# Documentation/Calc Functions/ACOSH

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## Function name:

ACOSH

## Category:

Mathematical

## Summary:

Calculates the inverse hyperbolic cosine (arcosh) of a real number. The value returned is non-negative and expressed in radians.

## Syntax:

ACOSH(**Number**)

## Returns:

Returns a real number in the range [0, ∞) that is the inverse hyperbolic cosine of **Number** in radians.

## Arguments:

**Number** is a real number in the range [1, ∞), or a reference to a cell containing that number, whose inverse hyperbolic cosine is to be calculated.

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

## Additional details:

The formula for the inverse hyperbolic cosine of x is:

[math]\displaystyle{ \operatorname{arcosh}(x) = \ln\left (x+\sqrt{(x^2-1)}\right ) }[/math]

The figure below illustrates the function ACOSH.

## Examples:

Formula | Description | Returns |
---|---|---|

=ACOSH(1) | Inverse hyperbolic cosine of 1. | 0 |

=ACOSH(COSH(4)) | Inverse hyperbolic cosine of hyperbolic cosine of 4. | 4 |

=ACOSH(D1) where cell D1 contains the value 1.5. | Inverse hyperbolic cosine of 1.5. | 0.962423650119207 |

## Related LibreOffice functions:

## ODF standard:

## Related (or similar) Excel functions:

ACOSH