Sector Area Calculator

Calculate the area, arc length, and perimeter of a circular sector. Enter the radius and central angle for instant results.

Sector Calculator
Sector Area
78.54
sq ft
Arc Length
15.71
ft
Perimeter
35.71
ft

What is Sector Area Calculator?

A sector area calculator computes the area of a "pie slice" — the region of a circle enclosed between two radii and the arc connecting them. Sectors appear in pie charts, pizza slices, fan-shaped windows, curved garden beds, and irrigation sprinkler coverage patterns.

This tool exists because the sector area depends on both the radius and the central angle. A 90° sector is exactly one-quarter of the full circle area. A 180° sector (semicircle) is exactly half. The calculator handles any angle from 0° to 360° and also computes the arc length and total perimeter of the sector shape.

Sector Area Calculator Formula

Area = (θ / 360) × π × r²

Sector Area: A = (θ/360) × πr². For 90° and r = 10: A = (90/360) × π × 100 = 78.54 sq ft.

Arc Length: L = (θ/360) × 2πr. For 90° and r = 10: L = (90/360) × 2π × 10 = 15.71 ft.

Perimeter: P = 2r + L. For the same: P = 20 + 15.71 = 35.71 ft.

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Frequently Asked Questions

What is a sector of a circle?
A sector is a 'pie slice' of a circle — the region bounded by two radii and the arc between them. A full circle is a 360° sector. A semicircle is a 180° sector. A quarter circle is a 90° sector.
How do I calculate sector area?
Use the formula A = (θ/360) × π × r², where θ is the central angle in degrees and r is the radius. For a 90° sector with radius 10 ft: A = (90/360) × π × 100 = 78.54 sq ft.
How do I find the arc length of a sector?
Arc length = (θ/360) × 2πr. For a 90° sector with radius 10 ft: Arc = (90/360) × 2π × 10 = 15.71 ft. The arc length is the curved edge of the sector.
What is the perimeter of a sector?
The perimeter of a sector = 2r + arc length = 2r + (θ/360) × 2πr. For a 90° sector with radius 10 ft: Perimeter = 20 + 15.71 = 35.71 ft.
How do I convert degrees to radians for sector calculations?
Radians = Degrees × (π/180). For example, 90° = 90 × π/180 = π/2 ≈ 1.5708 radians. This calculator accepts degrees directly — no conversion needed.