files/en-us/web/javascript/reference/global_objects/math/atan2/index.md

metadata

title: Math.atan2()
short-title: atan2()
slug: Web/JavaScript/Reference/Global_Objects/Math/atan2
page-type: javascript-static-method
browser-compat: javascript.builtins.Math.atan2
sidebar: jsref

The Math.atan2() static method returns the angle in the plane (in radians) between the positive x-axis and the ray from (0, 0) to the point (x, y), for Math.atan2(y, x).

{{InteractiveExample("JavaScript Demo: Math.atan2()")}}

function calcAngleDegrees(x, y) {
  return (Math.atan2(y, x) * 180) / Math.PI;
}

console.log(calcAngleDegrees(5, 5));
// Expected output: 45

console.log(calcAngleDegrees(10, 10));
// Expected output: 45

console.log(calcAngleDegrees(0, 10));
// Expected output: 90

Syntax

Math.atan2(y, x)

Parameters

• y
  • : The y coordinate of the point.
• x
  • : The x coordinate of the point.

Return value

The angle in radians (between -π and π, inclusive) between the positive x-axis and the ray from (0, 0) to the point (x, y).

Description

The Math.atan2() method measures the counterclockwise angle θ, in radians, between the positive x-axis and the point (x, y). Note that the arguments to this function pass the y-coordinate first and the x-coordinate second.

Math.atan2() is passed separate x and y arguments, while Math.atan() is passed the ratio of those two arguments. Math.atan2(y, x) differs from Math.atan(y / x) in the following cases:

x	y	Math.atan2(y, x)	Math.atan(y / x)
Infinity	Infinity	π / 4	NaN
Infinity	-Infinity	-π / 4	NaN
-Infinity	Infinity	3π / 4	NaN
-Infinity	-Infinity	-3π / 4	NaN
0	0	0	NaN
0	-0	-0	NaN
< 0 (including -0)	0	π	0
< 0 (including -0)	-0	-π	0
-Infinity	> 0	π	-0
-0	> 0	π / 2	-π / 2
-Infinity	< 0	-π	0
-0	< 0	-π / 2	π / 2

In addition, for points in the second and third quadrants (x < 0), Math.atan2() would output an angle less than $-\frac{\pi }{2}-\backslash frac\{\backslash pi\}\{2\}$ or greater than $\frac{\pi }{2}\backslash frac\{\backslash pi\}\{2\}$.

Because atan2() is a static method of Math, you always use it as Math.atan2(), rather than as a method of a Math object you created (Math is not a constructor).

Examples

Using Math.atan2()

Math.atan2(90, 15); // 1.4056476493802699
Math.atan2(15, 90); // 0.16514867741462683

Difference between Math.atan2(y, x) and Math.atan(y / x)

The following script prints all inputs that produce a difference between Math.atan2(y, x) and Math.atan(y / x).

const formattedNumbers = new Map([
  [-Math.PI, "-π"],
  [(-3 * Math.PI) / 4, "-3π/4"],
  [-Math.PI / 2, "-π/2"],
  [-Math.PI / 4, "-π/4"],
  [Math.PI / 4, "π/4"],
  [Math.PI / 2, "π/2"],
  [(3 * Math.PI) / 4, "3π/4"],
  [Math.PI, "π"],
  [-Infinity, "-∞"],
  [Infinity, "∞"],
]);

function format(template, ...args) {
  return String.raw(
    { raw: template },
    ...args.map((num) =>
      (Object.is(num, -0)
        ? "-0"
        : (formattedNumbers.get(num) ?? String(num))
      ).padEnd(5),
    ),
  );
}

console.log(`| x     | y     | atan2 | atan  |
|-------|-------|-------|-------|`);

for (const x of [-Infinity, -1, -0, 0, 1, Infinity]) {
  for (const y of [-Infinity, -1, -0, 0, 1, Infinity]) {
    const atan2 = Math.atan2(y, x);
    const atan = Math.atan(y / x);
    if (!Object.is(atan2, atan)) {
      console.log(format`| ${x} | ${y} | ${atan2} | ${atan} |`);
    }
  }
}

The output is:

| x     | y     | atan2 | atan  |
|-------|-------|-------|-------|
| -∞    | -∞    | -3π/4 | NaN   |
| -∞    | -1    | -π    | 0     |
| -∞    | -0    | -π    | 0     |
| -∞    | 0     | π     | -0    |
| -∞    | 1     | π     | -0    |
| -∞    | ∞     | 3π/4  | NaN   |
| -1    | -∞    | -π/2  | π/2   |
| -1    | -1    | -3π/4 | π/4   |
| -1    | -0    | -π    | 0     |
| -1    | 0     | π     | -0    |
| -1    | 1     | 3π/4  | -π/4  |
| -1    | ∞     | π/2   | -π/2  |
| -0    | -∞    | -π/2  | π/2   |
| -0    | -1    | -π/2  | π/2   |
| -0    | -0    | -π    | NaN   |
| -0    | 0     | π     | NaN   |
| -0    | 1     | π/2   | -π/2  |
| -0    | ∞     | π/2   | -π/2  |
| 0     | -0    | -0    | NaN   |
| 0     | 0     | 0     | NaN   |
| ∞     | -∞    | -π/4  | NaN   |
| ∞     | ∞     | π/4   | NaN   |

Specifications

{{Specifications}}

Browser compatibility

{{Compat}}

See also

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