Circle Sector Calculator
Compute the area and arc length of a circle sector given a radius and central angle in degrees or radians. Use it for pie-chart segments, pizza slices, irrigation pivot coverage, or any circular region problem.
About this calculator
A circle sector is the 'pie slice' region bounded by two radii and the arc between them. Its area is a fraction of the full circle area: Sector Area = π × r² × (θ / 360°) when θ is in degrees, or Sector Area = ½ × r² × θ when θ is in radians. The arc length — the curved edge of the slice — is Arc Length = 2πr × (θ / 360°) in degrees, or simply Arc Length = r × θ in radians. Both formulas scale linearly with the central angle: a 90° sector is exactly one-quarter of the circle. Converting between angle units is straightforward: θ(rad) = θ(deg) × π / 180.
How to use
Say you have a circle with radius r = 8 units and a central angle of 45°. First calculate sector area: Area = π × 8² × (45 / 360) = π × 64 × 0.125 = 8π ≈ 25.13 square units. Then find arc length: Arc = 2π × 8 × (45 / 360) = 16π × 0.125 = 2π ≈ 6.28 units. Enter 8 in the Radius field, 45 in the Central Angle field, select Degrees, and the calculator returns both values immediately.
Frequently asked questions
How do I find the area of a circle sector using degrees?
Use the formula Sector Area = π × r² × (θ / 360), where r is the radius and θ is the central angle in degrees. The ratio θ/360 represents what fraction of the full circle the sector occupies. For example, a 120° sector covers one-third of the circle, so its area is (1/3)πr². Always ensure your angle is less than or equal to 360° for a valid sector.
What is the difference between a circle sector and a circle segment?
A sector is the pie-slice region between two radii and the connecting arc — it includes the two straight edges. A segment is the region between a chord (straight line) and the arc it subtends, with no straight radii involved. To find a segment's area you subtract the triangle formed by the two radii and the chord from the sector area. This calculator focuses on sectors, so for segments you would need an extra step.
How do I convert the central angle from degrees to radians for the arc length formula?
Multiply degrees by π/180 to get radians: θ(rad) = θ(deg) × π / 180. For example, 90° becomes 90 × π/180 = π/2 ≈ 1.5708 radians. In radian mode the arc length formula simplifies to L = r × θ, which is often easier to compute by hand. This calculator accepts both units directly, so you can enter either and it handles the conversion internally.