Value of Radian in Degrees

Theorem
The value of a radian in degrees is given by:
 * $1 \radians = \dfrac {180 \degrees} {\pi} \approx 57 \cdotp 29577 \, 95130 \ 82320 \, 87679 \, 8154 \ldots \degrees$

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

Also see

 * Value of Degree in Radians