Hemisphere Volume and Surface Area
The volume of a hemisphere is V = ⅔πr³, exactly half of a sphere. Its total surface area is 3πr²: the curved part plus the flat circle.
3D Solids
Hemisphere
A hemisphere is half a sphere. Its total surface area includes the curved dome plus the flat circular base.
- Volume
- V = (2 ⁄ 3) πr3
- Curved surface area
- CSA = 2πr2
- Total surface area
- TSA = 3πr2
- r radius
Where the formulas come from
- Volume: half of ⁴⁄₃πr³ is ⅔πr³.
- Curved surface: half of 4πr² is 2πr².
- Flat base: a circle, πr².
- Total surface: 2πr² + πr² = 3πr².
Worked example
A bowl is a hemisphere with radius 6 cm.
- Volume = ⅔ × π × 6³ = ⅔ × π × 216 = 452.39 cm³
- Curved surface = 2 × π × 6² = 226.19 cm²
- Total surface (with a lid) = 3 × π × 6² = 339.29 cm²
Live calculator
Try the hemisphere calculator
Try it yourself
A dome has a radius of 10 m. How much space is inside it?
Show the answer
V = ⅔ × π × 1,000 = 2,094.4 m³
More on the hemisphere formulas and sphere formulas pages.
Hemisphere: FAQ
What is the volume of a hemisphere?
V = ⅔πr³, half the volume of a sphere.
What is the surface area of a hemisphere?
Curved surface 2πr², or 3πr² including the flat base.
Is a bowl a hemisphere?
Often roughly. Use the inside radius to find how much it holds.