Numbers · geometry · ellipseArea of an ellipse — formula and calculator
Work out the area of an ellipse with the formula S = πab — your numbers substituted and a diagram drawn. The perimeter is 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 = πab
Perimeter (Ramanujan)
P ≈ π(3(a + b) − √((3a + b)(a + 3b)))
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Worked example
with real numbersGivena = 5 cm, b = 3 cm
Solution
S = πab = 3.1416 × 5 × 3 = 47.1239 cm²
P ≈ π(3(a + b) − √((3a + b)(a + 3b))) = 3.1416 × (3 × (5 + 3) − √((3 × 5 + 3) × (5 + 3 × 3))) ≈ 25.527 cm
Answer: area — 47.12 cm², perimeter (ramanujan) — ≈ 25.53 cm.
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Common mistakes
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Nearby shapes
CircleS = πr²Circular sectorS = πr² × α / 360°Annulus (ring)S = π(R² − r²)CalculatorAll 19 shapes, the composite shape and hectares →
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