What this calculator does
A hemisphere is exactly half a sphere, cut through its centre, such as the shape of a dome roof or a mixing bowl. Its volume is worked out with the same πr³ relationship as a full sphere, simply halved, which is where the volume of hemisphere formula comes from.
The other figure worth knowing alongside volume is surface area, and a hemisphere has two distinct surfaces: the curved dome and the flat circular base where it was cut from the sphere. This calculator reports both separately as well as combined, since some uses, like coating only the dome, need just the curved figure.
The formula
Volume is two-thirds of π times the radius cubed. The curved surface is worked out the same way as half a sphere’s surface, and the flat base is a plain circle of the same radius; adding the two gives the total surface area.
| Term | Meaning |
|---|---|
| r | The radius of the hemisphere, the same as the radius of the sphere it was cut from. |
| V | Volume: (2/3)πr³. |
| Curved surface | The area of the dome: 2πr². |
| Flat base | The area of the circular cut face: πr². |
The inputs explained
| Field | What to enter |
|---|---|
| Value | The radius or diameter of the hemisphere, in whatever unit you are working in; the result will be in that same unit cubed. |
| This value is the | Choose whether the value entered above is the radius or the diameter. |
When to use it
Estimating the capacity of a dome or bowl
Anything shaped like half a sphere, from a mixing bowl to a dome roof, has its capacity or displacement estimated using the hemisphere volume formula rather than the full-sphere one.
Working out material for a curved surface
Coating, painting or cladding only the curved dome of a hemisphere, rather than the flat base as well, needs the curved surface area specifically, which this calculator reports separately from the total.
Comparing a hemisphere against the full sphere it came from
Seeing the full-sphere volume alongside the hemisphere figure makes clear that a hemisphere is exactly half, which is a useful sanity check when working from a half-built or half-filled shape.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How volume and surface area scale with radius
A range of radius values, each treated as the radius directly.
| Radius | Volume | Total surface area |
|---|---|---|
| 1 | 2.094 | 9.425 |
| 2 | 16.755 | 37.699 |
| 5 | 261.799 | 235.619 |
| 10 | 2,094.40 | 942.478 |
| 20 | 16,755.16 | 3,769.91 |
| 50 | 261,799.39 | 23,561.94 |
How volume and curved surface area scale with diameter
The same range of sizes, entered as diameters instead of radii.
| Diameter | Volume | Curved surface area |
|---|---|---|
| 2 | 2.094 | 6.283 |
| 4 | 16.755 | 25.133 |
| 10 | 261.799 | 157.080 |
| 20 | 2,094.40 | 628.319 |
| 40 | 16,755.16 | 2,513.27 |
| 100 | 261,799.39 | 15,707.96 |
Questions
What is the volume of hemisphere formula?
V = (2/3)πr³, where r is the radius. It is exactly half the full-sphere volume formula of (4/3)πr³, since a hemisphere is half a sphere.
Does the surface area include the flat base?
This calculator reports the curved surface, the flat base and the total separately, since some situations only need the curved dome figure and others need the whole outer surface including the cut face.
How is a hemisphere different from a half-sphere shell?
A solid hemisphere, as calculated here, is a full half-ball with volume. A hemispherical shell, like a thin dome or bowl, is closer to a curved surface with negligible thickness, and is better described by its curved surface area than by this volume figure.
Can I enter the diameter instead of the radius?
Yes. Choose "Diameter" for the value type and the calculator halves it to get the radius before working out volume and surface area, so either measurement gives the correct result.
For the volume of a full sphere and other common solids, see the volume of common shapes calculator. For the surface area of a cylinder, another solid built from circular faces, see the surface area of a cylinder calculator.