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JavaScript - Math.atan2() method example

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telsa
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The Math.atan2() function returns the angle in radians in the range -Math.PI/2 to +Math.PI/2 between the positive x-axis and the ray to the point (x, y) ‚Ȇ (0, 0).

// ONLINE-RUNNER:browser;

//                       y   x         angle in radians
console.log( Math.atan2( 2,  4) ); //  0.4636476090008061 <-   ~26.6 degrees
console.log( Math.atan2( 4, -2) ); //  2.0344439357957027 <-  ~116.6 degrees
console.log( Math.atan2(-2, -4) ); // -2.6779450445889870 <- ~-153.4 degrees
console.log( Math.atan2(-4,  2) ); // -1.1071487177940904 <-  ~-63.4 degrees

atan2() method has been visualized on below image:

atan2(y, x) function visualization - JavaScript Math Object.
atan2(y, x) function visualization - JavaScript Math Object.

1. Documentation

SyntaxMath.atan2(y, x)
Parametersy, x - integer or float number values that are coordinates of point (primitive value).
Result

number value of angle between two lines OP and OX in radians in the range -Math.PI/2 to +Math.PI/2 (primitive value).

Where:

  • O=(0, 0)¬†- intersection point of coordinate system axes,
  • P=(x, y)¬†- out point,
  • OX - positive part of x-axis.

If point is in the 1st (I) or 2nd (II) quadrant angle is measured in a counterclockwise direction.

If point is in the 3rd (III) or 4th (IV) quadrant angle is measured in a clockwise direction.

Note: angle arrows show measured angles for points located in different quadrants.

Description

atan2 is a static method that takes two parameters and returns an approximation of the arctangent(y/x) function taking into account quadrants of a point location (P=(x, y)).


2. Working with degrees

// ONLINE-RUNNER:browser;

function calculateAngle(y, x) {
	var angle = Math.atan2(y, x);
    return (180 / Math.PI) * angle; // rad to deg conversion
}

// Example usage:

console.log( calculateAngle( 2,  4) ); //   26.56505117707799 degrees
console.log( calculateAngle( 4, -2) ); //  116.56505117707799 degrees
console.log( calculateAngle(-2, -4) ); // -153.43494882292200 degrees
console.log( calculateAngle(-4,  2) ); //  -63.43494882292201 degrees

3.  Conversion to only clockwise angles in degrees

This section shows how to convert angles to clockwise angles (from 0 to 360 degrees).

// ONLINE-RUNNER:browser;

function calculateAngle(y, x) {
	var angle = Math.atan2(y, x);
  	if (angle < 0.0) {
    	angle += 2.0 * Math.PI;
    }
    return (180 / Math.PI) * angle; // rad to deg conversion
}

// Example usage:

console.log( calculateAngle( 2,  4) ); //  26.56505117707799 degrees
console.log( calculateAngle( 4, -2) ); // 116.56505117707799 degrees
console.log( calculateAngle(-2, -4) ); // 206.56505117707800 degrees
console.log( calculateAngle(-4,  2) ); // 296.56505117707800 degrees

4.  Conversion to only counterclockwise angles in degrees

This section shows how to convert angles to counterclockwise angles (from -360 to 0 degrees).

// ONLINE-RUNNER:browser;

function calculateAngle(y, x) {
	var angle = Math.atan2(y, x);
  	if (angle > 0.0) {
    	angle -= 2.0 * Math.PI;
    }
    return (180 / Math.PI) * angle; // rad to deg conversion
}

// Example usage:

console.log( calculateAngle( 2,  4) ); // -333.434948822922 degrees
console.log( calculateAngle( 4, -2) ); // -243.434948822922 degrees
console.log( calculateAngle(-2, -4) ); // -153.434948822922 degrees
console.log( calculateAngle(-4,  2) ); // -63.4349488229220 degrees

References

  1. atan2 - Wikipedia
  2. Inverse trigonometric functions - Wikipedia

JavaScript - Math documentation (EN)

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