Master PHP’s atan2() Function: Compute Angles with Two Arguments

Description

PHP function atan2(float $y, float $x) returns the arctangent of the point ( $x, $y) expressed in radians. It computes the angle between the positive x‑axis and the vector to the point, using the signs of both arguments to place the result in the correct quadrant (‑π, π].

Parameters

$y – y‑coordinate (dividend)

$x – x‑coordinate (divisor)

Return value

Float representing the angle in radians.

Typical usage

When converting Cartesian coordinates to polar coordinates, atan2 provides the angle without needing to manually adjust for quadrant.

Example

<?php
// Basic examples showing different quadrants
echo atan2(0.5, 0.5);   // 0.78539816339745  (45°)
echo "
";
echo atan2(-0.5, -0.5); // -2.3561944901923  (‑135°)
echo "
";
echo atan2(5, 5);       // 0.78539816339745
echo "
";
echo atan2(-5, -5);     // -2.3561944901923
echo "
";
echo atan2(10, 20);     // 0.46364760900081  (≈26.565°)
echo "
";
echo atan2(-10, 10);    // -0.78539816339745 (‑45°)
?>

Output

0.78539816339745
-2.3561944901923
0.78539816339745
-2.3561944901923
0.46364760900081
-0.78539816339745

Notes

The function always returns a value in the interval (‑π, π].

If $x is zero, the sign of $y determines whether the result is π/2 or -π/2.

Both arguments are cast to float; non‑numeric values generate a warning.