Web/JavaScript/Reference/Global objects/Math/acosh

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

<math display="block">\forall x \geq 1,\mathtt{\operatorname{Math.acosh}(x)} = \operatorname{arcosh}(x) = \text{the\ unique}\; y \geq 0\;\text{such\ that}\;\cosh(y) = x</math>

Syntax

Math.acosh(x)

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()

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 <math display="inline">x \geq 1</math>, we have <math display="inline">\operatorname{arcosh}(x) = \ln\left( {x + \sqrt{x^{2} - 1}} \right)</math> 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
ECMAScript (ECMA-262)The definition of 'Math.acosh' in that specification.

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	Safari on iOS	Samsung Internet	Node.js
`acosh`	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 38	Chrome Android Full support 38	Firefox Android Full support 25	Opera Android Full support 25	Safari iOS Full support 8	Samsung Internet Android Full support 3.0	nodejs Full support 0.12

Legend

Full support: Full support
No support: No support