# Documentation/Calc Functions/COSH

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## Function name:

COSH

## Category:

Mathematical

## Summary:

Calculates the hyperbolic cosine (cosh) of a hyperbolic angle expressed in radians.

## Syntax:

COSH(**Number**)

## Returns:

Returns a real number in the range [1, ∞) that is the hyperbolic cosine of the specified hyperbolic angle.

## Arguments:

**Number** is a real number, or a reference to a cell containing that number, that is the hyperbolic angle in radians whose hyperbolic cosine is to be calculated.

- If
**Number**is non-numeric, then COSH reports a #VALUE! error.

## Additional details:

The formula for the hyperbolic cosine of x is:

[math]\displaystyle{ \cosh(x)~=~\frac{e^x+e^{-x}}{2} }[/math]

The figure below illustrates the function COSH.

## Examples:

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

=COSH(0) | Hyperbolic cosine of 0. | 1 |

=COSH(D1) where cell D1 contains the number -2. | Hyperbolic cosine of -2. | 3.76219569108363 |

=ACOSH(COSH(3)) | The hyperbolic cosine of 3 radians is taken and then the inverse hyperbolic cosine of that value is calculated. Note that `=ACOSH(COSH(-3))` also returns 3, because COSH is an even function. |
3 |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

COSH