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 > Engineering

Engineering 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 > Engineering

BESSELI function

Excel 2007

Returns the modified Bessel function, which is equivalent to the Bessel function evaluated for purely imaginary arguments.

Syntax

BESSELI(x,n)

X   is the value at which to evaluate the function.

N   is the order of the Bessel function. If n is not an integer, it is truncated.

Remarks

• If x is nonnumeric, BESSELI returns the #VALUE! error value.
• If n is nonnumeric, BESSELI returns the #VALUE! error value.
• If n < 0, BESSELI returns the #NUM! error value.
• The n-th order modified Bessel function of the variable x 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

• BESSELJ function
• BESSELK function
• BESSELY function
• Engineering functions

Excel > Function reference > Engineering

BESSELJ function

Returns the Bessel function.

Syntax

BESSELJ(x,n)

X   is the value at which to evaluate the function.

N   is the order of the Bessel function. If n is not an integer, it is truncated.

Remarks

• If x is nonnumeric, BESSELJ returns the #VALUE! error value.
• If n is nonnumeric, BESSELJ returns the #VALUE! error value.
• If n < 0, BESSELJ returns the #NUM! error value.
• The n-th order Bessel function of the variable x is:

where:

is the Gamma 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

• BESSELI function
• BESSELK function
• BESSELY function
• Engineering functions

Excel > Function reference > Engineering

BESSELK function

Returns the modified Bessel function, which is equivalent to the Bessel functions evaluated for purely imaginary arguments.

Syntax

BESSELK(x,n)

X   is the value at which to evaluate the function.

N   is the order of the function. If n is not an integer, it is truncated.

Remarks

• If x is nonnumeric, BESSELK returns the #VALUE! error value.
• If n is nonnumeric, BESSELK returns the #VALUE! error value.
• If n < 0, BESSELK returns the #NUM! error value.
• The n-th order modified Bessel function of the variable x is:

where Jn and Yn are the J and Y Bessel functions, respectively.

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

• BESSELI function
• BESSELJ function
• BESSELY function
• Engineering functions

Excel > Function reference > Engineering

BESSELY function

Returns the Bessel function, which is also called the Weber function or the Neumann function.

Syntax

BESSELY(x,n)

X   is the value at which to evaluate the function.

N   is the order of the function. If n is not an integer, it is truncated.

Remarks

• If x is nonnumeric, BESSELY returns the #VALUE! error value.
• If n is nonnumeric, BESSELY returns the #VALUE! error value.
• If n < 0, BESSELY returns the #NUM! error value.
• The n-th order Bessel function of the variable x 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

• BESSELI function
• BESSELJ function
• BESSELK function
• Engineering functions

Excel > Function reference > Engineering

BIN2DEC function

Converts a binary number to decimal.

Syntax

BIN2DEC(number)

Number    is the binary number you want to convert. Number cannot contain more than 10 characters (10 bits). The most significant bit of number is the sign bit. The remaining 9 bits are magnitude bits. Negative numbers are represented using two's-complement notation.

Remark

If number is not a valid binary number, or if number contains more than 10 characters (10 bits), BIN2DEC 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

• DEC2BIN function
• Engineering functions
• HEX2BIN function
• OCT2BIN function

Excel > Function reference > Engineering

BIN2HEX function

Converts a binary number to hexadecimal.

Syntax

BIN2HEX(number,places)

Number   is the binary number you want to convert. Number cannot contain more than 10 characters (10 bits). The most significant bit of number is the sign bit. The remaining 9 bits are magnitude bits. Negative numbers are represented using two's-complement notation.

Places   is the number of characters to use. If places is omitted, BIN2HEX uses the minimum number of characters necessary. Places is useful for padding the return value with leading 0s (zeros).

Remarks

• If number is not a valid binary number, or if number contains more than 10 characters (10 bits), BIN2HEX returns the #NUM! error value.
• If number is negative, BIN2HEX ignores places and returns a 10-character hexadecimal number.
• If BIN2HEX requires more than places characters, it returns the #NUM! error value.
• If places is not an integer, it is truncated.
• If places is nonnumeric, BIN2HEX returns the #VALUE! error value.
• If places is negative, BIN2HEX 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

• DEC2BIN function
• DEC2HEX function
• Engineering functions
• HEX2BIN function
• OCT2BIN function
• OCT2HEX function

Excel > Function reference > Engineering

BIN2OCT function

Converts a binary number to octal.

Syntax

BIN2OCT(number,places)

Number   is the binary number you want to convert. Number cannot contain more than 10 characters (10 bits). The most significant bit of number is the sign bit. The remaining 9 bits are magnitude bits. Negative numbers are represented using two's-complement notation.

Places   is the number of characters to use. If places is omitted, BIN2OCT uses the minimum number of characters necessary. Places is useful for padding the return value with leading 0s (zeros).

Remarks

• If number is not a valid binary number, or if number contains more than 10 characters (10 bits), BIN2OCT returns the #NUM! error value.
• If number is negative, BIN2OCT ignores places and returns a 10-character octal number.
• If BIN2OCT requires more than places characters, it returns the #NUM! error value.
• If places is not an integer, it is truncated.
• If places is nonnumeric, BIN2OCT returns the #VALUE! error value.
• If places is negative, BIN2OCT 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

• DEC2BIN function
• DEC2OCT function
• Engineering functions
• HEX2BIN function
• HEX2OCT function
• OCT2BIN function

Excel > Function reference > Engineering

COMPLEX function

Converts real and imaginary coefficients into a complex number of the form x + yi or x + yj.

Syntax

COMPLEX(real_num,i_num,suffix)

Real_num   is the real coefficient of the complex number.

I_num   is the imaginary coefficient of the complex number.

Suffix   is the suffix for the imaginary component of the complex number. If omitted, suffix is assumed to be "i".

 Note    All complex number functions accept "i" and "j" for suffix, but neither "I" nor "J". Using uppercase results in the #VALUE! error value. All functions that accept two or more complex numbers require that all suffixes match.

Remarks

• If real_num is nonnumeric, COMPLEX returns the #VALUE! error value.
• If i_num is nonnumeric, COMPLEX returns the #VALUE! error value.
• If suffix is neither "i" nor "j", COMPLEX 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

• Engineering functions
• IMABS function
• IMAGINARY function
• IMREAL function

Excel > Function reference > Engineering

CONVERT function

Converts a number from one measurement system to another. For example, CONVERT can translate a table of distances in miles to a table of distances in kilometers.

Syntax

CONVERT(number,from_unit,to_unit)

Number   is the value in from_units to convert.

From_unit   is the units for number.

To_unit   is the units for the result. CONVERT accepts the following text values (in quotation marks) for from_unit and to_unit.

The following abbreviated unit prefixes can be prepended to any metric from_unit or to_unit.

Remarks

• If the input data types are incorrect, CONVERT returns the #VALUE! error value.
• If the unit does not exist, CONVERT returns the #N/A error value.
• If the unit does not support an abbreviated unit prefix, CONVERT returns the #N/A error value.
• If the units are in different groups, CONVERT returns the #N/A error value.
• Unit names and prefixes are case-sensitive.

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

• BIN2DEC function
• BIN2HEX function
• BIN2OCT function
• Convert measurements
• Convert times
• DEC2BIN function
• Engineering functions
• HEX2BIN function
• OCT2BIN function

Excel > Function reference > Engineering

DEC2BIN function

Converts a decimal number to binary.

Syntax

DEC2BIN(number,places)

Number   is the decimal integer you want to convert. If number is negative, valid place values are ignored and DEC2BIN returns a 10-character (10-bit) binary number in which the most significant bit is the sign bit. The remaining 9 bits are magnitude bits. Negative numbers are represented using two's-complement notation.

Places   is the number of characters to use. If places is omitted, DEC2BIN uses the minimum number of characters necessary. Places is useful for padding the return value with leading 0s (zeros).

Remarks

• If number < -512 or if number > 511, DEC2BIN returns the #NUM! error value.
• If number is nonnumeric, DEC2BIN returns the #VALUE! error value.
• If DEC2BIN requires more than places characters, it returns the #NUM! error value.
• If places is not an integer, it is truncated.
• If places is nonnumeric, DEC2BIN returns the #VALUE! error value.
• If places is zero or negative, DEC2BIN 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

• BIN2DEC function
• Engineering functions
• HEX2BIN function
• HEX2DEC function
• OCT2BIN function
• OCT2DEC function

Excel > Function reference > Engineering

DEC2HEX function

Converts a decimal number to hexadecimal.

Syntax

DEC2HEX(number,places)

Number   is the decimal integer you want to convert. If number is negative, places is ignored and DEC2HEX returns a 10-character (40-bit) hexadecimal number in which the most significant bit is the sign bit. The remaining 39 bits are magnitude bits. Negative numbers are represented using two's-complement notation.

Places   is the number of characters to use. If places is omitted, DEC2HEX uses the minimum number of characters necessary. Places is useful for padding the return value with leading 0s (zeros).

Remarks

• If number < -549,755,813,888 or if number > 549,755,813,887, DEC2HEX returns the #NUM! error value.
• If number is nonnumeric, DEC2HEX returns the #VALUE! error value.
• If DEC2HEX requires more than places characters, it returns the #NUM! error value.
• If places is not an integer, it is truncated.
• If places is nonnumeric, DEC2HEX returns the #VALUE! error value.
• If places is negative, DEC2HEX 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

• BIN2DEC function
• BIN2HEX function
• DEC2BIN function
• DEC2OCT function
• Engineering functions
• HEX2DEC function
• OCT2DEC function
• OCT2HEX function

Excel > Function reference > Engineering

DEC2OCT function

Converts a decimal number to octal.

Syntax

DEC2OCT(number, places)

Number   is the decimal integer you want to convert. If number is negative, places is ignored and DEC2OCT returns a 10-character (30-bit) octal number in which the most significant bit is the sign bit. The remaining 29 bits are magnitude bits. Negative numbers are represented using two's-complement notation.

Places   is the number of characters to use. If places is omitted, DEC2OCT uses the minimum number of characters necessary. Places is useful for padding the return value with leading 0s (zeros).

Remarks

• If number < -536,870,912 or if number > 536,870,911, DEC2OCT returns the #NUM! error value.
• If number is nonnumeric, DEC2OCT returns the #VALUE! error value.
• If DEC2OCT requires more than places characters, it returns the #NUM! error value.
• If places is not an integer, it is truncated.
• If places is nonnumeric, DEC2OCT returns the #VALUE! error value.
• If places is negative, DEC2OCT 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

• BIN2DEC function
• DEC2BIN function
• DEC2HEX function
• Engineering functions
• HEX2DEC function
• OCT2DEC function

Excel > Function reference > Engineering

DELTA function

Tests whether two values are equal. Returns 1 if number1 = number2; returns 0 otherwise. Use this function to filter a set of values. For example, by summing several DELTA functions you calculate the count of equal pairs. This function is also known as the Kronecker Delta function.

Syntax

DELTA(number1,number2)

Number1   is the first number.

Number2   is the second number. If omitted, number2 is assumed to be zero.

Remarks

• If number1 is nonnumeric, DELTA returns the #VALUE! error value.
• If number2 is nonnumeric, DELTA 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

• Engineering functions
• EXACT function
• GESTEP function

Excel > Function reference > Engineering

ERF function

Returns the error function integrated between lower_limit and upper_limit.

Syntax

ERF(lower_limit,upper_limit)

Lower_limit   is the lower bound for integrating ERF.

Upper_limit   is the upper bound for integrating ERF. If omitted, ERF integrates between zero and lower_limit.

Remarks

• If lower_limit is nonnumeric, ERF returns the #VALUE! error value.
• If lower_limit is negative, ERF returns the #NUM! error value.
• If upper_limit is nonnumeric, ERF returns the #VALUE! error value.
• If upper_limit is negative, ERF 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

• Engineering functions
• ERFC function

Excel > Function reference > Engineering

ERFC function

Returns the complementary ERF function integrated between x and infinity.

Syntax

ERFC(x)

X   is the lower bound for integrating ERF.

Remarks

• If x is nonnumeric, ERFC returns the #VALUE! error value.
• If x is negative, ERFC 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

• Engineering functions
• ERF function

Excel > Function reference > Engineering

GESTEP function

Returns 1 if number ≥ step; returns 0 (zero) otherwise. Use this function to filter a set of values. For example, by summing several GESTEP functions you calculate the count of values that exceed a threshold.

Syntax

GESTEP(number,step)

Number   is the value to test against step.

Step   is the threshold value. If you omit a value for step, GESTEP uses zero.

Remark

If any argument is nonnumeric, GESTEP 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

• DELTA function
• Engineering functions

Excel > Function reference > Engineering

HEX2BIN function

Converts a hexadecimal number to binary.

Syntax

HEX2BIN(number,places)

Number   is the hexadecimal number you want to convert. Number cannot contain more than 10 characters. The most significant bit of number is the sign bit (40th bit from the right). The remaining 9 bits are magnitude bits. Negative numbers are represented using two's-complement notation.

Places   is the number of characters to use. If places is omitted, HEX2BIN uses the minimum number of characters necessary. Places is useful for padding the return value with leading 0s (zeros).

Remarks

• If number is negative, HEX2BIN ignores places and returns a 10-character binary number.
• If number is negative, it cannot be less than FFFFFFFE00, and if number is positive, it cannot be greater than 1FF.
• If number is not a valid hexadecimal number, HEX2BIN returns the #NUM! error value.
• If HEX2BIN requires more than places characters, it returns the #NUM! error value.
• If places is not an integer, it is truncated.
• If places is nonnumeric, HEX2BIN returns the #VALUE! error value.
• If places is negative, HEX2BIN 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

• BIN2HEX function
• DEC2BIN function
• DEC2HEX function
• Engineering functions
• HEX2DEC function
• HEX2OCT function
• OCT2BIN function
• OCT2HEX function

Excel > Function reference > Engineering

HEX2DEC function

Converts a hexadecimal number to decimal.

Syntax

HEX2DEC(number)

Number   is the hexadecimal number you want to convert. Number cannot contain more than 10 characters (40 bits). The most significant bit of number is the sign bit. The remaining 39 bits are magnitude bits. Negative numbers are represented using two's-complement notation.

Remark

If number is not a valid hexadecimal number, HEX2DEC 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

• BIN2DEC function
• BIN2HEX function
• DEC2HEX function
• Engineering functions
• HEX2BIN function
• HEX2OCT function
• OCT2DEC function
• OCT2HEX function

Excel > Function reference > Engineering

HEX2OCT function

Converts a hexadecimal number to octal.

Syntax

HEX2OCT(number,places)

Number   is the hexadecimal number you want to convert. Number cannot contain more than 10 characters. The most significant bit of number is the sign bit. The remaining 39 bits are magnitude bits. Negative numbers are represented using two's-complement notation.

Places   is the number of characters to use. If places is omitted, HEX2OCT uses the minimum number of characters necessary. Places is useful for padding the return value with leading 0s (zeros).

Remarks

• If number is negative, HEX2OCT ignores places and returns a 10-character octal number.
• If number is negative, it cannot be less than FFE0000000, and if number is positive, it cannot be greater than 1FFFFFFF.
• If number is not a valid hexadecimal number, HEX2OCT returns the #NUM! error value.
• If HEX2OCT requires more than places characters, it returns the #NUM! error value.
• If places is not an integer, it is truncated.
• If places is nonnumeric, HEX2OCT returns the #VALUE! error value.
• If places is negative, HEX2OCT 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

• BIN2HEX function
• BIN2OCT function
• DEC2HEX function
• DEC2OCT function
• Engineering functions
• HEX2BIN function
• HEX2DEC function
• OCT2HEX function

Excel > Function reference > Engineering

IMABS function

Returns the absolute value (modulus) of a complex number in x + yi or x + yj text format.

Syntax

IMABS(inumber)

Inumber   is a complex number for which you want the absolute value.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex number.
• The absolute value of a complex number is:

where:

z = x + yi

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

• COMPLEX function
• Engineering functions
• IMAGINARY function
• IMREAL function
• IMSUM function

Excel > Function reference > Engineering

IMAGINARY function

Returns the imaginary coefficient of a complex number in x + yi or x + yj text format.

Syntax

IMAGINARY(inumber)

Inumber   is a complex number for which you want the imaginary coefficient.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex 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

• COMPLEX function
• Engineering functions
• IMABS function
• IMREAL function
• IMSUM function

Excel > Function reference > Engineering

IMARGUMENT function

Returns the argument (theta), an angle expressed in radians, such that:

Syntax

IMARGUMENT(inumber)

Inumber   is a complex number for which you want the argument .

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex number.
• IMARGUMENT is calculated as follows:

where:

 and

z = x + yi

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

• COMPLEX function
• Engineering functions
• IMAGINARY function
• IMREAL function
• IMSUM function

Excel > Function reference > Engineering

IMCONJUGATE function

Returns the complex conjugate of a complex number in x + yi or x + yj text format.

Syntax

IMCONJUGATE(inumber)

Inumber   is a complex number for which you want the conjugate.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex number.
• The conjugate of a complex number 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

• COMPLEX function
• Engineering functions
• IMAGINARY function
• IMREAL function
• IMSUM function

Excel > Function reference > Engineering

IMCOS function

Returns the cosine of a complex number in x + yi or x + yj text format.

Syntax

IMCOS(inumber)

Inumber   is a complex number for which you want the cosine.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex number.
• If inumber is a logical value, IMCOS returns the #VALUE! error value.
• The cosine of a complex number 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

• COMPLEX function
• Engineering functions
• IMAGINARY function
• IMREAL function
• IMSUM function

Excel > Function reference > Engineering

IMDIV function

Returns the quotient of two complex numbers in x + yi or x + yj text format.

Syntax

IMDIV(inumber1,inumber2)

Inumber1   is the complex numerator or dividend.

Inumber2   is the complex denominator or divisor.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex number.
• The quotient of two complex numbers 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

• COMPLEX function
• Engineering functions
• IMAGINARY function
• IMREAL function
• IMSUM function

Excel > Function reference > Engineering

IMEXP function

Returns the exponential of a complex number in x + yi or x + yj text format.

Syntax

IMEXP(inumber)

Inumber   is a complex number for which you want the exponential.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex number.
• The exponential of a complex number 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

• COMPLEX function
• Engineering functions
• IMAGINARY function
• IMREAL function
• IMSUM function

Excel > Function reference > Engineering

IMLN function

Returns the natural logarithm of a complex number in x + yi or x + yj text format.

Syntax

IMLN(inumber)

Inumber   is a complex number for which you want the natural logarithm.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex number.
• The natural logarithm of a complex number 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

• COMPLEX function
• Engineering functions
• IMAGINARY function
• IMREAL function
• IMSUM function

Excel > Function reference > Engineering

IMLOG10 function

Returns the common logarithm (base 10) of a complex number in x + yi or x + yj text format.

Syntax

IMLOG10(inumber)

Inumber   is a complex number for which you want the common logarithm.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex number.
• The common logarithm of a complex number can be calculated from the natural logarithm as follows:

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

• COMPLEX function
• Engineering functions
• IMAGINARY function
• IMREAL function
• IMSUM function

Excel > Function reference > Engineering

IMLOG2 function

Returns the base-2 logarithm of a complex number in x + yi or x + yj text format.

Syntax

IMLOG2(inumber)

Inumber   is a complex number for which you want the base-2 logarithm.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex number.
• The base-2 logarithm of a complex number can be calculated from the natural logarithm as follows:

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

• COMPLEX function
• Engineering functions
• IMAGINARY function
• IMREAL function
• IMSUM function

Excel > Function reference > Engineering

IMPOWER function

Returns a complex number in x + yi or x + yj text format raised to a power.

Syntax

IMPOWER(inumber,number)

Inumber   is a complex number you want to raise to a power.

Number   is the power to which you want to raise the complex number.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex number.
• If number is nonnumeric, IMPOWER returns the #VALUE! error value.
• Number can be an integer, fractional, or negative.
• A complex number raised to a power is calculated as follows:

where:

and:

and:

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

• COMPLEX function
• Engineering functions
• IMAGINARY function
• IMREAL function
• IMSUM function

Excel > Function reference > Engineering

IMPRODUCT function

Returns the product of 1 to 255 complex numbers in x + yi or x + yj text format.

Syntax

IMPRODUCT(inumber1,inumber2,...)

Inumber1, inumber2,…   are 1 to 255 complex numbers to multiply.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex number.
• The product of two complex numbers 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

• COMPLEX function
• Engineering functions
• IMAGINARY function
• IMREAL function
• IMSUM function

Excel > Function reference > Engineering

IMREAL function

Returns the real coefficient of a complex number in x + yi or x + yj text format.

Syntax

IMREAL(inumber)

Inumber   is a complex number for which you want the real coefficient.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex 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

• COMPLEX function
• Engineering functions
• IMABS function
• IMAGINARY function
• IMSUM function

Excel > Function reference > Engineering

IMSIN function

Returns the sine of a complex number in x + yi or x + yj text format.

Syntax

IMSIN(inumber)

Inumber   is a complex number for which you want the sine.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex number.
• The sine of a complex number 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

• COMPLEX function
• Engineering functions
• IMAGINARY function
• IMREAL function
• IMSUM function

Excel > Function reference > Engineering

IMSQRT function

Returns the square root of a complex number in x + yi or x + yj text format.

Syntax

IMSQRT(inumber)

Inumber   is a complex number for which you want the square root.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex number.
• The square root of a complex number is:

where:

and:

and:

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

• COMPLEX function
• Engineering functions
• IMAGINARY function
• IMREAL function
• IMSUM function

Excel > Function reference > Engineering

IMSUB function

Returns the difference of two complex numbers in x + yi or x + yj text format.

Syntax

IMSUB(inumber1,inumber2)

Inumber1   is the complex number from which to subtract inumber2.

Inumber2   is the complex number to subtract from inumber1.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex number.
• The difference of two complex numbers 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

• COMPLEX function
• Engineering functions
• IMAGINARY function
• IMREAL function
• IMSUM function

Excel > Function reference > Engineering

IMSUM function

Returns the sum of two or more complex numbers in x + yi or x + yj text format.

Syntax

IMSUM(inumber1,inumber2,...)

Inumber1,inumber2,...   are 1 to 255 complex numbers to add.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex number.
• The sum of two complex numbers 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

• COMPLEX function
• Engineering functions
• IMABS function
• IMAGINARY function
• IMREAL function

Excel > Function reference > Engineering

OCT2BIN function

Converts an octal number to binary.

Syntax

OCT2BIN(number,places)

Number   is the octal number you want to convert. Number may not contain more than 10 characters. The most significant bit of number is the sign bit. The remaining 29 bits are magnitude bits. Negative numbers are represented using two's-complement notation.

Places   is the number of characters to use. If places is omitted, OCT2BIN uses the minimum number of characters necessary. Places is useful for padding the return value with leading 0s (zeros).

Remarks

• If number is negative, OCT2BIN ignores places and returns a 10-character binary number.
• If number is negative, it cannot be less than 7777777000, and if number is positive, it cannot be greater than 777.
• If number is not a valid octal number, OCT2BIN returns the #NUM! error value.
• If OCT2BIN requires more than places characters, it returns the #NUM! error value.
• If places is not an integer, it is truncated.
• If places is nonnumeric, OCT2BIN returns the #VALUE! error value.
• If places is negative, OCT2BIN 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

• BIN2OCT function
• DEC2BIN function
• DEC2OCT function
• Engineering functions
• HEX2BIN function
• HEX2OCT function
• OCT2DEC function
• OCT2HEX function

Excel > Function reference > Engineering

OCT2DEC function

Converts an octal number to decimal.

Syntax

OCT2DEC(number)

Number   is the octal number you want to convert. Number may not contain more than 10 octal characters (30 bits). The most significant bit of number is the sign bit. The remaining 29 bits are magnitude bits. Negative numbers are represented using two's-complement notation.

Remark

If number is not a valid octal number, OCT2DEC 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

• BIN2DEC function
• BIN2OCT function
• DEC2OCT function
• Engineering functions
• HEX2DEC function
• HEX2OCT function
• OCT2BIN function
• OCT2HEX function

Excel > Function reference > Engineering

OCT2HEX function

Converts an octal number to hexadecimal.

Syntax

OCT2HEX(number,places)

Number   is the octal number you want to convert. Number may not contain more than 10 octal characters (30 bits). The most significant bit of number is the sign bit. The remaining 29 bits are magnitude bits. Negative numbers are represented using two's-complement notation.

Places   is the number of characters to use. If places is omitted, OCT2HEX uses the minimum number of characters necessary. Places is useful for padding the return value with leading 0s (zeros).

Remarks

• If number is negative, OCT2HEX ignores places and returns a 10-character hexadecimal number.
• If number is not a valid octal number, OCT2HEX returns the #NUM! error value.
• If OCT2HEX requires more than places characters, it returns the #NUM! error value.
• If places is not an integer, it is truncated.
• If places is nonnumeric, OCT2HEX returns the #VALUE! error value.
• If places is negative, OCT2HEX 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.