Case 1
- Radius
- 5
261.799388
Open with these valuesHemisphere Volume Calculator
261.799388units³
Result: 261.799388 units³Exactly half a sphere: ⅔πr³. A dome of radius 5 holds 261.8 units³. Note that a hemisphere and a cone of the same radius and height are not the same — the cone holds half as much again less, at ⅓πr³.
Worked examples
How it's calculated
V = ⅔ × π × r³
- StepMeasure the radius of the flat circular face.
- StepEnter it in any single length unit.
- ResultRead the volume in the cube of that unit.
Reference table
| Radius | Exact | Volume |
|---|---|---|
| 1 | 2π ÷ 3 | 2.094395 |
| 2.5 | 125π ÷ 12 | 32.724923 |
| 3 | 18π | 56.548668 |
| 5 | 250π ÷ 3 | 261.799388 |
| 10 | 2000π ÷ 3 | 2094.395102 |
Questions
How do you calculate the volume of a hemisphere?
Two thirds of π times the radius cubed — half of the full sphere. A radius of 5 gives 250π ÷ 3, about 261.8 cubic units.
Is a hemisphere the same as a dome?
Only if the dome is exactly half a sphere. A shallower dome is a spherical cap and needs its own formula, because its height is less than the radius.
How does it compare to a cone of the same size?
A cone with the same radius and height holds ⅓πr³ — exactly half the hemisphere. Three cones fill a cylinder; two of them fill a hemisphere.
Does the flat face count?
Not for the volume, which is the space inside. The flat circle only matters for surface area, where it adds πr² to the curved 2πr².
Sources and last check
Information, not professional advice.