Math.atan2()

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

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 $-\frac{\pi}{2}$ or greater than $\frac{\pi}{2}$.

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()

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

Browser compatibility

See also

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