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---
title: Math.atanh()
short-title: atanh()
slug: Web/JavaScript/Reference/Global_Objects/Math/atanh
page-type: javascript-static-method
browser-compat: javascript.builtins.Math.atanh
sidebar: jsref
---

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

<!-- prettier-ignore-start -->
<math display="block">
  <semantics><mtable columnalign="right left right left right left right left right left" columnspacing="0em" displaystyle="true"><mtr><mtd><mo>βˆ€</mo><mi>x</mi><mo>∊</mo><mo stretchy="false">(</mo><mrow><mo>βˆ’</mo><mn>1</mn></mrow><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo><mo>,</mo><mspace width="0.2777777777777778em"></mspace><mrow><mo lspace="0em" rspace="0.16666666666666666em">π™ΌπšŠπšπš‘.πšŠπšπšŠπš—πš‘</mo><mo stretchy="false">(</mo><mi>𝚑</mi><mo stretchy="false">)</mo></mrow></mtd><mtd><mo>=</mo><mo lspace="0em" rspace="0.16666666666666666em">artanh</mo><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mtext>the unique&nbsp;</mtext><mi>y</mi><mtext>&nbsp;such that&nbsp;</mtext><mo lspace="0em" rspace="0em">tanh</mo><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo>=</mo><mi>x</mi></mtd></mtr><mtr><mtd></mtd><mtd><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mspace width="0.16666666666666666em"></mspace><mo lspace="0em" rspace="0em">ln</mo><mrow><mo>(</mo><mfrac><mrow><mn>1</mn><mo>+</mo><mi>x</mi></mrow><mrow><mn>1</mn><mo>βˆ’</mo><mi>x</mi></mrow></mfrac><mo>)</mo></mrow></mtd></mtr></mtable><annotation encoding="TeX">\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}</annotation></semantics>
</math>
<!-- prettier-ignore-end -->

{{InteractiveExample("JavaScript Demo: Math.atanh()")}}

```js interactive-example
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

```js-nolint
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 {{jsxref("Infinity")}}. If `x` is -1, returns `-Infinity`. If `x` is less than -1 or greater than 1, returns {{jsxref("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()

```js
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

{{Specifications}}

## Browser compatibility

{{Compat}}

## See also

- [Polyfill of `Math.atanh` in `core-js`](https://github.com/zloirock/core-js#ecmascript-math)
- [es-shims polyfill of `Math.atanh`](https://www.npmjs.com/package/math.atanh)
- {{jsxref("Math.acosh()")}}
- {{jsxref("Math.asinh()")}}
- {{jsxref("Math.cosh()")}}
- {{jsxref("Math.sinh()")}}
- {{jsxref("Math.tanh()")}}