Definition:Angle/Unit/Radian

Definition
The radian is a measure of plane angles symbolized either by the word $\mathrm{rad}$ or without any unit.

Radians are pure numbers, as they are ratios of lengths. The addition of $\mathrm{rad}$ is merely for clarification.

$1 \ \mathrm{rad}$ is the angle subtended at the center of a circle by an arc whose length is equal to the radius:


 * Radian.png

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