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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




A number.

Return value

The hyperbolic arctangent of the given number.


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).


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.


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;


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.

Browser compatibility

Update compatibility data on GitHub
ChromeEdgeFirefoxInternet ExplorerOperaSafariAndroid webviewChrome for AndroidFirefox for AndroidOpera for AndroidSafari on iOSSamsung InternetNode.js
atanhChrome Full support 38Edge Full support 12Firefox Full support 25IE No support NoOpera Full support 25Safari Full support 8WebView Android Full support YesChrome Android Full support 38Firefox Android Full support 25Opera Android Full support YesSafari iOS Full support 8Samsung Internet Android Full support Yesnodejs Full support 0.12


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See also