Volume of a Hemisphere Calculator

Free Volume of a Hemisphere Calculator

Find the volume of a hemisphere from its radius: V = (2/3)πr³.

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Last updated October 10, 2026 · Report an error

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A hemisphere is exactly half a sphere by volume, so its volume formula is simply half the classic sphere volume formula. This calculation is used in civil and structural engineering (estimating the volume of a domed roof or a hemispherical water tank), chemistry and cooking (volume of a hemispherical bowl or mold), and manufacturing (rounded end-caps on pressure vessels and tanks, where knowing the enclosed volume matters for capacity ratings).

How it works

Enter the radius r. A full sphere's volume is V = (4/3)πr³; since a hemisphere is precisely one half of a sphere sliced through its center, its volume is exactly half of that: V = (2/3)πr³.

Enter radius.
Click Calculate to see your results.

Examples

Radius = 3

V = (2/3)π(27) ≈ 56.55 cubic units.

Radius = 6

V = (2/3)π(216) ≈ 452.39 cubic units — eight times the radius-3 volume, since volume scales with the cube of the radius (2³=8).

Common mistakes to avoid

Using the full sphere volume formula (4/3)πr³ by mistake instead of halving it.
Confusing volume with surface area, which uses a completely different formula and units.
Forgetting to cube the radius (using r² or r instead of r³).
Using the diameter in place of the radius without first dividing it by 2.

Frequently asked questions

A sphere's volume is (4/3)πr³; a hemisphere is exactly half of that solid, giving (2/3)πr³.

The volume increases eightfold (2³=8), since volume depends on the cube of the radius, not the radius itself.

No — they measure completely different things (enclosed space vs. the covering "skin" of the shape) and use different formulas: volume uses r³, while surface area uses r².

No — this gives the volume enclosed by a solid hemisphere of radius r. For a hollow shell (like a tank), you'd need to compute the volume for the outer radius and subtract the volume for the inner radius separately.

It falls directly out of halving the sphere's (4/3)πr³ formula — the sphere's own constant, 4/3, itself comes from integrating circular cross-sections through the whole solid, so there's no simpler underlying constant to reduce it to.

A satellite dish is roughly a paraboloid rather than a true hemisphere, but a mixing bowl, a snow-globe base, a planetarium dome, and the rounded end of many storage tanks are all commonly modeled as hemispheres for volume estimates.

A cylinder with height equal to its radius has volume πr³, which is 1.5 times the hemisphere's (2/3)πr³ volume — a handy sanity check when estimating enclosed capacity for dome-topped tanks built on a cylindrical base.