Web/JavaScript/Reference/Global objects/Math/atanh

The Math.atanh() function returns the hyperbolic arctangent of a number, that is

<math display="block">\forall x \in \left( {- 1,1} \right),\mathtt{\operatorname{Math.atanh}(x)} = \operatorname{arctanh}(x) = \text{the\ unique}\; y\;\text{such\ that}\;\tanh(y) = x</math>

Syntax

Math.atanh(x)

Parameters

x: A number.

Return value

The hyperbolic arctangent of the given number.

Description

Because atanh() is a static method of Math, you always use it as Math.atanh(), rather than as a method of a Math object you created (Math is not a constructor).

Examples

Using Math.atanh()

Math.atanh(-2);  // NaN
Math.atanh(-1);  // -Infinity
Math.atanh(0);   // 0
Math.atanh(0.5); // 0.5493061443340548
Math.atanh(1);   // Infinity
Math.atanh(2);   // NaN

For values greater than 1 or less than -1, NaN is returned.

Polyfill

For <math display="inline">\left| x \right| < 1</math>, we have <math display="inline">\operatorname{artanh}(x) = \frac{1}{2}\ln\left( \frac{1 + x}{1 - x} \right)</math> so this can be emulated by the following function:

Math.atanh = Math.atanh || function(x) {
  return Math.log((1+x)/(1-x)) / 2;
};

Specifications

Specification
ECMAScript (ECMA-262)The definition of 'Math.atanh' 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
`atanh`	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