# Math.atanh()

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

$∀x∊(-1,1),Math.atanh(x)=arctanh(x)= the unique ysuch thattanh(y)=x\forall x \in \left( -1, 1 \right), \mathtt{\operatorname{Math.atanh}(x)} = \operatorname{arctanh}(x) = \text{ the unique } \; y \; \text{such that} \; \tanh(y) = x$

## Syntax

Math.atanh(x)

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 $\left|x\right| < 1$, we have $\operatorname \left\{artanh\right\} \left(x\right) = \frac\left\{1\right\}\left\{2\right\}\ln \left\left( \frac\left\{1 + x\right\}\left\{1 - x\right\} \right\right)$ 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

Update compatibility data on GitHub
Desktop Mobile Server Chrome Edge Firefox Internet Explorer Opera Safari Android webview Chrome for Android Edge Mobile Firefox for Android Opera for Android 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 Yes Chrome Android Full support Yes Edge Mobile Full support Yes Firefox Android Full support 25 Opera Android Full support Yes Safari iOS Full support 8 Samsung Internet Android Full support Yes nodejs Full support 0.12

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