# Math.atan2()

## BaselineWidely 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).

## Syntax

js
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:

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

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))
),
);
}

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

Specification
ECMAScript Language Specification
# sec-math.atan2

## Browser compatibility

BCD tables only load in the browser