Value of Degree in Radians

Theorem
The value of a degree in radians is given by:
 * $1 \degrees = \dfrac {\pi} {180} \radians \approx 0 \cdotp 01745 \, 32925 \, 19943 \, 29576 \, 9236 \ldots \radians$

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:
 * $1 \degrees = \dfrac {2 \pi} {360} = \dfrac {\pi} {180}$

Also see

 * Value of Radian in Degrees