The **length** of an [[Arc]] is a fraction of the [[circumference]] of the entire [[Circle|circle]]. If an arc $\overparen{AB}$ length $\ell$ of circle $C$ radius $r$ is intercepted from a central angle $\theta$ (radians) then $\frac{\ell}{2\pi r} = \frac{\theta}{2\pi} \implies \ell=\theta r$ If the angle $\theta\degree$ is given in degrees, $\frac{\ell}{2\pi r} = \frac{\theta\degree}{360\degree} \implies \ell=\frac{\theta \pi r}{180}$ (In a way, this is co-defined with [[angle]], since an angle in radians is an arc length on a [[‡ Unit Circle]])