Hemisphere Volume Calculator
A hemisphere is exactly half of a sphere cut through its centre.
Enter Values
How to use this calculator
- Enter the radius of the hemisphere, or leave radius blank and enter the diameter instead — the tool halves it for you.
- Read off the volume plus the curved, flat-base and total surface areas.
- Because the maths is unit-agnostic, whatever length unit you type in (cm, m, in) gives volume in that unit cubed and areas in that unit squared.
How it works
A hemisphere is exactly half of a sphere cut through its centre. Its volume is therefore half the full sphere volume: V = (1/2) x (4/3) x pi x r^3 = (2/3) x pi x r^3, where r is the radius. If you know the diameter d instead, the radius is r = d / 2.
The surface of a solid hemisphere has two parts: the curved (dome) surface of area 2 x pi x r^2, which is half a sphere's 4 x pi x r^2, plus the flat circular base of area pi x r^2. Adding them gives the total surface area 3 x pi x r^2. A hollow hemisphere (an open bowl with no base) would use only the curved 2 x pi x r^2.
Worked example
Volume of a hemisphere with radius 3. A dome-shaped bowl is a hemisphere with radius r = 3. Volume = (2/3) x pi x r^3 = (2/3) x pi x 27 = 18 x pi = 56.549 cubic units. Its curved surface area is 2 x pi x 3^2 = 56.549 square units, the flat circular base is pi x 3^2 = 28.274 square units, and the total surface area is 3 x pi x 3^2 = 84.823 square units.
Common mistakes
- Using the diameter in place of the radius. The radius is half the diameter — plug the diameter into the diameter field (or halve it first) to avoid a result that is 8x too large in volume.
- Forgetting the flat base when a total surface area is needed. A solid hemisphere's total surface is 3 x pi x r^2, not the curved 2 x pi x r^2 alone.
- Mixing length units. All dimensions must share one unit; the volume then comes out in that unit cubed and areas in that unit squared.
Frequently asked questions
How is a hemisphere's volume related to a full sphere's?
It is exactly half. A full sphere of radius r has volume (4/3) x pi x r^3, so a hemisphere is (2/3) x pi x r^3 — half that value.
What is the difference between curved and total surface area?
The curved (dome) surface is 2 x pi x r^2. The flat circular base adds pi x r^2. For a solid hemisphere the total surface area is the sum, 3 x pi x r^2. An open bowl with no base uses just the curved 2 x pi x r^2.
Can I enter the diameter instead of the radius?
Yes. Leave the radius blank and fill in the diameter; the calculator uses r = d / 2. Enter only one of the two.
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Tip: Enter any known values to calculate the remaining results.
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