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Numbers · geometry · circleArea of a circle — formula and calculator

Work out the area of a circle with the formula S = πr² — your numbers substituted and a diagram drawn. The circumference is calculated too. Units can be mixed, and the answer comes in the units you need, hectares and acres included.

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01Calculator02Formula03Example04Mistakes05Nearby06Related
01

Calculator

enter the sizes — the formula and diagram follow

Circle

area · perimeter
r = 5 cm
diagram · not to scale
Result
Area
78.5398cm²
= 0.00785398 m²
Circumference
31.4159cm
= 0.314159 m
How it was calculated
S = πr² = 3.1416 × 5² = 78.5398 cm²
C = 2πr = 2 × 3.1416 × 5 = 31.4159 cm
← Other shapes and the composite shape
02

Formula

and what each letter means
Area
S = πr²
Circumference
C = 2πr
Notation
r
radius — from the centre to the edge
π
pi ≈ 3.1416
03

Worked example

with real numbers
Givenr = 5 cm
Solution
S = πr² = 3.1416 × 5² = 78.5398 cm²
C = 2πr = 2 × 3.1416 × 5 = 31.4159 cm
Answer: area — 78.54 cm², circumference — 31.42 cm.
04

Common mistakes

The formula takes the radius, not the diameter. If you know the diameter, halve it.

πr² is the area, 2πr is the circumference. They are often swapped.

05

Nearby shapes

Circular sectorS = πr² × α / 360°Annulus (ring)S = π(R² − r²)EllipseS = πabSphereV = ⁴⁄₃ πr³CalculatorAll 19 shapes, the composite shape and hectares →
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2·8·16

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