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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) ≠ (0, 0).

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//                       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

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atan2() method has been visualized on below image:

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

1. Documentation

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Syntax	`Math.atan2(y, x)`
Parameters	`y`, `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

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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

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3. Conversion to only clockwise angles in degrees

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

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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

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4. Conversion to only counterclockwise angles in degrees

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

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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