A hemisphere’s volume — exactly half of a full sphere with the same radius.
How it works
The standard sphere volume formula (4/3 × π × radius cubed) is simply halved to get the hemisphere volume.
What this does not include
This does not include a full sphere — for that, use this site’s general volume calculator instead, which covers the complete sphere shape.
How to use this calculator
- Enter the radius.
A worked example
A hemisphere with radius 3: volume = (2/3)πr³ = 56.5487.
Radius 5: volume = 261.7994 — exactly half of a full sphere’s volume at the same radius.
What the variables mean
| Variable | Meaning |
|---|---|
| Radius | Distance from the flat face’s center to the curved surface |
Edge cases worth knowing
A hemisphere’s volume is always exactly half a full sphere’s volume at the same radius — dividing this site’s sphere volume formula by 2 gives the identical result.
Volume scales with the cube of the radius — the jump from radius 3 to radius 5 here isn’t proportional, since 5/3 ≈ 1.67 but the volume ratio is closer to 4.6, matching (5/3)³.
Frequently asked questions
Why is the hemisphere formula exactly half the sphere formula?
Because a hemisphere is, by definition, precisely one half of a sphere cut through its center — no additional geometry is needed beyond halving the known sphere volume.
What’s a real-world example of a hemisphere?
A dome roof, a mixing bowl, or half of a ball — any shape that’s precisely half a sphere.
Does doubling the radius double the volume?
No — volume scales with the cube of the radius, so doubling the radius makes the volume eight times larger, not twice.
