Sector Area Calculator

A sector is a “pie slice” region of a circle bounded by two radii and the arc between them. Its area depends on the circle's radius and the central angle.

Use $A = \frac{\theta}{360} \times \pi r^2$ when the angle is in degrees, or $A = \frac{1}{2}r^2\theta$ when in radians. For example, a $90^\circ$ sector of a circle with radius 10 cm has area $= \frac{90}{360} \times \pi \times 100 = 25\pi \approx 78.54$ cm².

A sector is bounded by two radii and an arc (pie-slice shape). A segment is bounded by a chord and the arc it cuts off. Segment area = sector area minus the triangle formed by the two radii and the chord.

Rearrange the formula: $\theta = \frac{A \times 360}{\pi r^2}$ for degrees, or $\theta = \frac{2A}{r^2}$ for radians. For example, if $A = 50$ cm² and $r = 10$ cm, then $\theta = \frac{50 \times 360}{\pi \times 100} \approx 57.3^\circ$.

An annular sector is a sector of a ring (annulus) — bounded by two radii and two concentric arcs. Its area is $A = \frac{\theta}{2}(R^2 - r^2)$, where $R$ is the outer radius and $r$ is the inner radius, with $\theta$ in radians.