Hemisphere Volume Calculator

A hemisphere is half a sphere — cut along a great circle through the center. The volume is half the sphere’s volume:

V = (2/3) × π × r³

Worked example — half-spherical mixing bowl: A 10-inch-diameter stainless mixing bowl that is exactly hemispherical (rare in real life — most “round” bowls have flatter or rolled bottoms). r = 5 in. V = (2/3) × π × 125 ≈ 261.8 in³ ≈ 1.13 US gallons.

Real mixing bowls usually hold about 80% of the geometric hemisphere volume because the bottom is flattened for stability.

Where hemisphere volumes show up:

• Mixing bowls and salad bowls (when approximated as half-spheres).
• Domed roofs and architecture. A pure hemispherical dome of internal radius r contains (2/3)πr³ of interior volume.
• Half-buried propane tanks. Some pressure vessels have hemispherical end caps. The end cap volume is (2/3)πr³.
• Geodesic domes. Used in greenhouses and exhibition halls. The geometric shape is approximated as a hemisphere.
• Hot air balloons. When inflated to roughly spherical shape, the lower half resembles a hemisphere.

Hemisphere vs. half-spherical “cap”:

A hemisphere is exactly half — the cap height equals the radius. A “spherical cap” is a more general shape where the cap height can be any value from 0 (a thin slice) to 2r (the full sphere). For h = r, the spherical cap collapses into the hemisphere. For smaller h, you get a flatter “dome slice.”

Comparing hemisphere to other half-shapes:

• Half a cube (cut horizontally): V = ½ × s³.
• Half a cylinder (cut along the axis): V = ½ × π × r² × h.
• Half a sphere (hemisphere): V = (2/3) × π × r³.

So a hemisphere holds 2/3 the volume of a cylinder with the same radius and a height equal to that radius. This is part of the classical Archimedes result: cylinder, sphere, cone have volumes in the ratio 3:2:1 when all share the same radius and the cone/cylinder share their height as 2r.

Surface area note (different page): Hemisphere surface includes both the curved dome and the flat circular base — SA = 3πr².

Sanity check:

• r = 0: V = 0. ✓
• Hemisphere volume = ½ × sphere volume. ✓ (2/3 = ½ × 4/3.)
• A 1-cm-radius hemisphere has volume 2π/3 ≈ 2.094 cm³.