A radian is the angle you get when the curved edge of a circle is exactly as long as the circle's radius. That makes it the natural unit for anything involving circles, and it is the unit the International System of Units uses for angles.

One radian is about 57.3 degrees, and a full turn is 2π radians — roughly 6.28. Because radians link an angle directly to arc length, they keep formulas in mathematics, physics, and programming simple. Most calculators and code libraries expect angles in radians unless you tell them otherwise.

In writing, the radian is usually shortened to "rad". One radian is 57.29577951 degrees, and that ratio is what every number on this page is built from.