Value of Radian in Degrees

Theorem
The value of a radian in degrees is given by:
 * $1 \ \mathrm{rad} = \dfrac {180^\circ} {\pi} \approx 57.29577 \ 95130 \ 8232 \ldots ^\circ$

Proof
By Full Angle measures 2 Pi Radians, a full angle measures $2 \pi$ radians.

By definition of degree of arc, a full angle measures $360$ degrees.

Thus $1$ radian is given by:
 * $1 \ \mathrm{rad} = \dfrac {360^\circ} {2 \pi} = \dfrac {180^\circ} {\pi}$

Also see

 * Value of Degree in Radians