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

x1,Math.acosh(x)=arcosh(x)= the unique y0such 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)

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 x1x \geq 1, we have arcosh(x)=ln(x+x2-1)\operatorname {arcosh} (x) = \ln \left(x + \sqrt{x^{2} - 1} \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
DesktopMobileServer
ChromeEdgeFirefoxInternet ExplorerOperaSafariAndroid webviewChrome for AndroidEdge MobileFirefox for AndroidOpera for AndroidiOS SafariSamsung InternetNode.js
Basic supportChrome Full support 38Edge Full support YesFirefox Full support 25IE No support NoOpera Full support 25Safari Full support 8WebView Android Full support YesChrome Android Full support YesEdge Mobile Full support YesFirefox Android Full support 25Opera Android Full support YesSafari iOS Full support 8Samsung Internet Android Full support Yesnodejs Full support 0.12

Legend

Full support  
Full support
No support  
No support

See also

Document Tags and Contributors

Last updated by: wbamberg,