# Math.acosh()

The Math.acosh() function returns the hyperbolic arc-cosine of a number, that is

$∀x≥1,Math.acosh(x)=arcosh(x)= the unique y≥0such thatcosh(y)=x\forall x \geq 1, \mathtt{\operatorname{Math.acosh}(x)} = \operatorname{arcosh}(x) = \text{ the unique } \; y \geq 0 \; \text{such that} \; \cosh(y) = x$

## Syntax

JavaScript
Math.acosh(<var>x</var>)

### Parameters

x
A number.

### Return value

The hyperbolic arc-cosine of the given number. If the number is less than 1, NaN.

## Description

Because acosh() is a static method of Math, you always use it as Math.acosh(), rather than as a method of a Math object you created (Math is no constructor).

## Examples

### Using Math.acosh()

JavaScript
Math.acosh(-1); // NaN
Math.acosh(0);  // NaN
Math.acosh(0.5) // NaN
Math.acosh(1);  // 0
Math.acosh(2);  // 1.3169578969248166

For values less than 1 Math.acosh() returns NaN.

## Polyfill

For all $x \geq 1$, we have $\operatorname \left\{arcosh\right\} \left(x\right) = \ln \left\left(x + \sqrt\left\{x^\left\{2\right\} - 1\right\} \right\right)$ and so this can be emulated with the following function:

JavaScript
Math.acosh = Math.acosh || function(x) {
return Math.log(x + Math.sqrt(x * x - 1));
};

## Specifications

Specification Status Comment
ECMAScript 2015 (6th Edition, ECMA-262)
The definition of 'Math.acosh' in that specification.
Standard Initial definition.
ECMAScript 2017 Draft (ECMA-262)
The definition of 'Math.acosh' in that specification.
Draft

## Browser compatibility

Feature Chrome Firefox (Gecko) Internet Explorer Opera Safari
Basic support 38 25 (25) No support 25 7.1
Feature Android Chrome for Android Firefox Mobile (Gecko) IE Mobile Opera Mobile Safari Mobile
Basic support No support No support 25.0 (25) No support No support 8