What is a sector area calculator?
A circular sector is the "pie-slice" region of a circle bounded by two radii and the arc between them. This calculator finds the area of that slice when you know the circle's radius and the central angle measured in degrees. It also returns the arc length of the curved edge.
How to use it
Enter the radius (\(r\)) of the circle and the central angle (\(\theta\)) in degrees, then read off the sector area. The angle can be anything from 0° (no area) up to 360° (the entire circle). Use any consistent length unit — the area comes out in those units squared.
The formula explained
A full circle has area \(\pi r^2\) and spans 360°. A sector covers only a fraction \(\theta/360\) of the full turn, so its area is simply that fraction of the whole circle:
$$A = \frac{\theta}{360} \times \pi \times r^2$$
The arc length follows the same logic applied to the circumference \(2\pi r\): $$L = \frac{\theta}{360} \times 2\pi r$$.
Worked example
Suppose \(r = 10\) and \(\theta = 90°\). The sector is a quarter circle. $$\text{Area} = \frac{90}{360} \times \pi \times 10^2 = 0.25 \times \pi \times 100 = 25\pi \approx 78.54 \text{ square units}.$$ $$\text{Arc length} = \frac{90}{360} \times 2\pi \times 10 = 0.25 \times 62.832 \approx 15.71 \text{ units}.$$
FAQ
What if my angle is in radians? This tool expects degrees. To convert, multiply radians by \(180/\pi\) first, or use a radians-based sector calculator where \(A = \tfrac{1}{2}r^2\theta\).
Can the angle exceed 360°? Geometrically a sector tops out at 360° (the whole circle). Larger values just represent more than one full revolution.
What units does the result use? Whatever unit you used for the radius, squared. If \(r\) is in centimeters, the area is in square centimeters.
