Math.atanh()

The Math.atanh() static method returns the inverse hyperbolic tangent of a number. That is,

$$\begin{aligned}\forall x \in ({-1}, 1),\;\mathtt{\operatorname{Math.atanh}(x)} &= \operatorname{artanh}(x) = \text{the unique } y \text{ such that } \tanh(y) = x \\&= \frac{1}{2}\,\ln\left(\frac{1+x}{1-x}\right)\end{aligned}$$

console.log(Math.atanh(-1));
// Expected output: -Infinity

console.log(Math.atanh(0));
// Expected output: 0

console.log(Math.atanh(0.5));
// Expected output: 0.549306144334055 (approximately)

console.log(Math.atanh(1));
// Expected output: Infinity

Syntax

Math.atanh(x)

Parameters

• x
  • : A number between -1 and 1, inclusive.

Return value

The inverse hyperbolic tangent of x. If x is 1, returns Infinity. If x is -1, returns -Infinity. If x is less than -1 or greater than 1, returns NaN.

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); // 0
Math.atanh(0.5); // 0.5493061443340548
Math.atanh(1); // Infinity
Math.atanh(2); // NaN

Specifications

Browser compatibility

See also

• Polyfill of Math.atanh in core-js
• es-shims polyfill of Math.atanh
• acosh()
• asinh()
• cosh()
• sinh()
• tanh()