Value of Degree in Radians

Theorem
The value of a degree in radians is given by:
 * $1 \degrees = \dfrac {\pi} {180 \degrees} \ \mathrm{rad} \approx 0.01745 \ 32925 \ 19943 \ 29576 \ 92 \ldots \ \mathrm{rad}$

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 $1$ degree of arc is given by:
 * $1^\circ = \dfrac {2 \pi} {360 \degrees} = \dfrac {\pi} {180 \degrees}$

Also see

 * Value of Radian in Degrees