The Excel SECH Function

Hyperbolic Secant

The hyperbolic secant is the reciprocal of the hyperbolic cosine.

Therefore, the value of the hyperbolic secant is given by the equation:

Hyperbolic Secant Equation
For further information on the hyperbolic functions, see the Wikipedia Hyperbolic Functions page.

Function Description

The Excel Sech function calculates the hyperbolic secant (sech) of a supplied angle.

Note: the Sech function was only introduced in Excel 2013 and so is not available in earlier versions of Excel.

The syntax of the function is:

SECH( number )

Where the number argument is the angle (in radians) that you want to calculate the hyperbolic secant of. This must be between -2^27 and +2^27.

Converting from Degrees to Radians

If your angle is in degrees, you will need to convert it into radians before supplying it to the Sech function. This can be done using the Excel Radians function:

=RADIANS( degrees )
An example of this is provided below.

Sech Function Examples

In the following spreadsheet, the Excel Sech Function is used to calculate the hyperbolic secant of four different angles:

1 =SECH( -3.14159265358979 )
2 =SECH( 0 )
3 =SECH( PI() / 4 )
4 =SECH( RADIANS( 60 ) )
1 0.86266738
2 1
3 0.754939709
4 0.624887966

Note that, in the examples above:

For further details and examples of the Excel Sech function, see the Microsoft Office website.

Sech Function Errors

If you get an error from the Excel Sech function, this is likely to be one of the following:

Common Errors
#NUM! - Occurs if the supplied number is less than -2^27 or is greater than 2^27.
#VALUE! - Occurs if the supplied number argument is not recognized as a numeric value.