Math.atanh

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

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

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 $\left|x\right| < 1$, we have $\operatorname {artanh} (x) = \frac{1}{2}\ln \left( \frac{1 + x}{1 - x} \right)$ 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 2017 Draft (ECMA-262) The definition of 'Math.atanh' in that specification.	Draft

Browser compatibility

See also

• Math.acosh()
• Math.asinh()
• Math.cosh()
• Math.sinh()
• Math.tanh()