Hemisphere Volume Calculator
Calculate the volume of a hemisphere (half sphere) from its radius. Uses V = (2/3) x pi x r^3. Handy for domes, bowls, and scientific calculations.
How to use this tool
- Enter radius in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your volume and the full breakdown beneath it.
Formula
V = (2/3) x pi x r^3
How it works
A hemisphere is half a sphere: V = ⅔πr³.
Worked example
Hemisphere r=3
- r = 3
- r^3 = 27
- V = (2/3) x pi x 27 = 18 x pi
- V = 56.5486...
Volume = 56.5487 cubic units
Common mistakes to avoid
- Using the diameter instead of the radius — entering the full width of the hemisphere instead of half of it cubes the error, producing a volume eight times too large.
- Using the full sphere formula (4/3)*pi*r^3 and forgetting to halve it, giving twice the correct hemisphere volume.
- Confusing a hemisphere (half of a solid sphere) with a hemispherical shell — the formula V = (2/3)*pi*r^3 gives the solid volume, not a thin hollow shell.
Key terms
- What is a hemisphere?
- A hemisphere is exactly half of a sphere, created by cutting a sphere along a great circle.
- Does the volume include the flat circular base?
- The volume formula accounts for the solid 3D region; the flat base is a surface, not part of the volume.
Frequently asked questions
- How does the hemisphere volume relate to the full sphere volume?
- A hemisphere is exactly half a sphere. The sphere volume is (4/3)*pi*r^3, so the hemisphere volume is (2/3)*pi*r^3.
- Does the formula include the flat circular face?
- The volume formula captures the entire enclosed solid, including the region under the flat circular base. The flat face is part of the bounding surface but does not affect the enclosed volume calculation.
- How do I find the surface area of a hemisphere?
- The total surface area is 3*pi*r^2: the curved surface is 2*pi*r^2 and the flat circular base adds pi*r^2.