# Documentation/Calc Functions/ATANH

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## Function name:

ATANH

## Category:

Mathematical

## Summary:

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

## Syntax:

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).

## Additional details:

The formula for the inverse hyperbolic tangent of x is:

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

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 |

## Related LibreOffice functions:

## ODF standard:

## Related (or similar) Excel functions:

ATANH