Definition:Angle/Unit/Radian

Definition
Radians are a measurement 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 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 $2 \pi \ \mathrm{rad}$.

Thus we see that:
 * $1 \ \mathrm{rad} = \dfrac {180^\circ}{\pi} \approx 57.29577 \ 95130 \ 8232 \ldots ^\circ$