# How do you convert 360 degrees to radians?

${360}^{o} = 2 \pi \text{radians}$
${360}^{o}$ represents a complete revolution, tracing out an arc of $2 \pi$ radians.
A radian is the angle subtended by an arc of length equal to the radius and the complete length of the circumference is $2 \pi r$, where $r$ is the radius.
So a complete circular arc subtends $\frac{2 \pi r}{r} = 2 \pi$ radians.