# Math.acosh()

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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

Math.acosh(x)

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()

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:

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 Latest Draft (ECMA-262)
The definition of 'Math.acosh' in that specification.
Draft

## Browser compatibility

Update compatibility data on GitHub
Desktop Mobile Server Chrome Edge Firefox Internet Explorer Opera Safari Android webview Chrome for Android Firefox for Android Opera for Android Chrome Full support 38 Edge Full support 12 Firefox Full support 25 IE No support No Opera Full support 25 Safari Full support 8 WebView Android Full support Yes Chrome Android Full support Yes Firefox Android Full support 25 Opera Android Full support Yes Safari iOS Full support 8 Samsung Internet Android Full support Yes nodejs Full support 0.12

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