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Numbers · geometry · sphereVolume of a sphere — formula and calculator

Work out the volume of a sphere with the formula V = ⁴⁄₃ πr³ — your numbers substituted and a diagram drawn. The surface area is calculated too. Units can be mixed, and the answer comes in the units you need, litres included.

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01Calculator02Formula03Example04Mistakes05Nearby06Related
01

Calculator

enter the sizes — the formula and diagram follow

Sphere

volume · surface
r = 2 cm
diagram · not to scale
Result
Volume
33.5103cm³
= 0.0000335103 m³ = 0.0335103 L
Surface area
50.2655cm²
= 0.00502655 m²
How it was calculated
V = ⁴⁄₃ πr³ = 4 × 3.1416 × 2³ / 3 = 33.5103 cm³
S = 4πr² = 4 × 3.1416 × 2² = 50.2655 cm²
← Other shapes and the composite shape
02

Formula

and what each letter means
Volume
V = ⁴⁄₃ πr³
Surface area
S = 4πr²
Notation
r
radius of the sphere
03

Worked example

with real numbers
Givenr = 2 cm
Solution
V = ⁴⁄₃ πr³ = 4 × 3.1416 × 2³ / 3 = 33.5103 cm³
S = 4πr² = 4 × 3.1416 × 2² = 50.2655 cm²
Answer: volume — 33.51 cm³, surface area — 50.27 cm².
04

Common mistakes

The radius is cubed in the volume and squared in the surface. Double the radius and the volume grows eightfold.

If you know the diameter (a ball, a tank), the radius is half of it: a radius off by two gives a volume off by eight.

05

Nearby shapes

CircleS = πr²CylinderV = πr²hConeV = ⅓ πr²hCalculatorAll 19 shapes, the composite shape and hectares →
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