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

x(-1,1),Math.atanh(x)=arctanh(x)= the unique ysuch thattanh(y)=x\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

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 |x|<1\left|x\right| < 1, we have artanh(x)=12ln(1+x1-x)\operatorname {artanh} (x) = \frac{1}{2}\ln \left( \frac{1 + x}{1 - x} \right) 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 Status Comment
ECMAScript 2015 (6th Edition, ECMA-262)
The definition of 'Math.atanh' in that specification.
Standard Initial definition.
ECMAScript Latest Draft (ECMA-262)
The definition of 'Math.atanh' in that specification.
Draft  

Browser compatibility

FeatureChromeEdgeFirefoxInternet ExplorerOperaSafari
Basic support38 Yes25 No258
FeatureAndroid webviewChrome for AndroidEdge mobileFirefox for AndroidOpera AndroidiOS SafariSamsung Internet
Basic support Yes Yes Yes25 Yes8 Yes

See also

Document Tags and Contributors

Last updated by: wbamberg,