radian

Radian

One radian is the angle created when the arc length (i.e. a distance along the circle) is equal to the radius of the circle.

Usually radian and radius are taken to be $1$.
Since the circumference of a circle is $2\pi r$, the angle for a full circle is $2\pi$ radians.
$\frac{r}{2\pi }=\frac{\theta }{360^{\circ }}$, $\theta$ being the angle in degrees, and $r$ being the angle in radians.
→
$\theta =\frac{360^{\circ }r}{2\pi }=\frac{180^{\circ }r}{\pi }$
$r=\frac{\pi \theta }{180^{\circ }}$