TheMath.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), forMath.atan2(y, x).

Try it

function calcAngleDegrees(x, y) {  return (Math.atan2(y, x) * 180) / Math.PI;}console.log(calcAngleDegrees(5, 5));// Expected output: 45console.log(calcAngleDegrees(10, 10));// Expected output: 45console.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

TheMath.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 separatex andy arguments, whileMath.atan() is passed the ratio of those two arguments.Math.atan2(y, x) differs fromMath.atan(y / x) in the following cases:

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

Becauseatan2() is a static method ofMath, you always use it asMath.atan2(), rather than as a method of aMath object you created (Math is not a constructor).

Examples

Using Math.atan2()

Math.atan2(90, 15); // 1.4056476493802699Math.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 betweenMath.atan2(y, x) andMath.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

Browser compatibility

See also

• Math.acos()
• Math.asin()
• Math.atan()
• Math.cos()
• Math.sin()
• Math.tan()