Math.atan2()

Baseline Widely available

This feature is well established and works across many devices and browser versions. It’s been available across browsers since July 2015.

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).

Try it

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

The y coordinate of the point.

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).

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 -π2-\frac{\pi}{2} or greater than π2\frac{\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()

js
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).

js
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 |