# The Excel ATANH Function

Inverse Hyperbolic Tangent

The atanh function returns the inverse hyperbolic tangent. Therefore,

ATANH( TANH( z ) ) = z

The equation used to calculate the inverse hyperbolic tangent is:

Further information on the inverse hyperbolic functions can be found on Wikipedia

## Function Description

The Excel Atanh function calculates the inverse hyperbolic tangent of a supplied number.

The syntax of the function is:

ATANH( number )

Where the number argument is a real number, between (but not equal to) -1 and 1, that you want to calculate the inverse hyperbolic tangent of.

## Excel Atanh Function Examples

Column B of the following spreadsheet shows the Excel Atanh Function, used to calculate the inverse hyperbolic tangent of three different values:

Formulas:
A B
1 number ATANH
2 -0.8 =ATANH( A2 )
3 0 =ATANH( A3 )
4 0.5 =ATANH( A4 )
Results:
A B
1 number ATANH
2 -0.8 -1.098612289
3 0 0
4 0.5 0.549306144

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

## Atanh Function Errors

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

Common Errors
 #NUM! - Occurs if the supplied number is ≤ -1 or ≥ 1. #VALUE! - Occurs if the supplied number argument is not recognized as a numeric value.