Math.atan2()

The Math.atan2() function 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

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 (in [ - π , π ] [-\pi, \pi] ) between the positive x-axis and the ray from (0,0) to the point (x,y).

Description

The Math.atan2() method returns a numeric value between -π and π representing the angle theta of an (x, y) point. This is the counterclockwise angle, measured 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.

A simple diagram showing the angle returned by atan2(y, x)

Math.atan2() is passed separate x and y arguments, and Math.atan() is passed the ratio of those two arguments.

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

Math.atan2(±0, -0);               // ±PI.
Math.atan2(±0, +0);               // ±0.
Math.atan2(±0, -x);               // ±PI for x > 0.
Math.atan2(±0, x);                // ±0 for x > 0.
Math.atan2(-y, ±0);               // -PI/2 for y > 0.
Math.atan2(y, ±0);                // PI/2 for y > 0.
Math.atan2(±y, -Infinity);        // ±PI for finite y > 0.
Math.atan2(±y, +Infinity);        // ±0 for finite y > 0.
Math.atan2(±Infinity, x);         // ±PI/2 for finite x.
Math.atan2(±Infinity, -Infinity); // ±3*PI/4.
Math.atan2(±Infinity, +Infinity); // ±PI/4.

Specifications

Specification
ECMAScript Language Specification (ECMAScript)
# sec-math.atan2

Browser compatibility

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See also