Hemisphere Volume Calculator
A hemisphere is exactly half of a sphere, created by slicing a sphere along a plane through its center. The result is a solid with a flat circular base and a curved dome-shaped top, like a bowl or a domed building. Because a hemisphere is half a sphere, its volume is exactly half that of a sphere with the same radius. The volume is calculated as (2/3) * π * r³. The surface area of a hemisphere has three components: the curved dome surface area (2 * π * r²), the flat circular base area (π * r²), and the total surface area including both parts (3 * π * r²). This calculator computes the volume and all three surface area measurements from the radius. Enter the radius in any unit (centimeters, inches, meters, feet), and the calculator will return the volume and surface areas in the corresponding cubic and square units.
Hemisphere volume formulas
Volume = (2/3) * π * r³
Curved Surface Area = 2 * π * r²
Base Area = π * r²
Total Surface Area = 3 * π * r²
Reference volumes
| Radius | Volume | Curved Surface | Total Surface |
|---|---|---|---|
| 1 cm | 2.09 cm³ | 6.28 cm² | 9.42 cm² |
| 5 cm | 261.80 cm³ | 157.08 cm² | 235.62 cm² |
| 10 cm | 2,094.40 cm³ | 628.32 cm² | 942.48 cm² |
| 1 m | 2.09 m³ | 6.28 m² | 9.42 m² |
| 5 m | 261.80 m³ | 157.08 m² | 235.62 m² |
Hemisphere volume calculator: frequently asked questions
What is a hemisphere?
A hemisphere is exactly half of a sphere, cut along a plane through its center. It has a flat circular base and a curved dome-shaped top. Examples include a dome building, a bowl, or the Earth's Northern Hemisphere.
What is the formula for the volume of a hemisphere?
The volume of a hemisphere is half the volume of a sphere: V = (2/3) * π * r³. Since a full sphere is (4/3) * π * r³, dividing by 2 gives (2/3) * π * r³.
What are the surface area formulas for a hemisphere?
A hemisphere has three surface measurements. The curved surface area is 2 * π * r². The base (circular) area is π * r². The total surface area including both the curved surface and base is 3 * π * r².
How is a hemisphere different from a sphere?
A hemisphere is exactly half a sphere with a flat circular base. Its volume is half that of a sphere. Its curved surface area is half that of a sphere. The total surface area includes both the curved part and the flat circular base.
What are some examples of hemispheres?
Common hemispheres include domed buildings, hemispherical bowls, snow globes (the glass dome), domed stadium roofs, the Earth's Northern or Southern Hemisphere, and hemispherical candy molds.
Official sources
- Khan Academy: Solid geometry volume and surface area.
- NIST: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.