A bibliography of financial, statistical, and engineering methods

The following books provide detailed information on financial, statistical, and engineering methods.

Abramowitz, Milton, and Irene A. Stegun. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. 10th ed. New York, NY: Dover Publications, 1974.

Antkies, Candace Mary. Standard Securities Calculation Methods: Fixed Income Securities Formulas for Price, Yield and Accrued Interest: Volume 1. New York, NY: Securities Industry Association.

Antkies, Candace Mary. Standard Securities Calculation Methods, Fixed Income Securities Formulas for Analytic Measures: Volume 2. New York, NY: Securities Industry Association.

Devore, Jay L. Probability and Statistics for Engineering and the Sciences. 5th ed. Pacific Grove, CA: Duxbury Press, 1998.

Fabozzi, Frank J. The Handbook of Fixed-Income Securities. 6th ed. New York, NY: Mcgraw-Hill Trade, 2000.

Hewlett-Packard, HP-12C Solutions Handbook. Palo Alto, CA: Hewlett-Packard, 2001.

McCall, Robert B. Fundamental Statistics for the Behavioral Sciences. 7th ed. Pacific Grove, CA: Brooks Cole, 1998.

Monks, Joseph G. Operations Management: Theory and Problems. 3rd ed. New York, NY: Macmillan/McGraw-Hill, 1988.

Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes in C: The Art of Scientific Computing. 2nd ed. New York, NY: Cambridge University Press, 1993.

Sokal, Robert R., and F. James Rohlf. Biometry: The Principles and Practice of Statistics in Biological Research. 3rd ed. New York, NY: W. H. Freeman, 1994.

Stigum, Marcia, and John Mann. Money Market Calculations: Yields, Break-Evens, & Arbitrage. 2nd ed. Homewood, IL: Irwin Professional, 1991.

See Also

• List of worksheet functions (by category)

Excel > Function reference > Math and trigonometry

Math and trigonometry functions

Click one of the links in the following list to see detailed help about the function.

See Also

• List of worksheet functions (alphabetical)
• List of worksheet functions (by category)

Excel > Function reference > Math and trigonometry

ABS function

Excel 2007

Returns the absolute value of a number. The absolute value of a number is the number without its sign.

Syntax

ABS(number)

Number   is the real number of which you want the absolute value.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• Calculate percentages
• IMABS function
• Math and trigonometry functions
• SIGN function

Excel > Function reference > Math and trigonometry

ACOS function

Excel 2007

Returns the arccosine, or inverse cosine, of a number. The arccosine is the angle whose cosine is number. The returned angle is given in radians in the range 0 (zero) to pi.

Syntax

ACOS(number)

Number   is the cosine of the angle you want and must be from -1 to 1.

Remark

If you want to convert the result from radians to degrees, multiply it by 180/PI() or use the DEGREES function.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• COS function
• Math and trigonometry functions
• PI function

Excel > Function reference > Math and trigonometry

ACOSH function

Excel 2007

Returns the inverse hyperbolic cosine of a number. Number must be greater than or equal to 1. The inverse hyperbolic cosine is the value whose hyperbolic cosine is number, so ACOSH(COSH(number)) equals number.

Syntax

ACOSH(number)

Number   is any real number equal to or greater than 1.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• ASINH function
• ATANH function
• COSH function
• Math and trigonometry functions

Excel > Function reference > Math and trigonometry

ASIN function

Excel 2007

Returns the arcsine, or inverse sine, of a number. The arcsine is the angle whose sine is number. The returned angle is given in radians in the range -pi/2 to pi/2.

Syntax

ASIN(number)

Number   is the sine of the angle you want and must be from -1 to 1.

Remark

To express the arcsine in degrees, multiply the result by 180/PI( ) or use the DEGREES function.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• ASINH function
• Math and trigonometry functions
• PI function
• SIN function

Excel > Function reference > Math and trigonometry

ASINH function

Excel 2007

Returns the inverse hyperbolic sine of a number. The inverse hyperbolic sine is the value whose hyperbolic sine is number, so ASINH(SINH(number)) equals number.

Syntax

ASINH(number)

Number   is any real number.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• ACOSH function
• ATANH function
• Math and trigonometry functions
• SINH function

Excel > Function reference > Math and trigonometry

ATAN function

Excel 2007

Returns the arctangent, or inverse tangent, of a number. The arctangent is the angle whose tangent is number. The returned angle is given in radians in the range -pi/2 to pi/2.

Syntax

ATAN (number)

Number   is the tangent of the angle you want.

Remark

To express the arctangent in degrees, multiply the result by 180/PI( ) or use the DEGREES function.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• ATAN2 function
• ATANH function
• Math and trigonometry functions
• PI function
• TAN function

Excel > Function reference > Math and trigonometry

ATANH function

Excel 2007

Returns the inverse hyperbolic tangent of a number. Number must be between -1 and 1 (excluding -1 and 1). The inverse hyperbolic tangent is the value whose hyperbolic tangent is number, so ATANH(TANH(number)) equals number.

Syntax

ATANH(number)

Number   is any real number between 1 and -1.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• ACOSH function
• ASINH function
• Math and trigonometry functions
• TANH function

Excel > Function reference > Math and trigonometry

ATAN2 function

Excel 2007

Returns the arctangent, or inverse tangent, of the specified x- and y-coordinates. The arctangent is the angle from the x-axis to a line containing the origin (0, 0) and a point with coordinates (x_num, y_num). The angle is given in radians between -pi and pi, excluding -pi.

Syntax

ATAN2(x_num,y_num)

X_num   is the x-coordinate of the point.

Y_num   is the y-coordinate of the point.

Remarks

• A positive result represents a counterclockwise angle from the x-axis; a negative result represents a clockwise angle.
• ATAN2(a,b) equals ATAN(b/a), except that a can equal 0 in ATAN2.
• If both x_num and y_num are 0, ATAN2 returns the #DIV/0! error value.
• To express the arctangent in degrees, multiply the result by 180/PI( ) or use the DEGREES function.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• ATAN function
• ATANH function
• Math and trigonometry functions
• PI function
• TAN function

Excel > Function reference > Math and trigonometry

CEILING function

Excel 2007

Returns number rounded up, away from zero, to the nearest multiple of significance. For example, if you want to avoid using pennies in your prices and your product is priced at $4.42, use the formula =CEILING(4.42,0.05) to round prices up to the nearest nickel.

Syntax

CEILING(number,significance)

Number   is the value you want to round.

Significance   is the multiple to which you want to round.

Remarks

• If either argument is nonnumeric, CEILING returns the #VALUE! error value.
• Regardless of the sign of number, a value is rounded up when adjusted away from zero. If number is an exact multiple of significance, no rounding occurs.
• If number and significance have different signs, CEILING returns the #NUM! error value.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• EVEN function
• FLOOR function
• INT function
• Math and trigonometry functions
• ODD function
• ROUND function
• ROUNDDOWN function
• ROUNDUP function
• TRUNC function

Excel > Function reference > Math and trigonometry

COMBIN function

Excel 2007

Returns the number of combinations for a given number of items. Use COMBIN to determine the total possible number of groups for a given number of items.

Syntax

COMBIN(number,number_chosen)

Number   is the number of items.

Number_chosen   is the number of items in each combination.

Remarks

• Numeric arguments are truncated to integers.
• If either argument is nonnumeric, COMBIN returns the #VALUE! error value.
• If number < 0, number_chosen < 0, or number < number_chosen, COMBIN returns the #NUM! error value.
• A combination is any set or subset of items, regardless of their internal order. Combinations are distinct from permutations, for which the internal order is significant.
• The number of combinations is as follows, where number = n and number_chosen = k:

where:

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• BINOMDIST function
• CRITBINOM function
• FACT function
• HYPGEOMDIST function
• Math and trigonometry functions
• NEGBINOMDIST function
• PERMUT function

Excel > Function reference > Math and trigonometry

COS function

Excel 2007

Returns the cosine of the given angle.

Syntax

COS(number)

Number   is the angle in radians for which you want the cosine.

Remark

If the angle is in degrees, either multiply the angle by PI()/180 or use the RADIANS function to convert the angle to radians.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• ACOS function
• COSH function
• Math and trigonometry functions
• PI function

Excel > Function reference > Math and trigonometry

COSH function

Excel 2007

Returns the hyperbolic cosine of a number.

Syntax

COSH(number)

Number   is any real number for which you want to find the hyperbolic cosine.

Remark

The formula for the hyperbolic cosine is:

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• ACOSH function
• Math and trigonometry functions
• SINH function
• TANH function

Excel > Function reference > Math and trigonometry

DEGREES function

Excel 2007

Converts radians into degrees.

Syntax

DEGREES(angle)

Angle   is the angle in radians that you want to convert.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• Math and trigonometry functions
• RADIANS function

Excel > Function reference > Math and trigonometry

EVEN function

Excel 2007

Returns number rounded up to the nearest even integer. You can use this function for processing items that come in twos. For example, a packing crate accepts rows of one or two items. The crate is full when the number of items, rounded up to the nearest two, matches the crate's capacity.

Syntax

EVEN(number)

Number   is the value to round.

Remarks

• If number is nonnumeric, EVEN returns the #VALUE! error value.
• Regardless of the sign of number, a value is rounded up when adjusted away from zero. If number is an even integer, no rounding occurs.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• CEILING function
• FLOOR function
• INT function
• ISEVEN function
• ISODD function
• Math and trigonometry functions
• ODD function
• Round a number
• ROUND function
• TRUNC function

Excel > Function reference > Math and trigonometry

EXP function

Excel 2007

Returns e raised to the power of number. The constant e equals 2.71828182845904, the base of the natural logarithm.

Syntax

EXP(number)

Number   is the exponent applied to the base e.

Remarks

• To calculate powers of other bases, use the exponentiation operator (^).
• EXP is the inverse of LN, the natural logarithm of number.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• IMEXP function
• LN function
• LOG function
• Math and trigonometry functions
• POWER function

Excel > Function reference > Math and trigonometry

FACT function

Excel 2007

Returns the factorial of a number. The factorial of a number is equal to 1*2*3*...* number.

Syntax

FACT(number)

Number   is the nonnegative number for which you want the factorial. If number is not an integer, it is truncated.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• Calculate the factorial or permutation of a number
• FACTDOUBLE function
• Math and trigonometry functions
• PRODUCT function

Excel > Function reference > Math and trigonometry

FACTDOUBLE function

Returns the double factorial of a number.

Syntax

FACTDOUBLE(number)

Number   is the value for which to return the double factorial. If number is not an integer, it is truncated.

Remarks

• If number is nonnumeric, FACTDOUBLE returns the #VALUE! error value.
• If number is negative, FACTDOUBLE returns the #NUM! error value.
• If number is even:

• If number is odd:

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• FACT function
• Math and trigonometry functions
• MULTINOMIAL function

Excel > Function reference > Math and trigonometry

FLOOR function

Excel 2007

Rounds number down, toward zero, to the nearest multiple of significance.

Syntax

FLOOR(number,significance)

Number   is the numeric value you want to round.

Significance   is the multiple to which you want to round.

Remarks

• If either argument is nonnumeric, FLOOR returns the #VALUE! error value.
• If number and significance have different signs, FLOOR returns the #NUM! error value.
• Regardless of the sign of number, a value is rounded down when adjusted away from zero. If number is an exact multiple of significance, no rounding occurs.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• CEILING function
• EVEN function
• INT function
• Math and trigonometry functions
• ODD function
• ROUND function
• ROUNDDOWN function
• TRUNC function

Excel > Function reference > Math and trigonometry

GCD function

Returns the greatest common divisor of two or more integers. The greatest common divisor is the largest integer that divides both number1 and number2 without a remainder.

Syntax

GCD(number1,number2, ...)

Number1, number2, ...   are 1 to 255 values. If any value is not an integer, it is truncated.

Remarks

• If any argument is nonnumeric, GCD returns the #VALUE! error value.
• If any argument is less than zero, GCD returns the #NUM! error value.
• One divides any value evenly.
• A prime number has only itself and one as even divisors.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• LCM function
• Math and trigonometry functions

Excel > Function reference > Math and trigonometry

INT function

Excel 2007

Rounds a number down to the nearest integer.

Syntax

INT(number)

Number   is the real number you want to round down to an integer.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• Calculate the difference between two times
• CEILING function
• Convert times
• FLOOR function
• Math and trigonometry functions
• MOD function
• MROUND function
• Round a number
• ROUND function
• TRUNC function

Excel > Function reference > Math and trigonometry

LCM function

Returns the least common multiple of integers. The least common multiple is the smallest positive integer that is a multiple of all integer arguments number1, number2, and so on. Use LCM to add fractions with different denominators.

Syntax

LCM(number1,number2, ...)

Number1, number2,...   are 1 to 255 values for which you want the least common multiple. If value is not an integer, it is truncated.

Remarks

• If any argument is nonnumeric, LCM returns the #VALUE! error value.
• If any argument is less than zero, LCM returns the #NUM! error value.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• GCD function
• Math and trigonometry functions

Excel > Function reference > Math and trigonometry

LN function

Excel 2007

Returns the natural logarithm of a number. Natural logarithms are based on the constant e (2.71828182845904).

Syntax

LN(number)

Number   is the positive real number for which you want the natural logarithm.

Remark

LN is the inverse of the EXP function.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• EXP function
• IMLN function
• IMLOG10 function
• IMLOG2 function
• LOG function
• LOG10 function
• Math and trigonometry functions

Excel > Function reference > Math and trigonometry

LOG function

Excel 2007

Returns the logarithm of a number to the base you specify.

Syntax

LOG(number,base)

Number   is the positive real number for which you want the logarithm.

Base   is the base of the logarithm. If base is omitted, it is assumed to be 10.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• EXP function
• IMLN function
• IMLOG10 function
• IMLOG2 function
• LN function
• LOG10 function
• Math and trigonometry functions

Excel > Function reference > Math and trigonometry

LOG10 function

Excel 2007

Returns the base-10 logarithm of a number.

Syntax

LOG10(number)

Number   is the positive real number for which you want the base-10 logarithm.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• EXP function
• IMLN function
• IMLOG10 function
• IMLOG2 function
• LN function
• LOG function
• Math and trigonometry functions

Excel > Function reference > Math and trigonometry

MDETERM function

Excel 2007

Returns the matrix determinant of an array.

Syntax

MDETERM(array)

Array   is a numeric array with an equal number of rows and columns.

Remarks

• Array can be given as a cell range, for example, A1:C3; as an array constant, such as {1,2,3;4,5,6;7,8,9}; or as a name to either of these.
• MDETERM returns the #VALUE! error when:
  • Any cells in array are empty or contain text.
  • Array does not have an equal number of rows and columns.
• The matrix determinant is a number derived from the values in array. For a three-row, three-column array, A1:C3, the determinant is defined as:

MDETERM(A1:C3)

equals

A1*(B2*C3-B3*C2) + A2*(B3*C1-B1*C3) + A3*(B1*C2-B2*C1)

• Matrix determinants are generally used for solving systems of mathematical equations that involve several variables.
• MDETERM is calculated with an accuracy of approximately 16 digits, which may lead to a small numeric error when the calculation is not complete. For example, the determinant of a singular matrix may differ from zero by 1E-16.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• Math and trigonometry functions
• MINVERSE function
• MMULT function
• TRANSPOSE function

Excel > Function reference > Math and trigonometry

MINVERSE function

Excel 2007

Returns the inverse matrix for the matrix stored in an array.

Syntax

MINVERSE(array)

Array   is a numeric array with an equal number of rows and columns.

Remarks

• Array can be given as a cell range, such as A1:C3; as an array constant, such as {1,2,3;4,5,6;7,8,9}; or as a name for either of these.
• If any cells in array are empty or contain text, MINVERSE returns the #VALUE! error value.
• MINVERSE also returns the #VALUE! error value if array does not have an equal number of rows and columns.
• Formulas that return arrays must be entered as array formulas.
• Inverse matrices, like determinants, are generally used for solving systems of mathematical equations involving several variables. The product of a matrix and its inverse is the identity matrix — the square array in which the diagonal values equal 1, and all other values equal 0.
• As an example of how a two-row, two-column matrix is calculated, suppose that the range A1:B2 contains the letters a, b, c, and d that represent any four numbers. The following table shows the inverse of the matrix A1:B2.

• MINVERSE is calculated with an accuracy of approximately 16 digits, which may lead to a small numeric error when the cancellation is not complete.
• Some square matrices cannot be inverted and will return the #NUM! error value with MINVERSE. The determinant for a noninvertable matrix is 0.

Example 1

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

 Note    The formula in the example must be entered as an array formula. After copying the example to a blank worksheet, select the range A5:B6 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER. If the formula is not entered as an array formula, the single result is 0.

Example 2

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

 Note    The formula in the example must be entered as an array formula. After copying the example to a blank worksheet, select the range A6:C8 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER. If the formula is not entered as an array formula, the single result is 0.25.

Tip  Use the INDEX function to access individual elements from the inverse matrix.

See Also

• Excel specifications and limits
• INDEX function
• Math and trigonometry functions
• MMULT function
• TRANSPOSE function

Excel > Function reference > Math and trigonometry

MMULT function

Excel 2007

Returns the matrix product of two arrays. The result is an array with the same number of rows as array1 and the same number of columns as array2.

Syntax

MMULT(array1,array2)

Array1, array2   are the arrays you want to multiply.

Remarks

• The number of columns in array1 must be the same as the number of rows in array2, and both arrays must contain only numbers.
• Array1 and array2 can be given as cell ranges, array constants, or references.
• MMULT returns the #VALUE! error when:
  • Any cells are empty or contain text.
  • The number of columns in array1 is different from the number of rows in array2.
• The matrix product array a of two arrays b and c is:

where i is the row number, and j is the column number.

• Formulas that return arrays must be entered as array formulas.

Example 1

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

 Note    The formula in the example must be entered as an array formula. After copying the example to a blank worksheet, select the range A8:B9 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER. If the formula is not entered as an array formula, the single result is 2.

Example 2

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

 Note    The formula in the example must be entered as an array formula. After copying the example to a blank worksheet, select the range A8:B9 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER. If the formula is not entered as an array formula, the single result is 6.

See Also

• Math and trigonometry functions
• MDETERM function
• MINVERSE function
• TRANSPOSE function

Excel > Function reference > Math and trigonometry

MOD function

Excel 2007

Returns the remainder after number is divided by divisor. The result has the same sign as divisor.

Syntax

MOD(number,divisor)

Number   is the number for which you want to find the remainder.

Divisor   is the number by which you want to divide number.

Remarks

• If divisor is 0, MOD returns the #DIV/0! error value.
• The MOD function can be expressed in terms of the INT function:

MOD(n, d) = n - d*INT(n/d)

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• INT function
• Math and trigonometry functions
• ROUND function
• ROUNDDOWN function
• ROUNDUP function
• TRUNC function

Excel > Function reference > Math and trigonometry

MROUND function

Excel 2007

Returns a number rounded to the desired multiple.

Syntax

MROUND(number,multiple)

Number   is the value to round.

Multiple   is the multiple to which you want to round number.

Remark

MROUND rounds up, away from zero, if the remainder of dividing number by multiple is greater than or equal to half the value of multiple.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• CEILING function
• EVEN function
• FLOOR function
• Math and trigonometry functions
• ODD function
• Round a number
• ROUND function
• ROUNDDOWN function
• ROUNDUP function
• TRUNC function

Excel > Function reference > Math and trigonometry

MULTINOMIAL function

Excel 2007

Returns the ratio of the factorial of a sum of values to the product of factorials.

Syntax

MULTINOMIAL(number1,number2, ...)

Number1,number2, ...   are 1 to 255 values for which you want the multinomial.

Remarks

• If any argument is nonnumeric, MULTINOMIAL returns the #VALUE! error value.
• If any argument is less than zero, MULTINOMIAL returns the #NUM! error value.
• The multinomial is:

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• FACT function
• FACTDOUBLE function
• Math and trigonometry functions

Excel > Function reference > Math and trigonometry

ODD function

Excel 2007

Returns number rounded up to the nearest odd integer.

Syntax

ODD(number)

Number   is the value to round.

Remarks

• If number is nonnumeric, ODD returns the #VALUE! error value.
• Regardless of the sign of number, a value is rounded up when adjusted away from zero. If number is an odd integer, no rounding occurs.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• CEILING function
• EVEN function
• FLOOR function
• INT function
• ISEVEN function
• ISODD function
• Math and trigonometry functions
• Round a number
• ROUND function
• TRUNC function

Excel > Function reference > Math and trigonometry

PI function

Excel 2007

Returns the number 3.14159265358979, the mathematical constant pi, accurate to 15 digits.

Syntax

PI( )

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• COS function
• Math and trigonometry functions
• SIN function
• TAN function

Excel > Function reference > Math and trigonometry

POWER function

Excel 2007

Returns the result of a number raised to a power.

Syntax

POWER(number,power)

Number   is the base number. It can be any real number.

Power   is the exponent to which the base number is raised.

Remark

The "^" operator can be used instead of POWER to indicate to what power the base number is to be raised, such as in 5^2.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• Math and trigonometry functions
• Raise a number to a power

Excel > Function reference > Math and trigonometry

PRODUCT function

Excel 2007

This article describes the formula syntax and usage of the PRODUCT function (function: A prewritten formula that takes a value or values, performs an operation, and returns a value or values. Use functions to simplify and shorten formulas on a worksheet, especially those that perform lengthy or complex calculations.) in Microsoft Office Excel.

Description

The PRODUCT function multiplies all the numbers given as arguments and returns the product. For example, if cells A1 and A2 contain numbers, you can use the formula =PRODUCT(A1, A2) to multiply those two numbers together. You can also perform the same operation by using the multiply (*) mathematical operator; for example, =A1 * A2.

The PRODUCT function is useful when you need to multiply many cells together. For example, the formula =PRODUCT(A1:A3, C1:C3) is equivalent to =A1 * A2 * A3 * C1 * C2 * C3.

Syntax

PRODUCT(number1, [number2], ...)

The PRODUCT function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

• number1  Required. The first number or range (range: Two or more cells on a sheet. The cells in a range can be adjacent or nonadjacent.) that you want to multiply.
• number2, ...  Optional. Additional numbers or ranges that you want to multiply, up to a maximum of 255 arguments.

 Note    If an argument is an array or reference, only numbers in the array or reference are multiplied. Empty cells, logical values, and text in the array or reference are ignored.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How do I copy an example?

1. Select the example in this article.

Important  Do not select the row or column headers.

Selecting an example from Help

2. Press CTRL+C.
3. In Excel, create a blank workbook or worksheet.
4. In the worksheet, select cell A1, and press CTRL+V.

Important  For the example to work properly, you must paste it into cell A1 of the worksheet.

5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• FACT function
• Math and trigonometry functions
• Multiply numbers
• SUM function
• SUMPRODUCT function

Excel > Function reference > Math and trigonometry

QUOTIENT function

Excel 2007

Returns the integer portion of a division. Use this function when you want to discard the remainder of a division.

Syntax

QUOTIENT(numerator,denominator)

Numerator   is the dividend.

Denominator   is the divisor.

Remark

If either argument is nonnumeric, QUOTIENT returns the #VALUE! error value.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• Math and trigonometry functions
• MOD function

Excel > Function reference > Math and trigonometry

RADIANS function

Excel 2007

Converts degrees to radians.

Syntax

RADIANS(angle)

Angle   is an angle in degrees that you want to convert.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• DEGREES function
• Math and trigonometry functions

Excel > Function reference > Math and trigonometry

RAND function

Excel 2007

Returns an evenly distributed random real number greater than or equal to 0 and less than 1. A new random real number is returned every time the worksheet is calculated.

Syntax

RAND( )

Remarks

• To generate a random real number between a and b, use:

RAND()*(b-a)+a

• If you want to use RAND to generate a random number but don't want the numbers to change every time the cell is calculated, you can enter =RAND() in the formula bar, and then press F9 to change the formula to a random number.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• Math and trigonometry functions

Excel > Function reference > Math and trigonometry

RANDBETWEEN function

Excel 2007

Returns a random integer number between the numbers you specify. A new random integer number is returned every time the worksheet is calculated.

Syntax

RANDBETWEEN(bottom,top)

Bottom   is the smallest integer RANDBETWEEN will return.

Top   is the largest integer RANDBETWEEN will return.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• Math and trigonometry functions
• RAND function

Excel > Function reference > Math and trigonometry

ROMAN function

Excel 2007

Converts an arabic numeral to roman, as text.

Syntax

ROMAN(number,form)

Number   is the Arabic numeral you want converted.

Form   is a number specifying the type of roman numeral you want. The roman numeral style ranges from Classic to Simplified, becoming more concise as the value of form increases. See the example following

ROMAN(499,0)

below.

Remarks

• If number is negative, the #VALUE! error value is returned.
• If number is greater than 3999, the #VALUE! error value is returned.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

 Note    Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

See Also

• Math and trigonometry functions

Excel > Function reference > Math and trigonometry

ROUND function

Excel 2007

This article describes the formula syntax and usage of the ROUND function (function: A prewritten formula that takes a value or values, performs an operation, and returns a value or values. Use functions to simplify and shorten formulas on a worksheet, especially those that perform lengthy or complex calculations.) in Microsoft Office Excel.

Description

The ROUND function rounds a number to a specified number of digits. For example, if cell A1 contains 23.7825, and you want to round that value to two decimal places, you can use the following formula:

=ROUND(A1, 2)

The result of this function is 23.78.

Syntax

ROUND(number, num_digits)

The ROUND function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

• number  Required. The number that you want to round.
• num_digits  Required. The number of digits to which you want to round the number argument.

Remarks

• If num_digits is greater than 0 (zero), then number is rounded to the specified number of decimal places.
• If num_digits is 0, the number is rounded to the nearest integer.
• If num_digits is less than 0, the number is rounded to the left of the decimal point.
• To always round up (away from zero), use the ROUNDUP function.
• To always round down (toward zero), use the ROUNDDOWN function.
• To round a number to a specific multiple (for example, to round to the nearest 0.5), use the MROUND function.

Example

The example may be easier to understand if you copy it to a blank worksheet.

How do I copy an example?

1. Select the example in this article.

Important  Do not select the row or column heade