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

metadata

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

$$𝙼𝚊𝚝𝚑.𝚊𝚝𝚊𝚗(𝚡)=arctan(x)=\text{the unique }y∊\left[-\frac{\pi }{2},\frac{\pi }{2}\right]\text{ such that }tan(y)=x\backslash mathtt\{\backslash operatorname\{Math.atan\}(x)\}\; =\; \backslash arctan(x)\; =\; \backslash text\{the\; unique\; \}\; y\; \backslash in\; \backslash left[-\backslash frac\{\backslash pi\}\{2\},\; \backslash frac\{\backslash pi\}\{2\}\backslash right]\; \backslash text\{\; such\; that\; \}\; \backslash tan(y)\; =\; x$$

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

// 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

Math.atan(x)

Parameters

• x
  • : A number.

Return value

The inverse tangent (angle in radians between $-\frac{\pi }{2}-\backslash frac\{\backslash pi\}\{2\}$ and $\frac{\pi }{2}\backslash frac\{\backslash pi\}\{2\}$, inclusive) of x. If x is {{jsxref("Infinity")}}, it returns $\frac{\pi }{2}\backslash frac\{\backslash pi\}\{2\}$. If x is -Infinity, it returns $-\frac{\pi }{2}-\backslash frac\{\backslash pi\}\{2\}$.

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()

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