# Documentation/Calc Functions/ATANH

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## Function name:

ATANH

## Category:

Mathematical

## Summary:

Returns the inverse hyperbolic tangent of a number.

## Syntax:

ATANH(**Number**)

## Returns:

This function returns the inverse hyperbolic tangent of **Number**, that is the value whose hyperbolic tangent is **Number**.

## Arguments:

**Number** is the real number, or a reference to a cell containing that number, which must be strictly between -1 and +1 whose inverse hyperbolic tangent value is to be calculated.

If the value of **Number** is outside this range, it returns an invalid error.

## Additional details:

The formula for ATANH function is:

where N in the **Number**

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. | 4 |

=ATANH(0.5) | Inverse hyperbolic tangent of 0.5. | 0.549306144334055 |

=ATANH(1) | Inverse hyperbolic tangent of 1 will return an invalid error because 1 is out of domain. | Err:502 |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

ATANH