How to Properly Handle Negative Angles When Using the PHP atan2 Function

<span><span><span class="hljs-meta">&lt;?php</span></span><span>
</span><span><span class="hljs-comment">// This section is unrelated to the main content and is for demonstration only</span></span><span>
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<p></span># How to Properly Handle Negative Angles When Using the PHP atan2 Function?<span></p>
<p>When performing 2D graphics calculations, coordinate transformations, or game development in PHP, we often need to calculate angles based on point coordinates. PHP's built-in <code>atan2

-π to π (i.e., -180° to 180°)

<span><span>This means that when a point is in the fourth quadrant, the returned angle will be negative. For example:
```php
</span><span><span class="hljs-meta">&lt;?php</span></span><span>
</span><span><span class="hljs-variable">$angle</span></span><span> = </span><span><span class="hljs-title function_ invoke__">atan2</span></span><span>(-</span><span><span class="hljs-number">1</span></span>, </span><span><span class="hljs-number">1</span></span><span>); 
</span><span><span class="hljs-keyword">echo</span></span><span> </span><span><span class="hljs-variable">$angle</span></span><span>; </span><span><span class="hljs-comment">// Outputs approximately -0.785398163 (i.e., -45°)</span></span><span>
</span></span>

2. Why Are There Negative Angles?

Mathematically, angles are measured counterclockwise from the positive x-axis. Due to the design of atan2, points in the fourth quadrant naturally yield negative angles. This is not an error; it is a characteristic of the function.

3. How to Convert Angles to the 0 to 2π Range?

In many applications (e.g., graphics rotation, navigation), we prefer angles to be uniformly within 0 to 360° (0 to 2π radians). This can be easily achieved with a simple conditional conversion:

<span><span><span class="hljs-meta">&lt;?php</span></span><span>
</span><span><span class="hljs-function"><span class="hljs-keyword">function</span></span></span><span> </span><span><span class="hljs-title">atan2To360</span></span><span>(</span><span><span class="hljs-params"><span class="hljs-variable">$y</span></span></span><span>, </span><span><span class="hljs-variable">$x</span></span><span>) {
    </span><span><span class="hljs-variable">$angle</span></span><span> = </span><span><span class="hljs-title function_ invoke__">atan2</span></span><span>(</span><span><span class="hljs-variable">$y</span></span><span>, </span><span><span class="hljs-variable">$x</span></span><span>); </span><span><span class="hljs-comment">// Returns -π to π</span></span><span>
    </span><span><span class="hljs-keyword">if</span></span><span> (</span><span><span class="hljs-variable">$angle</span></span><span> &lt; </span><span><span class="hljs-number">0</span></span><span>) {
        </span><span><span class="hljs-variable">$angle</span></span><span> += </span><span><span class="hljs-number">2</span></span><span> * M_PI; </span><span><span class="hljs-comment">// Convert to 0 to 2π</span></span><span>
    }
    </span><span><span class="hljs-keyword">return</span></span><span> </span><span><span class="hljs-variable">$angle</span></span><span>;
}
<p></span>echo atan2To360(-1, 1); // Outputs approximately 5.497787143 (i.e., 315°)<br>
</span>

4. Convert to Degrees (0° to 360°)

If you need the angle in degrees, you can combine it with the rad2deg function:

<span><span><span class="hljs-meta">&lt;?php</span></span><span>
</span><span><span class="hljs-function"><span class="hljs-keyword">function</span></span></span><span> </span><span><span class="hljs-title">atan2ToDegree360</span></span><span>(</span><span><span class="hljs-params"><span class="hljs-variable">$y</span></span></span><span>, </span><span><span class="hljs-variable">$x</span></span><span>) {
    </span><span><span class="hljs-variable">$angle</span></span><span> = </span><span><span class="hljs-title function_ invoke__">atan2</span></span><span>(</span><span><span class="hljs-variable">$y</span></span><span>, </span><span><span class="hljs-variable">$x</span></span><span>);
    </span><span><span class="hljs-keyword">if</span></span><span> (</span><span><span class="hljs-variable">$angle</span></span><span> &lt; </span><span><span class="hljs-number">0</span></span><span>) {
        </span><span><span class="hljs-variable">$angle</span></span><span> += </span><span><span class="hljs-number">2</span></span><span> * M_PI;
    }
    </span><span><span class="hljs-keyword">return</span></span><span> </span><span><span class="hljs-title function_ invoke__">rad2deg</span></span><span>(</span><span><span class="hljs-variable">$angle</span></span><span>); </span><span><span class="hljs-comment">// Convert to degrees</span></span><span>
}
<p></span>echo atan2ToDegree360(-1, 1); // Outputs 315<br>
</span>

5. Summary

• atan2 in PHP returns values in the range [-π, π].

• Negative angles are not errors; they are inherent to the function.

• To normalize the range, add 2π to convert the result to [0, 2π].

• For degrees, combine with rad2deg to normalize to 0°~360°.

This approach avoids confusion caused by negative angles and better suits practical needs in coordinate calculations and angle applications.