Value of Radian in Degrees

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Theorem

The value of a radian in degrees is given by:

$1 \radians = \dfrac {180 \degrees} {\pi} \approx 57.29577 \ 95130 \ 8232 \ldots \degrees$

This sequence is A072097 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


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:

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

$\blacksquare$


Also see


Sources