# Documentation/Calc Functions/ACOSH

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ACOSH

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).

The formula for the inverse hyperbolic cosine of x is:

$\displaystyle{ \operatorname{arcosh}(x) = \ln\left (x+\sqrt{(x^2-1)}\right ) }$

The figure below illustrates the function ACOSH.

ACOSH function

## 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

ACOSH