Hemisphere Volume Calculator
Compute the volume, curved surface area, total surface area and base area of a hemisphere from its radius.
How it works
V = (2/3)·π·r³ · Curved area = 2·π·r² · Total area = 3·π·r² · Base area = π·r²
A hemisphere is half of a sphere, cut through the centre. Its volume is exactly half the sphere’s, giving (2/3)πr³. The curved outer surface is half the sphere’s surface (2πr²); adding the flat circular base (πr²) gives a total surface area of 3πr². Which surface figure you want depends on whether the flat face is exposed — a solid dome sitting on the ground exposes only the curved area.
Worked example
For a radius of 5 units: volume = (2/3)·π·125 ≈ 261.80 units³; curved surface = 2·π·25 ≈ 157.08 units²; base area = π·25 ≈ 78.54 units²; total surface = 3·π·25 ≈ 235.62 units².
Sources: Hemisphere — Wolfram MathWorld
Frequently asked questions
Is a hemisphere’s volume half a sphere’s?
Yes. A hemisphere is a sphere sliced exactly in half, so its volume (2/3)πr³ is precisely half the sphere’s (4/3)πr³.
When should I use curved area instead of total area?
Use the curved area (2πr²) when only the dome is exposed, such as a bowl viewed from outside. Use the total area (3πr²) when the flat circular base is also a surface you need to account for.
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This calculator is for educational purposes. Double-check important results before acting on them.