atan2()

The atan2() function in PHP calculates the arc tangent of two numbers, $y and $x. It returns the angle (in radians) between the positive x-axis and the point ($x, $y), which is what you need whenever you want to turn a pair of coordinates back into a direction.

This page covers the function's syntax, what it returns, the key difference between atan2() and atan(), and runnable examples.

What is the atan2() Function?

atan2() is a built-in mathematical function that returns the arc tangent of the quotient $y / $x, but — crucially — it uses the signs of both arguments to place the result in the correct quadrant. The result is expressed in radians and ranges from -π to π (about -3.14159 to 3.14159).

Syntax

atan2(float $y, float $x): float

Parameters

Return value

A float in the range -π to π representing the angle in radians. Convert it to degrees with rad2deg() when you need a human-readable angle.

atan2() vs atan()

The single-argument atan() function only sees $y / $x as one number, so it cannot tell the difference between, say, (1, 1) and (-1, -1) — both reduce to a ratio of 1. It always returns an angle in -π/2 to π/2 and throws away the quadrant. It can also misbehave when $x is 0 because that would be a division by zero.

atan2($y, $x) keeps both signs, so it covers the full circle (-π to π) and safely handles $x = 0. Reach for atan2() whenever your inputs are real coordinates rather than a pre-computed ratio.

How to Use the atan2() Function

Pass the y value first, then the x value, and convert the radian result to degrees if you need it:

This prints:

Radians: 1.1071487177941
Degrees: 63.434948822922

We define $y and $x, pass them to atan2() to get the angle in radians, then use rad2deg() to convert that result to degrees.

Quadrant Handling

This example shows how atan2() returns a distinct angle for points in different quadrants — even when the ratio $y / $x is the same:

<?php
// Same ratio (1), but different quadrants
echo rad2deg(atan2(1, 1)), "\n";   // upper-right quadrant
echo rad2deg(atan2(-1, -1)), "\n"; // lower-left quadrant

// $x is zero — no division-by-zero error
echo rad2deg(atan2(1, 0)), "\n";   // straight up
?>

Output:

45
-135
90

Because atan2() inspects both signs, the points (1, 1) and (-1, -1) map to 45° and -135° respectively, and a zero $x is handled cleanly.

Conclusion

atan2() is the go-to function for converting a pair of coordinates into an angle in PHP. It returns radians in the -π to π range, correctly resolves all four quadrants, and avoids division-by-zero issues that affect the single-argument atan(). For related trigonometry, see atan(), tan(), and the deg2rad() / rad2deg() conversion helpers.

Practice