files/en-us/web/javascript/reference/global_objects/math/atan/index.md

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

The **`Math.atan()`** static method returns the inverse tangent (in radians) of a number, that is

<!-- prettier-ignore-start -->
<math display="block">
  <semantics><mrow><mrow><mo lspace="0em" rspace="0.16666666666666666em">𝙼𝚊𝚝𝚑.𝚊𝚝𝚊𝚗</mo><mo stretchy="false">(</mo><mi>𝚡</mi><mo stretchy="false">)</mo></mrow><mo>=</mo><mo lspace="0em" rspace="0em">arctan</mo><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mtext>the unique&nbsp;</mtext><mi>y</mi><mo>∊</mo><mrow><mo>[</mo><mrow><mo>−</mo><mfrac><mi>π</mi><mn>2</mn></mfrac><mo>,</mo><mfrac><mi>π</mi><mn>2</mn></mfrac></mrow><mo>]</mo></mrow><mtext>&nbsp;such that&nbsp;</mtext><mo lspace="0em" rspace="0em">tan</mo><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo>=</mo><mi>x</mi></mrow><annotation encoding="TeX">\mathtt{\operatorname{Math.atan}(x)} = \arctan(x) = \text{the unique } y \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \text{ such that } \tan(y) = x</annotation></semantics>
</math>
<!-- prettier-ignore-end -->

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

```js interactive-example
// Calculates angle of a right-angle triangle in radians
function calcAngle(opposite, adjacent) {
  return Math.atan(opposite / adjacent);
}

console.log(calcAngle(8, 10));
// Expected output: 0.6747409422235527

console.log(calcAngle(5, 3));
// Expected output: 1.0303768265243125
```

## Syntax

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

### Parameters

- `x`
  - : A number.

### Return value

The inverse tangent (angle in radians between <math><semantics><mrow><mo>-</mo><mfrac><mi>π</mi><mn>2</mn></mfrac></mrow><annotation encoding="TeX">-\frac{\pi}{2}</annotation></semantics></math> and <math><semantics><mfrac><mi>π</mi><mn>2</mn></mfrac><annotation encoding="TeX">\frac{\pi}{2}</annotation></semantics></math>, inclusive) of `x`. If `x` is {{jsxref("Infinity")}}, it returns <math><semantics><mfrac><mi>π</mi><mn>2</mn></mfrac><annotation encoding="TeX">\frac{\pi}{2}</annotation></semantics></math>. If `x` is `-Infinity`, it returns <math><semantics><mrow><mo>-</mo><mfrac><mi>π</mi><mn>2</mn></mfrac></mrow><annotation encoding="TeX">-\frac{\pi}{2}</annotation></semantics></math>.

## Description

Because `atan()` is a static method of `Math`, you always use it as `Math.atan()`, rather than as a method of a `Math` object you created (`Math` is not a constructor).

## Examples

### Using Math.atan()

```js
Math.atan(-Infinity); // -1.5707963267948966 (-π/2)
Math.atan(-0); // -0
Math.atan(0); // 0
Math.atan(1); // 0.7853981633974483  (π/4)
Math.atan(Infinity); // 1.5707963267948966  (π/2)

// The angle that the line (0,0) -- (x,y) forms with the x-axis in a Cartesian coordinate system
const theta = (x, y) => Math.atan(y / x);
```

Note that you may want to avoid the `theta` function and use {{jsxref("Math.atan2()")}} instead, which has a wider range (between -π and π) and avoids outputting `NaN` for cases such as when `x` is `0`.

## Specifications

{{Specifications}}

## Browser compatibility

{{Compat}}

## See also

- {{jsxref("Math.acos()")}}
- {{jsxref("Math.asin()")}}
- {{jsxref("Math.atan2()")}}
- {{jsxref("Math.cos()")}}
- {{jsxref("Math.sin()")}}
- {{jsxref("Math.tan()")}}
- CSS {{cssxref("atan()")}} function