Area and perimeter of a sector formula

Here are the formulas for the area and perimeter of a sector.

Let $r$ be the radius of the circle and $\theta$ be the angle of the sector.

Area of a Sector

• If the angle $\theta$ is in radians: $$\text{Area} = \frac{1}{2} r^2 \theta$$
• If the angle $\theta$ is in degrees: $$\text{Area} = \frac{\theta}{360^\circ} \pi r^2$$

Perimeter of a Sector

The perimeter of a sector is the sum of the lengths of the two radii and the arc length.

• If the angle $\theta$ is in radians: The arc length $L = r\theta$. $$\text{Perimeter} = 2r + r\theta$$
• If the angle $\theta$ is in degrees: The arc length $L = \frac{\theta}{360^\circ} 2\pi r$. $$\text{Perimeter} = 2r + \frac{\theta}{360^\circ} 2\pi r$$