The ATANH function 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)

Arguments

Argument Description
number Any real number between 1 and -1

Examples

  A B C
1 Formula Result Notes
2 =ATANH(-0.8) -1.09861229 Inverse hyperbolic tangent of -0.8
3 =ATANH(-0.1) -0.100335348 Inverse hyperbolic tangent of -0.1
4 =ATANH(0.76159416) 1.00000001 Inverse hyperbolic tangent of 0.76159416

Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if the supplied number argument is not a numeric value
#NUM! Occurs if the supplied number argument is ≤ -1 or ≥ 1

The ATANH function returns the inverse hyperbolic tangent, which is calculated as:  

    \[   atanh(x) = ln \frac {\sqrt{1 - x^2}}{1-x}    \]

See Wikipedia for more information on Inverse Hyperbolic Function.