Numbers · geometry · circular sectorArea of a sector — formula and calculator
Work out the area of a sector with the formula S = πr² × α / 360° — your numbers substituted and a diagram drawn. The arc length and perimeter are calculated too. Units can be mixed, and the answer comes in the units you need, hectares and acres included.
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Calculator
enter the sizes — the formula and diagram follow02
Formula
and what each letter meansArea
S = πr² × α / 360°
Arc length
L = πrα / 180°
Perimeter
P = 2r + L
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Worked example
with real numbersGivenr = 10 cm, α = 60°
Solution
S = πr² × α / 360° = 3.1416 × 10² × 60 / 360 = 52.3599 cm²
L = πrα / 180° = 3.1416 × 10 × 60 / 180 = 10.472 cm
P = 2r + L = 2 × 10 + 10.472 = 30.472 cm
Answer: area — 52.36 cm², arc length — 10.47 cm, perimeter — 30.47 cm.
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Common mistakes
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Nearby shapes
CircleS = πr²Annulus (ring)S = π(R² − r²)EllipseS = πabCalculatorAll 19 shapes, the composite shape and hectares →
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