Area of a Sector Calculator
A sector is the pizza-slice piece of a circle between two radii. Enter the radius and central angle — degrees or radians — for the sector area, arc length, and perimeter.
Example: with Radius (r) 10 · Central angle (θ) 90 · Angle unit Degrees → Sector area (A): 78.54.
Computed by the calculator below using its default values. Change any input to see your own numbers.
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Check it outSector area formula in degrees and radians
In degrees, take the angle’s share of the whole circle: A = (θ ÷ 360) × πr². A 90° sector of a radius-10 circle covers (90/360) × π × 100 ≈ 78.54 square units — exactly a quarter of the circle’s 314.16. In radians the sector area formula collapses to A = ½r²θ: radius 6 and θ = 2 rad give ½ × 36 × 2 = 36.
Real example: one of 8 equal slices of a 16 in pizza is a 45° sector with r = 8, so A = (45/360) × π × 64 ≈ 25.13 sq in. Already know the arc length L instead of the angle? Use the shortcut A = ½ × L × r — no angle needed.
How it’s calculated
Degrees: A = (θ ÷ 360) × πr². Radians: A = ½r²θ. Arc length L = rθ (radians) or 2πr × (θ/360) (degrees), and the sector perimeter is 2r + L. Degrees are converted by π/180 using JavaScript’s full-precision π ≈ 3.14159 (Math.PI).
Results update as you type and are estimates, not professional advice — verify important decisions with a qualified professional.
Common mistakes
- Using A = ½r²θ with a degree angle — that form needs radians; in degrees use (θ ÷ 360) × πr².
- Forgetting the perimeter includes the two straight radii — it's 2r + arc length, not the arc alone.
- Squaring the diameter instead of the radius — r in the formula is the center-to-edge distance.
Frequently asked questions
What is the area of a sector formula?
A = (θ ÷ 360) × πr² with θ in degrees, or A = ½r²θ with θ in radians. Both take the angle’s fraction of the full circle’s area.
How do you find the area of a sector in radians?
Multiply half the squared radius by the angle: A = ½r²θ. With r = 6 and θ = 2 rad, A = ½ × 36 × 2 = 36.
How do I find sector area from the arc length?
Use A = ½ × L × r. An arc of length 12 on a radius-6 circle encloses ½ × 12 × 6 = 36.
What's the difference between a sector and a segment?
A sector is bounded by two radii and the arc (a pizza slice); a segment is the region cut off by a single chord. This page computes sectors.