies that the payment is treated as being received or made at the end of each
period. 0 is the default value.
ÂÂ A value of 1 specifies that the payment is treated as being received or made at the beginning of
each period.
ÂÂ

Assume that you are purchasing a home. The mortgage broker offers you a loan with an initial
balance of $200,000, a term of 10 years, an annual interest rate of 6.0%, fixed monthly payments,
and a balance to be refinanced at maturity of $100,000. when-due would be 0 (the default) since
payments are made at the end of each month. Or assume you own an apartment that you rent and
that you require the tenant to pay rent on the first of each month. when-due would be 1, since this
payment is being made by the tenant at the beginning of the monthly period.

Chapter 13    Additional Examples and Topics

347

Choosing Which Time Value of Money Function to Use

This section provides additional information regarding the functions used to solve
time value of money problems. Time value of money, or TVM, problems involve cash
flows over time and interest rates. This section contains several parts.
“Regular Cash Flows and Time Intervals” on page 348 discusses the TVM functions used
with regular cash flows, regular time intervals, and fixed interest rates.
“Irregular Cash Flows and Time Intervals” on page 350 discusses the TVM functions
used with irregular cash flows, irregular time intervals, or both.
“Which Function Should You Use to Solve Common Financial Questions?” on page 351
describes several common TVM problems (such as which function would be used to
compute interest on a savings account) along with the functions that might be used in
solving the problem.

Regular Cash Flows and Time Intervals
The primary functions used with regular periodic cash flows (payments of a
constant amount and all cash flows at constant intervals) and fixed interest rates are
interrelated.
Function and its purpose

Arguments used by the function

“FV” (page 120) is the function to use if you wish periodic-rate, num-periods, payment, present-value,
when-due
to determine what the future value (what it is
worth at a future point in time) of a series of cash
flows will be, considering the other factors such
as the interest rate. It solves for the argument
future-value.

348		

“NPER” (page 130) is the function to use if you
wish to determine the number of periods it
would take to repay a loan or the number
of periods you might receive an annuity,
considering the other factors such as the interest
rate. It solves for the argument num-periods.

periodic-rate, payment, present-value, future-value,
when-due

“PMT” (page 134) is the function to use if you
wish to determine the amount of the payment
that would be required on a loan or received on
an annuity, considering the other factors such as
interest rate. It solves for the argument payment.

periodic-rate, num-periods, present-value, futurevalue, when-due

Chapter 13    Additional Examples and Topics

Function and its purpose

Arguments used by the function

“PV” (page 141) is the function to use if you wish periodic-rate, num-periods, payment, future-value,
to determine the present value (what it is worth when-due
today) of a series of cash flows, considering the
other factors such as the interest rate. It solves for
the argument present-value.
num-periods, payment, present-value, future-value,
“RATE” (page 144) is the function to use if you
wish to determine the periodic interest rate for a when-due, estimate
loan or annuity, based on the other factors such
as the number of periods in the loan or annuity. It
solves for the argument periodic-rate.

As illustrated by this table, these TVM functions each solve for, and return the value
of, one of the five primary arguments when the problem being solved involves
regular periodic cash flows and fixed interest rates. In addition, “IPMT” (page 123) and
“PPMT” (page 135) can solve for the interest and principal components of a particular
loan or annuity payment, and “CUMIPMT” (page 110) and “CUMPRINC” (page 112) can
solve for the interest and principal components of a consecutive series of loan or
annuity payments.
Related Topics
For related functions and additional information, see:
“Irregular Cash Flows and Time Intervals” on page 350
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15

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349

Irregular Cash Flows and Time Intervals
Some TVM problems involve irregular fixed periodic cash flows where cash flows occur
at regular time intervals but the amounts vary. Still other problems have cash flows
that have irregular time intervals where cash flows do not necessarily occur at regular
time intervals.
Function and its purpose

Arguments used by the function

“IRR” (page 125) is the function to use if you wish
to determine a periodic rate such that the net
present value of a series of potentially irregular
cash flows that occur at regular time intervals is
equal to 0. This is commonly called the internal
rate of return. IRR solves for the argument
periodic-rate.

flows-range, estimate

“MIRR” (page 128) is the function to use if you
wish to determine a periodic rate such that
the net present value of a series of potentially
irregular cash flows that occur at regular time
intervals is equal to 0. MIRR differs from IRR
in that it permits positive and negative cash
flows to be discounted at a different rate. This is
commonly called the modified internal rate of
return. MIRR solves for the argument periodic-rate.

flows-range, finance-rate, reinvest-rate

“NPV” is the function to use if you wish to
determine the present value of a series of
potentially irregular cash flows that occur at
regular time intervals. This is commonly called the
net present value. NPV solves for the argument
present-value.

periodic-rate, cash-flow, cash-flow…

flows-range is a specified range of cash flows that
may implicitly include a payment, a present-value,
and a future-value.

flows-range is a specified range of cash flows that
may implicitly include a payment, a present-value,
and a future-value.
finance-rate and reinvest-rate are specific cases of
periodic-rate.

cash-flow, cash-flow… is a specified series of one
or more cash flows that may implicitly include a
payment, present-value, and future-value.

Related Topics
For related functions and additional information, see:
“Regular Cash Flows and Time Intervals” on page 348
“Common Arguments Used in Financial Functions” on page 341
“Listing of Financial Functions” on page 96
“Value Types” on page 36
“The Elements of Formulas” on page 15

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Which Function Should You Use to Solve Common Financial
Questions?
This section describes some common questions you might want to address and lists
the financial function that might be helpful. The questions help with everyday financial
questions. More complex uses of the financial functions are described in “Regular Cash
Flows and Time Intervals” on page 348, “Irregular Cash Flows and Time Intervals” on
page 350, and “Example of a Loan Amortization Table” on page 353.
If you would like to know

This function may be helpful

Savings

  

The effective interest rate on an investment or
savings account that pays interest periodically

“EFFECT” (page 119)

How much a CD will be worth at maturity

“FV” (page 120). Note that payment will be 0.

The nominal rate of interest on a CD where the
issuer has advertised the “effective rate”

“NOMINAL” (page 129)

How many years it will take to save a specific
amount, given monthly deposits to a savings
account

“NPER” (page 130). Note that present-value will
be the amount deposited at the beginning and
could be 0.

How much to save each month to reach a savings “PMT” (page 134). Note that present-value will
goal in a given number of years
be the amount deposited at the beginning and
could be 0.
Loans

  

The amount of interest paid on a loan during the
third year

“CUMIPMT” (page 110)

The amount of principal paid on a loan during
the third year

“CUMPRINC” (page 112)

The amount of interest included in the 36th loan
payment

“IPMT” (page 123)

The amount of principal included in the 36th
loan payment

“PPMT” (page 135)

Bond Investments

  

The amount of interest that will need to be
added to a bond’s purchase price

“ACCRINT” (page 99) or “ACCRINTM” (page 101)

The number of coupon payments between the
time a bond is purchased and its maturity

“COUPNUM” (page 109)

“DISC” (page 117)
The annual discount rate for a bond that is sold
at a discount to its redemption value and pays no
interest (often known as a “zero coupon bond”)

Chapter 13    Additional Examples and Topics

351

If you would like to know

This function may be helpful

The effective annual interest rate for a bond that
pays interest only at its maturity (no periodic
payments, but the bond does have a coupon
rate)

“INTRATE” (page 122)

The expected purchase price of a bond that pays “PRICE” (page 137), “PRICEDISC” (page 138), and
“PRICEMAT” (page 140)
periodic interest, a bond sold at a discount that
does not pay interest, or a bond that pays interest
only at maturity

352		

The amount received on a bond that pays
interest only at its maturity (no periodic
payments, but the bond does have a coupon
rate), including interest

“RECEIVED” (page 146)

The effective annual interest rate of a bond that
pays periodic interest, a bond sold at a discount
that does not pay interest, or a bond that pays
interest only at maturity

“YIELD” (page 150), “YIELDDISC” (page 152), and
“YIELDMAT” (page 153)

Depreciation

  

The periodic amount of depreciation of an asset
using the fixed-declining balance method

“DB” (page 114)

The periodic depreciation of an asset using a
declining balance method such as “doubledeclining balance”

“DDB” (page 116)

The periodic depreciation of an asset using the
straight-line method

“SLN” (page 147)

The periodic depreciation of an asset using the
sum-of-the-years-digits method

“SYD” (page 148)

The total depreciation over a given period for
an asset depreciated using a declining balance
method

“VDB” (page 149)

Chapter 13    Additional Examples and Topics

Example of a Loan Amortization Table

This example uses IPMT, PPMT, and PMT to construct a loan amortization table. The
information returned by IPMT, PPMT, and PMT is related. This is illustrated in the
example.
Constructing the Amortization Table
Assume you wish to construct an amortization table for all periods of a loan with an initial principal
amount of $50,000, a term of 2 years, an annual interest rate of 7%, and a balance due at the end
of the term of $30,000. The first part of your amortization table (with formulas shown) could be
constructed like this:

Explanations of Cell Content
Cell B6 uses the PMT function to calculate the amount of each monthly payment. Note that this will
be the total of interest and principal for each month (for example, C9 + D9) as shown in F9.
Cells C9 and D9 use IPMT and PPMT, respectively, to calculate the portion of each monthly payment
that is interest and principal. Note that IPMT is the same as PMT – PPMT and, conversely, PPMT is the
same as PMT – IPMT.

Chapter 13    Additional Examples and Topics

353

The Completed Amortization Table
To complete the table, it would be necessary to select cells A10:A11 and extend the selection down to
A32 to include all 24 periods in the hypothetical loan. Then C9:F9 would be selected and extended to
C32:F32 to complete the formulas. Here is the complete table, showing the entire amortization using
the formulas shown in the previous table.

Final Comments
Note that the values returned by IPMT (column C) and PPMT (column D) do add up each month to
the PMT calculated in cell B6 (as shown in column F). Also note that the final principal remaining, as
shown in cell E32, is $30,000, as specified for balloon in cell B4.

354		

Chapter 13    Additional Examples and Topics

More on Rounding

iWork supports many different functions that round numbers. This section compares
these functions.
To

Use this function

“CEILING” (page 170)
Round a number away from
zero to the nearest multiple of a
given number

Round a number away from
zero to the nearest even
number

“EVEN” (page 173)

Comments
Rounding occurs in steps; for
example, the closest multiple of
10. Rounding is away from zero,
so =CEILING(0.4, 1) results in 1
and =CEILING (-0.4, -1) results
in -1.
Rounding is to the nearest
number evenly divisible by two.
Rounding is away from zero,
so =EVEN(0.4) returns 2 and
=EVEN(-0.4) returns -2.

Round a number toward zero to “FLOOR” (page 176)
the nearest multiple of a given
number

Rounding occurs in steps; for
example, the closest multiple of
10. Rounding is toward zero, so
=FLOOR(0.4, 1) results in 0 and
=FLOOR (-0.4, -1) also results
in 0.

Round a number to the nearest “INT” (page 178)
integer that is less than or equal
to a given number

Rounding is to the nearest
integer that is less than or
equal to the given number.
Therefore, =INT(0.4) returns 0
and =INT(-0.4) returns -1.

Round a number to the nearest
multiple of a given number

Rounding is to the nearest
multiple of the given number.
This differs from CEILING,
which rounds up to the
nearest multiple. Therefore,
=MROUND(4, 3) returns 3,
since 4 is closer to 3 than to
the next multiple of 3, which
is 6. =CEILING(4, 3) returns 6,
the nearest multiple of 3 when
rounding up.

“MROUND” (page 183)

Round a number away from
“ODD” (page 185)
zero to the nearest odd number

Chapter 13    Additional Examples and Topics

Rounding is to the nearest
number not evenly divisible
by two. Rounding is away from
zero, so =ODD(1.4) returns 3 and
=EVEN(-1.4) returns -3.

355

356		

To

Use this function

Comments

Round a number to the
specified number of places

“ROUND” (page 191)

A positive number indicates
the number of digits (decimal
places) to the right of the
decimal separator to include in
the rounded number. A negative
number indicates the number of
digits to the left of the decimal
separator to replace with zeros
(the number of zeros at the end
of the number). The number
is rounded based on this. So
=ROUND(1125, -2) returns
1,100 and =ROUND(1155, -2)
returns 1,200. Rounding
is away from zero, so
=ROUND(-1125, -2) returns -1,100
and =ROUND(-1155, -2) returns
-1,200.

Round a number down (toward
zero) to the specified number
of places

“ROUNDDOWN” (page 192)

A positive number indicates
the number of digits (decimal
places) to the right of the
decimal separator to include in
the rounded number. A negative
number indicates the number of
digits to the left of the decimal
separator to replace with zeros
(the number of zeros at the end
of the number). The number
is rounded based on this. So
=ROUND(1125, -2) returns
1,100 and =ROUND(1155, -2)
also returns 1,100, since
rounding is toward zero.
=ROUND(-1125, -2) returns -1,100
and =ROUND(-1155, -2) also
returns -1,100.

Chapter 13    Additional Examples and Topics

To

Use this function

Comments

Round a number up (away from “ROUNDUP” (page 193)
zero) to the specified number
of places

A positive number indicates
the number of digits (decimal
places) to the right of the
decimal separator to include in
the rounded number. A negative
number indicates the number of
digits to the left of the decimal
separator to replace with zeros
(the number of zeros at the end
of the number). The number
is rounded based on this. So
=ROUND(1125, -2) returns
1,200 and =ROUND(1155, -2)
also returns 1,200, since
rounding is away from zero.
=ROUND(-1125, -2) returns -1,200
and =ROUND(-1155, -2) also
returns -1,200.

Truncate a number at the
specified number of places

A positive number indicates
the number of digits (decimal
places) to the right of the
decimal separator to include
in the number. A negative
number indicates the number of
digits to the left of the decimal
separator to replace with zeros
(the number of zeros at the
end of the number). Extra digits
are stripped from the number.
So =TRUNC(1125, -2) returns
1,100 and =TRUNC(1155, -2) also
returns 1,100.

“TRUNC” (page 204)

Chapter 13    Additional Examples and Topics

357

Using Logical and Information Functions Together

Logical and information functions are often used together in a formula. Although
logical functions are used independently, it is rare for an information function to
be used on its own. This section includes more complex examples to illustrate how
the use of several logical and information functions in a single formula can be very
powerful.

Adding Comments Based on Cell Contents
This example uses IF, AND, OR, and ISBLANK to add comments to a table based on
existing cell contents. The IF function is quite powerful, especially when combined
with other logical functions like OR and AND.
Assume that you are a college professor and one of the graduate assistants has
handed you a table containing the names of students and their recent exam results.
You want to quickly identify the following situations:
ÂÂ The student passed, but should come in for a special study session (score in the

range 61–75).
ÂÂ There is an error (negative test score, a test score over 100, or no test score) in the

data.
ÂÂ The student failed the exam (score of 60 or below).

Breaking this into parts, the functions below will determine each of the things you
wish to know. When put together, you will be able to quickly glance at the table and
see the desired information. For purposes of the expressions below, assume the first
student’s name is in cell A2, and the first test score in cell B2.

358		

Chapter 13    Additional Examples and Topics

Expression 1
=AND(B2>60, B2<=75) tests for a low score. If the test score is in the range 61 to 75, AND will return
TRUE meaning the student should come in for a special study session. Otherwise it will return FALSE.
Expression 2
=OR(ISBLANK(B2), B2<0, B2>100) tests for invalid data. The first OR expression “ISBLANK(B2)” will be
TRUE if there is no test score. The second expression will return TRUE if the test score is negative and
the third expression will return TRUE if the test score is over 100. The OR will return TRUE if any of the
conditions is TRUE, meaning the data is invalid in some way. The OR will return FALSE if none of the
conditions are TRUE and therefore the data is valid.
Expression 3
=B2<=60 tests for a failing grade. This expression will return TRUE if the test score is 60 or below, a
failing grade. Otherwise it returns FALSE.
Putting it together in an IF function
=IF(AND(B2>60, B2<=75), “Needs study session”, IF(OR(ISBLANK(B2), B2<0, B2>100), “Invalid data”,
IF(B2<=60, “Exam failed”, “”)))
If the test expression (same as Expression 1 above) in the first IF evaluates to TRUE, the function will
return “Needs study session”; otherwise it will continue to the FALSE argument, the second IF.
If the test expression (same as Expression 2 above) of the second IF evaluates to TRUE, the function
will return “Invalid data”; otherwise it will continue to the FALSE argument, the third IF.
If the test expression (same as Expression 3 above) of the third IF evaluates to TRUE, the function will
return “Exam failed”; otherwise the expression will return an empty expression (“”).
The result might look like the following table.

Chapter 13    Additional Examples and Topics

359

Trapping Division by Zero
Sometimes it is not possible to construct a table in a manner that can avoid division
by zero. However, if division by zero occurs, the result is an error value in the cell, which
is usually not the desired result. This example shows three methods of preventing this
error.
Examples
Assume that cell D2 and E2 each contain a number. It is possible that E2 contains 0. You wish to
divide D2 by E2, but avoid a division by zero error. Each of the following three methods will return 0 if
cell E2 is equal to zero; otherwise each returns the result of D2/E2.
=IF(E2=0,0,D2/E2) operates by directly testing cell E2 to see if it is 0.
=IFERROR(D2/E2,0) operates by returning 0 if an error occurs. Division by zero is an error.
=IF(ISERROR(D2/E2),0,D2/E2) operates by doing a logical test to see if D2/E2 is TRUE.

Specifying Conditions and Using Wildcards

Some functions, such as SUM, operate on entire ranges. Other functions, such as SUMIF,
only operate on the cells in the range that meet a condition. For example you might
want to add up all the numbers in column B that are less than 5. To do this, you could
use =SUMIF(B, “<5”). The second argument of SUMIF is called a condition because it
causes the function to ignore cells that do not meet the requirements.
There are two types of functions that take conditions. The first type is functions that
have names ending in IF or IFS (except for the function IF, which does not take a
condition; it instead takes an expression that should evaluate to either TRUE or FALSE).
These functions can do numeric comparisons in their conditions, such as “>5”, “<=7”,
or “<>2”. These functions also accept wildcards in specifying conditions. For example,
to count the number of cells in column B that begin with the letter “a”, you could use
=COUNTIF(B, “a*”)
The second group of functions take conditions, such as HLOOKUP, but can’t do
numeric conditions. These functions sometimes permit the use of wildcards.

360		

Function

Allows numeric comparisons

Accepts wildcards

AVERAGEIF

yes

yes

AVERAGEIFS

yes

yes

COUNTIF

yes

yes

COUNTIFS

yes

yes

SUMIF

yes

yes

SUMIFS

yes

yes

Chapter 13    Additional Examples and Topics

Function

Allows numeric comparisons

Accepts wildcards

HLOOKUP

no

if exact match specified

MATCH

no

if exact match specified

VLOOKUP

no

if exact match specified

Examples of conditions, both with and without wildcards, are illustrated in this section.
Expression

Example

“>4” means match any number greater than 4.

=COUNTIF(B2:E7, “>4”) returns a count of the
number of cells in the range B2:E7 that contain a
value greater than 4.

“>=7” means match any number greater than or
equal to 7.

=SUMIF(B, “>=7”) sums the cells in the column B
that contain a value greater than or equal to 7.

“<=5” in combination with “>=15” means match
any number less than or equal to 5 or greater
than or equal to 15. Numbers 6 through 14,
inclusive, would not be included.

=SUMIF(A3:B12,”<=5”)+SUMIF(A3:B12,”>=15”)
sums the cells in the range A3:B12 that contain
a value less than or equal to 5 or greater than or
equal to 15.

“*it” means any value that ends with “it.” The
asterisk (*) matches any number of characters.

=COUNTIF(B2:E7, “*it”) returns a count of the
number of cells in the range B2:E7 that contain a
value that ends with “it” such as “bit” and “mit.” It
does not match “mitt.”

“~*” means to match the asterisk (*). The tilde
(~) character means to take the next character
literally, instead of treating it as a wildcard.

=COUNTIF(E, “~*”) returns a count of the number
of cells in column E that contain the asterisk
character.

B2 & “, “ & E2 returns the contents of cells B2 and
E2 separated by a comma and a space.

=B2&”, “&E2 returns “Last, First” if B2 contains “Last”
and E2 contains “First.”

“?ip” means any value that begins with a single
character followed by “ip.”

=COUNTIF(B2:E7, “?ip”) returns a count of the
number of cells in the range B2:E7 that contain
a value that starts with a character followed by
“ip” such as “rip” and “tip.” It does not match “drip”
or “trip.”

“~?” means to match the question mark (?).
The tilde (~) character means to take the next
character literally, instead of treating it as a
wildcard.

=SEARCH(“~?”, B2) returns 19 if cell B2 contains
“This is a question? Yes it is.”, since the question
mark is the 19th character in the string.

“*on?” means to match any value that begins
with any number of characters followed by “on”
and then a single character.

=COUNTIF(B2:E7, “*on?”) returns a count of the
number of cells in the range B2:E7 that contain a
value that starts with any number of characters
(including none) followed by “on” and then a
single character. This matches words such as
“alone”, “bone”, “one”, and “none.” This does not
match “only” (has two characters after the “on”) or
“eon” (has no characters after the “on”).

Chapter 13    Additional Examples and Topics

361

Survey Results Example

This example brings together the illustrations used throughout the statistical
functions. It is based on a hypothetical survey. The survey was short (only five
questions) and had a very limited number of respondents (10). Each question could
be answered on a scale of 1 to 5 (perhaps the range from “never” to “always”), or not
answered. Each survey was assigned a number before mailing. The following table
shows the results. Questions that were answered outside the range (incorrect) or not
answered are indicated with a blank cell in the table.

To illustrate some of the functions, assume that the survey control number included an
alphabetic prefix and that the scale was A–E, instead of 1–5. The table would then look
like this:

Using this table of data and some of the statistical functions available in iWork, you
can gather information about the survey results. Keep in mind that the example is
purposely small so results may seem obvious. However, if you had 50, 100, or more
respondents and perhaps many more questions, the results would not be obvious.

362		

Chapter 13    Additional Examples and Topics

Function and arguments

Description of result

=CORREL(B2:B11, C2:C11)

Determines the correlation of question 1 and
question 2 using linear regression analysis.
Correlation is a measure of how much two
variables (in this case, answers to survey
questions) change together. Specifically, this
would look at the question:  If a respondent
answered question 1 with a higher (or lower)
value than the average for question 1, did the
respondent also answer question 2 with a higher
(or lower) value than the average for question
2? In this case, the responses are not particularly
well correlated (-0.1732)

=COUNT(A2:A11) or =COUNTA(A2:A11)

Determines the total number of surveys returned
(10). Note that if the survey control identifier was
not numeric, you would need to use COUNTA
instead of COUNT.

=COUNT(B2:B11) or =COUNTA(B2:B11)

Determines the total number of responses to the
first question (9). By extending this formula across
the row, you could determine the total number
of responses to each question. Because all the
data is numeric, COUNTA returns the same results.
If, however, the survey had used A through E,
instead of 1 through 5, you would need to use
COUNTA to tally the results.

=COUNTBLANK(B2:B11)

Determines the number of empty cells,
representing invalid or no answers. If you
extended this formula across the row you would
find that question 3 (column D) had 3 invalid or
not-answered responses. This might cause you
to look at this question on the survey to see
if it was controversial or poorly worded, as no
other question had more than 1 incorrect or notanswered response.

=COUNTIF(B2:B11, “=5”)

Determines the number of respondents that gave
a 5 to a particular question (in this case, question
1). If you extended this formula across the row,
you would learn that only questions 1 and 4 had
any respondents give the question a 5. Had the
survey used A through E for the range, you would
have used =COUNTIF(B2:B11, “=E”).

Chapter 13    Additional Examples and Topics

363

Function and arguments

Description of result

=COVAR(B2:B11, C2:C11)

Determines the covariance of question 1 and
question 2. Covariance is a measure of how
much two variables (in this case, answers to
survey questions) change together. Specifically,
this would look at the question:  If a respondent
answered question 1 with a higher (or lower)
value than the average for question 1, did the
respondent also answer question 2 with a higher
(or lower) value than the average for question 2?
Note:  COVAR would not work with the table
using a scale of A–E, as it requires numeric
arguments.

364		

=STDEV(B2:B11) or =STDEVP(B2:B11)

Determines the standard deviation, one measure
of dispersion, of the answers to question 1. If
you extend this formula across the row, you
would see that the answers to question 3 had
the highest standard deviation. If the results
represented responses from the entire population
being studied, rather than a sample, STDEVP
would be used instead of STDEV. Note that STDEV
is the square root of VAR.

=VAR(B2:B11) or =VARP(B2:B11)

Determines the variance, one measure of
dispersion, of the answers to question 1. If you
extended this formula across the row, you would
see that the answers to question 5 had the lowest
variance. If the results represented responses
from the entire population being studied, rather
than a sample, VARP would be used instead of
VAR. Note that VAR is the square of STDEV.

Chapter 13    Additional Examples and Topics

Symbols

? wildcard  30, 361
* wildcard  30, 361
& string operator  30, 310
~ wildcard escape character  30, 361

A

ABS numeric function  170
absolute cell references  27
ACCRINT financial function  99, 351
ACCRINTM financial function  101
ACOS trigonometric function  327
ACOSH trigonometric function  328
ADDRESS reference function  207
ampersand string operator  30, 310
AND logical and information function  156, 358
any value type  36
AREAS reference function  209
arithmetic operators  28
array constant  35
array defined  35
array function
defined  35
FREQUENCY  257
INDEX  214
INDIRECT  216
LINEST  265
OFFSET  219
TRANSPOSE  222
ASIN trigonometric function  329
ASINH trigonometric function  329
asterisk wildcard  30, 361
ATAN trigonometric function  330
ATAN2 trigonometric function  331
ATANH trigonometric function  332
AVEDEV statistical function  230
AVERAGE statistical function  231
AVERAGEA statistical function  232
AVERAGEIF statistical function  233, 360
AVERAGEIFS statistical function  234, 360

B

BASETONUM engineering function  73

		

Index

Index

BESSELJ engineering function  74
BESSELY engineering function  75
BETADIST statistical function  236
BETAINV statistical function  237
BIN2DEC engineering function  76
BIN2HEX engineering function  77
BIN2OCT engineering function  78
BINOMDIST statistical function  238
bond investment related financial questions  351
BONDDURATION financial function  103
BONDMDURATION financial function  104
Boolean expression defined  35
Boolean value type  36

C

calculations, instant  17
CEILING numeric function  170, 355
cell comments example  358
cell references
distinguishing absolute and relative  27
inserting into formulas  26
CHAR text function  308
CHIDIST statistical function  239
CHIINV statistical function  239
CHITEST statistical function  240
CHOOSE reference function  209
choosing which TVM function to use  348
CLEAN text function  308
CODE text function  309
collection value type  36
colon as reference element separator  39
COLUMN reference function  210
COLUMNS reference function  211
COMBIN numeric function  172
commas as argument separators  34
common arguments used in financial functions  341
comparison operators  29
CONCATENATE text function  310
condition  30
comparison operators  29
defined  35
specifying  360
CONFIDENCE statistical function  242

365

constant defined  35
conversion units
distance  80
duration  80
energy  81
force  81
liquid  82
magnetism  82
metric prefixes  83
power  82
pressure  81
speed  81
temperature  82
weight and mass  80
CONVERT engineering function  79
copying help examples into a table  41
CORREL statistical function  242, 363
COS trigonometric function  333
COSH trigonometric function  334
COUNT statistical function  244, 363
COUNTA statistical function  245, 363
COUNTBLANK statistical function  246, 363
COUNTIF statistical function  247, 360, 361, 363
COUNTIFS statistical function  248, 253, 360
COUPDAYBS financial function  105
COUPDAYS financial function  107
COUPDAYSNC financial function  108
COUPNUM financial function  109, 351
COVAR statistical function  250, 364
CRITBINOM statistical function  252
CUMIPMT financial function  110, 112, 349
CUMPRINC financial function  349

D

date and time function
DATE  44
DATEDIF  45
DATEVALUE  47
DAY  47
DAYNAME  48
DAYS360  49
EDATE  50
EOMONTH  51
HOUR  51
MINUTE  52
MONTH  53
MONTHNAME  54
NETWORKDAYS  54
NOW  55
SECOND  56
TIME  56
TIMEVALUE  57
TODAY  58
WEEKDAY  59
WEEKNUM  60
WORKDAY  61

366		

Index

YEAR  62
YEARFRAC  63
DATE date and time function  44
DATEDIF date and time function  45
date/time value type  36
DATEVALUE date and time function  47
DAY date and time function  47
DAYNAME date and time function  48
DAYS360 date and time function  49
DB financial function  114, 352
DDB financial function  116, 352
DEC2BIN engineering function  83
DEC2HEX engineering function  84
DEC2OCT engineering function  85
DEGREES trigonometric function  334
DELTA engineering function  86
depreciation-related financial questions  352
DEVSQ statistical function  253
DISC financial function  117, 351
distance conversion units  80
DOLLAR financial function  311
double colon as reference element separator  39
DUR2DAYS duration function  65
DUR2HOURS duration function  65
DUR2MILLISECONDS duration function  66
DUR2MINUTES duration function  67
DUR2SECONDS duration function  68
DUR2WEEKS duration function  69
duration conversion units  80
DURATION duration function  70
duration function
DUR2DAYS  65
DUR2HOURS  65
DUR2MILLISECONDS  66
DUR2MINUTES  67
DUR2SECONDS  68
DUR2WEEKS  69
DURATION  70
STRIPDURATION  71
duration value type  37

E

EDATE date and time function  50
EFFECT financial function  119, 351
ellipsis syntax elements  35
energy conversion units  81
engineering function
BASETONUM  73
BESSELJ  74
BESSELY  75
BIN2DEC  76
BIN2HEX  77
BIN2OCT  78
CONVERT  79
DEC2BIN  83
DEC2HEX  84

DEC2OCT  85
DELTA  86
ERF  87
ERFC  87
GESTEP  88
HEX2BIN  89
HEX2DEC  90
HEX2OCT  91
NUMTOBASE  92
OCT2BIN  93
OCT2DEC  94
OCT2HEX  95
EOMONTH date and time function  51
ERF engineering function  87
ERFC engineering function  87
European days-basis  342
EVEN numeric function  173, 355
EXACT text function  312
EXP numeric function  174

F

FACT numeric function  174
FACTDOUBLE numeric function  175
FALSE logical and information function  157
FDIST statistical function  254, 255, 261
financial function
ACCRINT  99, 351
ACCRINTM  101
BONDDURATION  103
BONDMDURATION  104
COUPDAYBS  105
COUPDAYS  107
COUPDAYSNC  108
COUPNUM  109, 351
CUMIPMT  110
CUMPRINC  112
DB  114, 352
DDB  116, 352
DISC  117, 351
EFFECT  119, 351
FV  120, 348, 351
INTRATE  122, 352
IPMT  123, 353
IRR  125, 350
ISPMT  126
MIRR  128, 350
NOMINAL  129, 351
NPER  130, 348, 351
NPV  132, 350
PMT  134, 348, 351, 353
PPMT  135, 353
PRICE  137, 352
PRICEDISC  138
PRICEMAT  140
PV  349
RATE  144, 349

Index

RECEIVED  146, 352
SLN  147, 352
SYD  148, 352
VDB  149, 352
YIELD  150, 352
YIELDDISC  152
YIELDMAT  153
financial function argument defined
annual-rate  341
annual-yield  341
cash-flow  341
cost  341
cum-when-due  342, 347
days-basis  342
depr-factor  342
depr-period  343
effective-int-rate  343
end-per  343, 347
estimate  343
European days-basis  342
frequency  343
future-value  344
invest-amount  344
life  344
NASD days-basis  342
nominal-rate  344
num-periods  344
num-periodsyear  345
par  345
payment  345
period  345
periodic-discount-rate  345
periodic-rate  346
present-value  346
price  346
redemption  346
salvage  347
start-per  343, 347
when-due  347
FIND text function  312
finding and replacing
formula elements  32
text strings  312, 314, 316, 318, 319, 320
FIXED mathematical function  313
FLOOR numeric function  176, 355
force conversion units  81
FORECAST statistical function  256
formula bar  20
Formula Editor  19
formulas. See also operators; See also functions
adding a quick formula  18
copying and moving  30
creating  19
deleting  24
elements of  15
finding and replacing elements of  32

367

handling errors and warnings  23
inserting cell references  26
operators  28
performing instant calculations  17
using arithmetic operators  28
using cell references  24
using comparison operators  29
using the formula bar  20
using the Formula Editor  19
using the Function Browser  21
viewing all in a spreadsheet  31
formulas that reference the same cell in multiple
tables  39
FREQUENCY statistical function  257
Function Browser  21. See also functions
functions. See also formulas
adding to formulas  21
any value type defined  36
array constant defined  35
array defined  35
array function defined  35
Boolean expression defined  35
Boolean value type defined  36
collection value type defined  36
colon and double colon separators  39
comma and semicolon argument separators  34
condition defined  35
constant defined  35
date and time  42
date/time value type defined  36
duration  64
duration value type defined  37
ellipsis syntax element  35
engineering  72
financial  96
introduction to  33
italic text  34
list value type defined  38
logical and information  155
modal argument defined  35
modal value type defined  38
number value type defined  38
numeric  167
parentheses syntax element  34
range value type defined  38
reference  206
reference value type defined  39
statistical  225
string value type defined  39
syntax elements used in function definitions  34
table spanning formulas  39
text  306
trigonometric  326
uppercase text  34
FV financial function  120, 348, 351

368		

Index

G

GAMMADIST statistical function  259
GAMMAINV statistical function  260
GAMMALN statistical function  260
GCD numeric function  177
GESTEP engineering function  88

H

HARMEAN statistical function  262
HEX2BIN engineering function  89
HEX2DEC engineering function  90
HEX2OCT engineering function  91
HLOOKUP reference function  211, 361
HOUR date and time function  51
HYPERLINK reference function  213

I

IF logical and information function  158, 358
IF logical function  360
IFERROR logical and information function  159
IFERROR logical function  360
INDEX reference function  214
INDIRECT reference function  216
instant calculations  17
INT numeric function  178, 355
INTERCEPT statistical function  262
INTRATE financial function  122, 352
introduction to functions  33
IPMT financial function  123, 349, 353
IRR financial function  125, 350
ISBLANK logical and information function  160, 358
ISERROR logical and information function  161
ISERROR logical function  360
ISEVEN logical and information function  162
ISODD logical and information function  163
ISPMT financial function  126
italic text syntax elements  34

L

LARGE statistical function  264
LCM numeric function  179
LEFT text function  314
LEN text function  315
LINEST additional statistics  267
LINEST statistical function  265
liquid conversion units  82
list value type  38
LN numeric function  179
loan amortization table  353
loan related financial questions  351
LOG numeric function  180
LOG10 numeric function  181
logical and information function
AND  156, 358
FALSE  157

IF  158, 358
IFERROR  159
ISBLANK  160, 358
iserror  161
ISEVEN  162
ISODD  163
NOT  164
OR  165, 358
TRUE  166
LOGINV statistical function  268
LOGNORMDIST statistical function  269
LOOKUP reference function  217
LOWER text function  316

M

magnetism conversion units  82
MATCH reference function  218, 361
MAX statistical function  270
MAXA statistical function  270
MEDIAN statistical function  271
metric prefixes for conversion units  83
MID text function  316
MIN statistical function  272
MINA statistical function  273
MINUTE date and time function  52
MIRR financial function  128, 350
MOD numeric function  182
modal argument defined  35
modal value type  38
MODE statistical function  274
MONTH date and time function  53
MONTHNAME date and time function  54
MROUND numeric function  183, 355
MULTINOMIAL numeric function  184

N

NASD days-basis method  342
navigating to table cells referenced in formulas  26
NEGBINOMDIST statistical function  275
NETWORKDAYS date and time function  54
NOMINAL financial function  129, 351
NORMDIST statistical function  276
NORMINV statistical function  277
NORMSDIST statistical function  277
NORMSINV statistical function  278
NOT logical and information function  164
NOW date and time function  55
NPER financial function  130, 348, 351
NPV financial function  132, 350
number value type  38
numeric function
CEILING  355
EVEN  355
FLOOR  355
INT  355
MROUND  355

Index

ODD  355
ROUND  356
ROUNDDOWN  356
ROUNDUP  357
TRUNC  357
numeric functions
ABS  170
CEILING  170
COMBIN  172
EVEN  173
EXP  174
FACT  174
FACTDOUBLE  175
FLOOR  176
GCD  177
INT  178
LCM  179
LN  179
LOG  180
LOG10  181
MOD  182
MROUND  183
MULTINOMIAL  184
ODD  185
PI  186
POWER  186
PRODUCT  187
QUOTIENT  188
RAND  189
RANDBETWEEN  189
ROMAN  190
ROUND  191
ROUNDDOWN  192
ROUNDUP  193
SIGN  195
SQRT  195
SQRTPI  196
SUM  196
SUMIF  197, 360
SUMIFS  198, 360
SUMPRODUCT  200
SUMSQ  201
SUMX2MY2  202
SUMX2PY2  203
SUMXMY2  204
TRUNC  204
NUMTOBASE mathematical function  92

O

OCT2BIN engineering function  93
OCT2DEC engineering function  94
OCT2HEX engineering function  95
ODD numeric function  185, 355
OFFSET reference function  219
operators
arithmetic  28

369

comparison  29
string  30, 310
OR logical and information function  165, 358

P

parentheses syntax elements  34
pasting help examples into a table  41
PERCENTILE statistical function  279
PERCENTRANK statistical function  280
PERMUT statistical function  281
PI numeric function  186
PMT financial function  134, 348, 351, 353
POISSON statistical function  282
power conversion units  82
POWER numeric function  186
PPMT financial function  135, 349, 353
pressure conversion units  81
PRICE financial function  137, 352
PRICEDISC financial function  138
PRICEMAT financial function  140
PROB statistical function  282
PRODUCT numeric function  187
PROPER text function  317
PV financial function  141, 349

Q

QUARTILE statistical function  284
question mark wildcard  30, 361
quick formulas  18
QUOTIENT numeric function  188

R

RADIANS trigonometric function  335
RAND numeric function  189
RANDBETWEEN numeric function  189
range value type  38
RANK statistical function  285
RATE financial function  144, 349
RECEIVED financial function  146, 352
reference function
ADDRESS  207
AREAS  209
CHOOSE  209
COLUMN  210
COLUMNS  211
HLOOKUP  211, 361
HYPERLINK  213
INDEX  214
INDIRECT  216
LOOKUP  217
MATCH  218, 361
OFFSET  219
ROW  221
ROWS  221
TRANSPOSE  222

370		

Index

VLOOKUP  223, 361
reference value type  39
referencing the same cell in multiple tables  39
regular expressions using wildcards  361
relative cell references  27
REPLACE text function  318
REPT text function  319
RIGHT text function  319
ROMAN numeric function  190
ROUND numeric function  191, 356
ROUNDDOWN numeric function  192, 356
rounding  355
ROUNDUP numeric function  193, 357
ROW reference function  221
ROWS reference function  221

S

savings related financial questions  351
search expressions  361
SEARCH text function  320, 361
searching for formulas. See finding and replacing
SECOND date and time function  56
semicolons as argument separators  34
SIGN numeric function  195
SIN trigonometric function  336
SINH trigonometric function  337
SLN financial function  147, 352
SLOPE statistical function  287
SMALL statistical function  288
solving common financial questions  351
speed conversion units  81
spreadsheets
finding and replacing formula elements  32
viewing all formulas in  31
SQRT numeric function  195
SQRTPI numeric function  196
STANDARDIZE statistical function  289
statistical function
AVEDEV  230
AVERAGE  231
AVERAGEA  232
AVERAGEIF  233, 360
AVERAGEIFS  234, 360
BETADIST  236
BETAINV  237
BINOMDIST  238
CHIDIST  239
CHIINV  239
CHITEST  240
CONFIDENCE  242
CORREL  242, 363
COUNT  244, 363
COUNTA  245, 363
COUNTBLANK  246, 363
COUNTIF  247, 360, 363
COUNTIFS  248, 360

COVAR  250, 364
CRITBINOM  252
DEVSQ  253
EXPONDIST  253
FDIST  254
FINV  255
FORECAST  256
FREQUENCY  257
GAMMADIST  259
GAMMAINV  260
GAMMALN  260
GEOMEAN  261
HARMEAN  262
INTERCEPT  262
LARGE  264
LINEST  265
LOGINV  268
LOGNORMDIST  269
MAX  270
MAXA  270
MEDIAN  271
MIN  272
MINA  273
MODE  274
NEGBINOMDIST  275
NORMDIST  276
NORMINV  277
NORMSDIST  277
NORMSINV  278
PERCENTILE  279
PERCENTRANK  280
PERMUT  281
POISSON  282
PROB  282
QUARTILE  284
RANK  285
SLOPE  287
SMALL  288
STANDARDIZE  289
STDEV  290, 364
STDEVA  291
STDEVP  293, 364
STDEVPA  294
TDIST  296
TINV  297
TTEST  297
VAR  298, 364
VARA  300
VARP  302, 364
VARPA  303
ZTEST  305
STDEV statistical function  290, 364
STDEVA statistical function  291
STDEVP statistical function  293, 364
STDEVPA statistical function  294
string operator  30

Index

string value type  39
STRIPDURATION duration function  71
SUBSTITUTE text function  322
SUM numeric function  196
SUMIF mathematical function  360
SUMIF numeric function  197, 361
SUMIFS numeric function  198, 360
SUMPRODUCT numeric function  200
SUMSQ numeric function  201
SUMX2MY2 numeric function  202
SUMX2PY2 numeric function  203
SUMXMY2 numeric function  204
survey results example  362
SYD financial function  148, 352
syntax elements used in function definitions  34

T

T text function  323
table spanning formulas  39
TAN trigonometric function  338
TANH trigonometric function  339
TDIST statistical function  296
temperature conversion units  82
text function
CHAR  308
CLEAN  308
CODE  309
CONCATENATE  310
DOLLAR  311
EXACT  312
FIND  312
FIXED  313
LEFT  314
LEN  315
LOWER  316
MID  316
PROPER  317
REPLACE  318
REPT  319
RIGHT  319
SEARCH  320
SUBSTITUTE  322
T  323
TRIM  323
UPPER  324
VALUE  325
tilde wildcard escape character  30, 361
TIME date and time function  56
TIMEVALUE date and time function  57
TINV statistical function  297
TODAY date and time function  58
TRANSPOSE reference function  222
trapping division by zero  360
trigonometric function
ACOS  327
ACOSH  328

371

ASIN  329
ASINH  329
ATAN  330
ATAN2  331
ATANH  332
COS  333
COSH  334
DEGREES  334
RADIANS  335
SIN  336
SINH  337
TAN  338
TANH  339
TRIM text function  323
TRUE logical and information function  166
TRUNC numeric function  204, 357
TTEST statistical function  297

U

UPPER text function  324
uppercase text syntax elements  34
using a formula to reference the same cell in
multiple tables  39
using help examples in a table  41
using logical and information functions
together  358

V

VALUE text function  325
value types
any  36
Boolean  36
collection  36
date/time  36
duration  37
list  38
modal  38
number  38
range  38
reference  39
string  39
VAR statistical function  298, 364
VARA statistical function  300
VARP statistical function  302, 364
VARPA statistical function  303
VDB financial function  149, 352
VLOOKUP reference function  223, 361

W

WEEKDAY date and time function  59
WEEKNUM date and time function  60
weight and mass conversion units  80
wildcards  30, 360, 361
WORKDAY date and time function  61
working with help example tables  41

372		

Index

Y

YEAR date and time function  62
YEARFRAC date and time function  63
YIELD financial function  150, 352
YIELDDISC financial function  152
YIELDMAT financial function  153

Z

zero coupon bond  351
ZTEST statistical function  305



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Manifest Reference Document ID  : uuid:EAA2BA89933311DA9A6B9C90BDB5F4C7, uuid:E5E8219EBBED11DDB711BA9A63A1B210, uuid:5C7AD3C19C3111DDBDCEBB20DA5B74C1, uuid:2CFD8A70A9B611DD98798856A2073E47, uuid:D331596CB28111DD95A8979D28099526, uuid:4EB61972B62511DD9FC4CD8F844D3BF2, uuid:42761B51B26311DD95A8979D28099526, uuid:3433BA5CB30811DDB363D372443F8350, uuid:20E252AE2CAADD11B6AE86C2CF83E9F8, uuid:7B20F67CA9B5DD119772CE553DCF66ED, uuid:A9082F602CAADD11B6AE86C2CF83E9F8, uuid:7EC53C0EF7A9DD11B6AE86C2CF83E9F8, uuid:B73D7147EEACDD1180C2AEB89819AD4B, uuid:3285CD9BEEACDD1180C2AEB89819AD4B, uuid:F61FDFAFEDACDD1180C2AEB89819AD4B, uuid:947B559EEDACDD1180C2AEB89819AD4B, uuid:427D02201AACDD11A1F4FD804E7569DB, uuid:108B40071AACDD11A1F4FD804E7569DB, uuid:E10166EF19ACDD11A1F4FD804E7569DB, uuid:E10166EF19ACDD11A1F4FD804E7569DB, uuid:E10166EF19ACDD11A1F4FD804E7569DB, uuid:0FD518501CACDD11A1F4FD804E7569DB, uuid:C78856831CACDD11A1F4FD804E7569DB, uuid:BCC6A40C1CACDD11A1F4FD804E7569DB, uuid:FC66CDDC1BACDD11A1F4FD804E7569DB, uuid:B069A29219ACDD11A1F4FD804E7569DB, uuid:9AE9054D1DACDD11A1F4FD804E7569DB, uuid:9AE9054D1DACDD11A1F4FD804E7569DB, uuid:1CB382351DACDD11A1F4FD804E7569DB, uuid:89AA161F1DACDD11A1F4FD804E7569DB, uuid:239988071DACDD11A1F4FD804E7569DB, uuid:239988071DACDD11A1F4FD804E7569DB, uuid:239988071DACDD11A1F4FD804E7569DB, uuid:239988071DACDD11A1F4FD804E7569DB, uuid:9AE9054D1DACDD11A1F4FD804E7569DB, uuid:89AA161F1DACDD11A1F4FD804E7569DB, uuid:7E0FB9AA1CACDD11A1F4FD804E7569DB, uuid:A95532981CACDD11A1F4FD804E7569DB, uuid:89AA161F1DACDD11A1F4FD804E7569DB, uuid:1EE652241CACDD11A1F4FD804E7569DB, uuid:5D5AF16A1CACDD11A1F4FD804E7569DB, uuid:7A9C65681AACDD11A1F4FD804E7569DB, uuid:C4965D511AACDD11A1F4FD804E7569DB, uuid:7A9C65681AACDD11A1F4FD804E7569DB, uuid:89AA161F1DACDD11A1F4FD804E7569DB, uuid:7A9C65681AACDD11A1F4FD804E7569DB, uuid:DD60BC321AACDD11A1F4FD804E7569DB, uuid:DD60BC321AACDD11A1F4FD804E7569DB, uuid:DD60BC321AACDD11A1F4FD804E7569DB, uuid:DD60BC321AACDD11A1F4FD804E7569DB, uuid:BF50CE8A1DACDD11A1F4FD804E7569DB, uuid:E92F07611DACDD11A1F4FD804E7569DB, uuid:7A7EBC3D1CACDD11A1F4FD804E7569DB, uuid:6CD5F9D41CACDD11A1F4FD804E7569DB, uuid:A07F3CBF1CACDD11A1F4FD804E7569DB
Create Date                     : 2009:09:08 15:16:32-07:00
Modify Date                     : 2009:09:08 15:18:39-07:00
Metadata Date                   : 2009:09:08 15:18:39-07:00
Creator Tool                    : Adobe InDesign CS3 (5.0.4)
Format                          : application/pdf
Creator                         : Apple Inc.
Title                           : iWork - Formulas and Functions User Guide
Startup Profile                 : Print
Producer                        : Adobe PDF Library 8.0
Trapped                         : False
Page Count                      : 372
Page Layout                     : SinglePage
Author                          : Apple Inc.
Warning                         : [Minor] Ignored duplicate Info dictionary

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