Hemisphere Volume: worked example
| Radius | 5 |
|---|---|
| Volume | 261.8 |
| Curved surface area | 157.1 |
| Total surface area | 235.6 |
Hemisphere Volume: formula
Use one radius in the chosen length unit. Curved surface excludes the flat disk; total surface includes it. A hollow shell with thickness or an open tank’s material requirement needs the applicable interior and exterior dimensions rather than a solid-shape volume alone.
Hemisphere Volume: changing Radius
| Radius | Volume | Curved surface area | Total surface area |
|---|---|---|---|
| 4 | 134 | 100.5 | 150.8 |
| 4.5 | 190.9 | 127.2 | 190.9 |
| 5 (example) | 261.8 | 157.1 | 235.6 |
| 5.5 | 348.5 | 190.1 | 285.1 |
| 6 | 452.4 | 226.2 | 339.3 |
Hemisphere Volume: compare input ranges
| Input | Tested from | To | Volume: low input | Volume: high input | Swing |
|---|---|---|---|---|---|
| Radius | 4.5 | 5.5 | 190.9 | 348.5 | 157.6 (60%) |
Hemisphere Volume: individual input comparisons
| Input | Value | Volume | Curved surface area | Total surface area |
|---|---|---|---|---|
| Radius | 4 | 134 | 100.5 | 150.8 |
| 4.5 | 190.9 | 127.2 | 190.9 | |
| 5 | 261.8 | 157.1 | 235.6 | |
| 5.5 | 348.5 | 190.1 | 285.1 | |
| 6 | 452.4 | 226.2 | 339.3 |
Hemisphere Volume: which assumptions move the result?
Hemisphere Volume: values and definitions
| Quantity and definition | Value used |
|---|---|
| Radius | 5 |
| Volume | 261.8 |
| Curved surface area | 157.1 |
| Total surface area | 235.6 |
Hemisphere Volume: half and double Radius
| Radius | Volume |
|---|---|
| 2.5 | 32.7 |
| 5 | 261.8 |
| 10 | 2,094.4 |
Common error: Using the sphere's volume formula and forgetting to halve it. A radius-cubed result with four thirds in front is a full sphere, twice the size of a hemisphere.
Real domes and bowls are rarely perfect hemispheres, and a partial sphere, called a spherical cap, has its own formula. Wall thickness changes inside and outside dimensions. Units of volume are cubed, so convert with care.
Rounding of pi has a small effect.
Geometry calculators: Cone Frustum Calculator, Capsule Volume Calculator, Triangular Prism Volume Calculator, Law of Sines Calculator, Cube Calculator, Equilateral Triangle Calculator.
A hemisphere is half a sphere, so its volume is two thirds of pi times the radius cubed, and its curved surface is half the sphere's surface. With a radius of 5 that gives about 262 cubic units of volume and 157 of curved area. A flat base is a separate surface: adding it takes the total to about 236, which is what a solid dome needs and a shell does not.
Decide whether the flat face counts. Paint for a bowl's outside is the curved area, while a solid dome needs the total.
See the full sphere on the sphere volume calculator, the cylinder and cone pages for other solids, and the capsule calculator which combines a cylinder with two hemispheres. The circle area page gives the flat face, and the unit conversion calculators turn cubic units into gallons.
What is the total surface area of a hemisphere?
Three times pi times the radius squared, which adds the flat circular base to the curved surface.
How do I find the volume of a hollow bowl?
Subtract the volume of the inner hemisphere from the outer one, using the inner and outer radii.
What is the volume of a hemisphere?
Two thirds times pi times the radius cubed, exactly half the volume of a sphere with the same radius.