Definition:Angle/Unit/Radian

Radians are a measurement of plane angles symbolized either by the word rad or without any unit (note that radians are pure numbers, as they are ratios of lengths, and the addition of rad is merely for clarification).

1 radian is defined as the angle cut out by straight lines from the center of a circle to points whose distance apart along the outside of the circle is equal to the radius of the circle.

From this, it can be shown that a full rotation measures $2\pi$ rad.