How this calculator works
A hemisphere is half of a sphere cut through its centre. It has two different surfaces: the flat circular base and the curved cap, which is half of the sphere skin. The base area is πr², the cap area is 2πr², and the total is their sum, 3πr². Because every value depends on one radius, knowing any one of the listed measurements fixes all the others.
Formula
Base area = πr²; curved cap area = 2πr²; total surface area = 3πr²; volume = (2/3)πr³; total to volume ratio = 9/(2r).
Worked example
A hemisphere of radius 5 m has a base of 25π ≈ 78.540 m², a cap of 50π ≈ 157.080 m² and a total of 75π ≈ 235.619 m². Its volume is (2/3)π × 125 ≈ 261.799 m³, and the total surface to volume ratio is 9/10 = 0.9 per metre.
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Frequently asked questions
Does the total surface area include the flat base?
Yes. The total is the curved cap plus the circular base. If you only need the rounded part, read the cap area instead.
Why is the cap twice the base?
The curved surface has the same area as two circular discs of the same radius, which follows from the sphere area 4πr² being split in half. The base is one disc, so the cap is twice as large.
What does the surface to volume ratio mean?
It is the total area divided by the volume, in reciprocal metres. A small hemisphere loses heat and stores material less efficiently than a large one, because this ratio rises as the radius falls.