# Documentation/Calc Functions/ATANH

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ATANH

Mathematical

## Summary:

Calculates the inverse hyperbolic tangent (artanh) of a real number, in radians.

ATANH(Number)

## Returns:

Returns a real number that is the inverse hyperbolic tangent of Number in radians.

## Arguments:

Number is a real number in the range (-1, 1), or a reference to a cell containing that number, whose inverse hyperbolic tangent is to be calculated.

• If Number is non-numeric, then ATANH reports a #VALUE! error.
• If Number lies outside the range (-1, 1), the ATANH reports an invalid argument error (Err:502).

The formula for the inverse hyperbolic tangent of x is:

$\displaystyle{ \operatorname{artanh}(x) = \frac{1}{2}~ \ln\left (\dfrac{1+x}{1-x}\right ) }$

The figure below illustrates the function ATANH.

## Examples:

Formula Description Returns
=ATANH(0) Inverse hyperbolic tangent of 0. 0
=ATANH(TANH(4)) Inverse hyperbolic tangent of hyperbolic tangent of 4. 3.99999999999999
=ATANH(D1) where cell D1 contains the number 0.5. Inverse hyperbolic tangent of 0.5. 0.549306144334055

ATANH