degree

Name	Symbol	Quantity	SI units
degree	°	plane angle, phase angle	^π⁄₁₈₀ rad
The degree, symbol °, is a non-SI unit of plane angle accepted for use with the SI. By definition, one degree is equal to ¹⁄₃₆₀ of a turn, or ^π⁄₁₈₀ radians.
Definition
$1^\circ = \dfrac{\pi}{180} \mspace{6mu} \text{rad}$

The conversion between radians and degrees follows from the relation: 1 turn = 360°.

$360^\circ = 2 \pi \mspace{6mu} \text{rad}\\ \\ \\ 1^\circ \mspace{17mu} = \dfrac{\pi}{180} \mspace{6mu} \text{rad}$