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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 2017 Draft (ECMA-262)
The definition of 'Math.atanh' in that specification.

Browser compatibility

Feature Chrome Firefox (Gecko) Internet Explorer Opera Safari
Basic support 38 25 (25) No support 25 7.1
Feature Android Chrome for Android Firefox Mobile (Gecko) IE Mobile Opera Mobile Safari Mobile
Basic support No support No support 25.0 (25) No support No support 8

See also

Document Tags and Contributors

 Contributors to this page: eduardoboucas, fscholz, Mingun, realityking,
 Last updated by: eduardoboucas,