Hemisphere Calculator
This hemisphere calculator needs just one known value. Example: for r = 5 the volume is 261.799 and the total surface area is 235.619.
Source: Wikipedia – Sphere (hemisphere). Updated: .
How it is calculated
A hemisphere is half of a sphere, cut by a plane through its centre. It consists of a curved surface and a flat base circle.
Formulas and steps
With radius r the volume is V = 2/3 · π · r³, the curved surface 2πr², the base circle πr² and the total surface area 3πr². If the diameter is given instead, r = d / 2. From the volume r = ∛(3V / (2π)), and from the total surface area r = √(S / (3π)).
Worked example
For r = 5, V = 2/3 · π · 125 ≈ 261.799. The curved surface is 2π · 25 ≈ 157.08, the base circle π · 25 ≈ 78.5398 and the total surface area 3π · 25 ≈ 235.619. The diameter is 10. Conversely, the volume 261.799 leads back to r = 5.
- A hemisphere has exactly half the volume of a sphere: a sphere with r = 5 has 4/3 · π · 125, twice as much.
- The total surface area is 3πr², not half of the sphere’s 4πr², because the base circle is added.
Frequently asked questions
How do you calculate the volume of a hemisphere?
V = 2/3 · π · r³. For r = 5 that is about 261.799 cubic units, exactly half the volume of the sphere.
What is the surface area of a hemisphere?
The curved surface 2πr² plus the base circle πr², together 3πr². For r = 5 this gives about 235.619; without the base circle it is 157.08.
Can I find the radius from the volume?
Yes, with r = ∛(3V / (2π)). Choose “Volume V” above, enter the value, and the calculator returns the radius and all areas.
Sources and legal basis
As of: · Editorial policy
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