Sphere Calculator (Volume & Surface Area)

How to use this calculator

Type any one of radius, diameter, volume or surface area — the others are calculated. Choose litres or gallons as the volume unit for tanks.

Formulas

V = ⁴⁄₃ π r³ S = 4π r²

Worked example

A ball with a 6 cm radius:

• Volume = 4/3 × π × 6³ = 904.8 cm³ (0.905 litres)
• Surface area = 4 × π × 6² = 452.4 cm²

Volume grows fast

Volume depends on the cube of the radius. Doubling the radius makes the sphere 8 times heavier and larger in volume, while surface area grows only 4 times. This is why large spherical tanks store far more per square metre of steel.

Hemisphere

A hemisphere (half a sphere) has volume ⅔πr³ — half the result above. Its curved surface is 2πr², plus a flat base of πr².

Frequently asked questions

What is the formula for the volume of a sphere?

V = 4/3 × π × r³. A sphere with a 6 cm radius has a volume of about 904.8 cm³.

What is the surface area of a sphere?

S = 4πr². With a 6 cm radius that is about 452.4 cm².

How do I find the radius from the volume?

Type the volume — the radius is found with r = ∛(3V ÷ 4π).

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