Radians (angle)

We use two units in games for measuring angles: degrees and radians. In games and game engines, angles are usually measured in radians for efficiency.

You surely know what degrees are, but you may not be familiar with radians.

Degrees are based on the circumference of a circle. A circle is divided into 360 degrees.

Radians are based on the radius of a circle. A radian is equal to the angle of an arc whose length is the circle's radius.

Imagine a circle with a radius of one unit.

If you wrap a string along the circle that is one unit long, the corresponding angle from the circle center is one radian.

Because the perimeter of a circle is 2π multiplied by the circle radius, and one radian corresponds to an arc as long as the radius of the circle, there are 2π radians in a circle.

Here are common angles in degrees and radians:

• 360° = 2π radians
• 180° = π radians
• 90° = π/2 radians
• 45° = π/4 radians
• 30° = π/6 radians