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

The **`Math.acosh()`** static method returns the inverse hyperbolic cosine 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>∀</mo><mi>x</mi><mo>≥</mo><mn>1</mn><mo>,</mo><mspace width="0.2777777777777778em"></mspace><mrow><mo lspace="0em" rspace="0.16666666666666666em">𝙼𝚊𝚝𝚑.𝚊𝚌𝚘𝚜𝚑</mo><mo stretchy="false">(</mo><mi>𝚡</mi><mo stretchy="false">)</mo></mrow></mtd><mtd><mo>=</mo><mo lspace="0em" rspace="0.16666666666666666em">arcosh</mo><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mtext>the unique&nbsp;</mtext><mi>y</mi><mo>≥</mo><mn>0</mn><mtext>&nbsp;such that&nbsp;</mtext><mo lspace="0em" rspace="0em">cosh</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><mo lspace="0em" rspace="0em">ln</mo><mrow><mo>(</mo><mrow><mi>x</mi><mo>+</mo><msqrt><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>1</mn></mrow></msqrt></mrow><mo>)</mo></mrow></mtd></mtr></mtable><annotation encoding="TeX">\begin{aligned}\forall x \geq 1,\;\mathtt{\operatorname{Math.acosh}(x)} &= \operatorname{arcosh}(x) = \text{the unique } y \geq 0 \text{ such that } \cosh(y) = x\\&= \ln\left(x + \sqrt{x^2 - 1}\right)\end{aligned}</annotation></semantics>
</math>
<!-- prettier-ignore-end -->

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

```js interactive-example
console.log(Math.acosh(0.999999999999));
// Expected output: NaN

console.log(Math.acosh(1));
// Expected output: 0

console.log(Math.acosh(2));
// Expected output: 1.3169578969248166

console.log(Math.acosh(2.5));
// Expected output: 1.566799236972411
```

## Syntax

```js-nolint
Math.acosh(x)
```

### Parameters

- `x`
  - : A number greater than or equal to 1.

### Return value

The inverse hyperbolic cosine of `x`. If `x` is less than 1, returns {{jsxref("NaN")}}.

## Description

Because `acosh()` is a static method of `Math`, you always use it as `Math.acosh()`, rather than as a method of a `Math` object you created (`Math` is no constructor).

## Examples

### Using Math.acosh()

```js
Math.acosh(0); // NaN
Math.acosh(1); // 0
Math.acosh(2); // 1.3169578969248166
Math.acosh(Infinity); // Infinity
```

## Specifications

{{Specifications}}

## Browser compatibility

{{Compat}}

## See also

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