# Documentation/Calc Functions/ACOSH

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## Function name:

ACOSH

## Category:

Mathematical

## Summary:

Returns the inverse hyperbolic cosine of a number.

## Syntax:

ACOSH(**Number**)

## Returns:

This function returns the inverse hyperbolic cosine of **Number**, that is the value whose hyperbolic cosine is **Number**. The resultant value ranges from 0 and +∞, i.e. [0,+∞).

## Arguments:

**Number** is the real number, or a reference to a cell containing that number, which must be greater than or equal to 1 whose inverse hyperbolic cosine value is to be calculated.

If the **Number** is less than +1, the function returns an error value because it is out of domain.

## Additional details:

- The formula for inverse hyperbolic cosine is:

where N is the **Number**

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(1.5) | Inverse hyperbolic cosine of 1.5. | 0.962423650119207 |

=ACOSH(0.5) | Inverse hyperbolic cosine of 0.5 will return an error because 0.5 is out of its domain. | Err:502 |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

ACOSH