Calculation of arc lengths

The length $L$ of an arc of a circle with radius $r$ and central angle $\theta$ (in degrees) is given by $L = \frac{\theta}{360} \times 2\pi r.$ If the angle is in radians, then $L = r\theta.$

Important properties

• Arc length is proportional to the central angle.

• For a full circle ($\theta = 360^\circ$ or $2\pi$ radians), the arc length is the circumference: $2\pi r$.

• If the angle is in radians, the formula simplifies to $L = r\theta$.