How this calculator works
A hemisphere is exactly half of a sphere cut through its equator. Its volume is therefore half of four thirds pi r cubed, which simplifies to two thirds pi r cubed. The flat circular base has area πr², the curved dome has twice that, and the total surface area is three times the base. A known volume can be run backwards with a cube root to recover the radius, which is useful when a container is sized by how much it must hold.
Formula
V = (2/3)πr³; r = ∛(3V/(2π)); base area = πr²; curved area = 2πr²; total area = 3πr².
Worked example
A hemisphere of radius 3 m has a volume of 18π ≈ 56.549 m³, a base of 9π ≈ 28.274 m², a curved area of 18π ≈ 56.549 m² and a total surface area of 27π ≈ 84.823 m². A diameter of 10 m gives a radius of 5 m and a volume of about 261.799 m³.
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Frequently asked questions
Is the volume exactly half of a full sphere?
Yes. Cutting a sphere through its centre leaves two congruent hemispheres, so each has half the sphere volume. The curved surface area is also half the sphere surface, but the flat base adds extra area that a sphere does not have.
Does the total surface area include the flat face?
Yes, the total is the curved dome plus the flat circular base. If you only need the dome, read the curved surface area output.
Can a hemisphere be oriented differently?
Yes. Rotating it does not change its volume or surface areas. A bowl resting on its rim is still a hemisphere, and the flat face is still the base for these formulas.