Volume of a Hemisphere Calculator
Find the volume of a half-sphere — a bowl, dome, or tank end. Enter the radius or diameter in inches, feet, centimeters, or meters and get cubic volume, the liquid capacity in gallons and liters, and the matching full-sphere volume.
Example: with Measurement Radius · Value 5 · Unit inches → Hemisphere volume (2/3)πr³: 261.8 in³.
- Holds (liquid)≈ 1.13 gal (4.29 L)
- Full sphere would be (4/3)πr³523.6 in³
Computed by the calculator below using its default values. Change any input to see your own numbers.
V = (2/3)πr³ — exactly half a sphere. Doubling the radius multiplies volume by 8, because r is cubed.
Half a sphere, one third of a cylinder trick
A hemisphere is exactly half a sphere, so its volume is half of (4/3)πr³: V = (2/3)πr³. Archimedes' famous result makes this easy to sanity-check — a sphere fills exactly 2/3 of the cylinder that just contains it, so a hemisphere fills 2/3 of a cylinder with the same radius and height r. A mixing bowl 10 inches across (r = 5) holds about 262 cubic inches, or 4.5 quarts, if filled to the brim.
The cube on the radius is the number that surprises people. A dome twice as wide holds eight times as much; a 6-inch cereal bowl holds only about a quart while the 10-inch bowl holds four and a half. When you convert to liquid measure, remember the formula gives the geometric interior — real bowls and tanks have wall thickness and are rarely filled to the rim.
How it’s calculated
V = (2/3)πr³, with r = diameter/2 when you enter a diameter and π ≈ 3.14159265. Liquid conversions use exact factors: 1 gal = 231 in³, 1 ft³ = 7.480519 gal = 28.316847 L, 1 in³ = 16.387064 mL, 1 m³ = 1,000 L, 1 cm³ = 1 mL. The full-sphere row is simply 2× the hemisphere.
A perfect half-sphere cut flat through the center — shallow bowls and stretched domes hold less than the formula suggests.
Hemisphere volumes at common sizes
| Shape | Radius | Volume | Holds |
|---|---|---|---|
| Cereal bowl | 3 in | 56.5 in³ | ≈ 0.98 qt |
| Mixing bowl | 5 in | 261.8 in³ | ≈ 4.5 qt (1.13 gal) |
| Garden dome | 6 ft | 452.4 ft³ | ≈ 3,384 gal |
| Storage dome | 1 m | 2.09 m³ | ≈ 2,094 L |
Computed with V = (2/3)πr³; quarts at 57.75 in³/qt and gallons at 231 in³/gal (exact US definitions).
Common mistakes
- Entering the diameter as the radius — that inflates volume by 8×, since the radius is cubed.
- Using the sphere formula (4/3)πr³ for a half-sphere and doubling the true answer.
- Confusing volume with surface area: a dome's capacity is (2/3)πr³, but its curved skin is 2πr² — different formulas, different units.
- Quoting brim-full capacity for a real bowl; usable capacity is less once you account for wall thickness and headspace.
Frequently asked questions
What is the volume of a hemisphere?
V = (2/3)πr³, half the sphere formula (4/3)πr³. With a 5-inch radius that is (2/3)π(125) ≈ 261.8 cubic inches, about 1.13 gallons.
How do I use a diameter instead of a radius?
Halve it first — r = d/2 — or pick the diameter option here. A 12-cm-wide bowl has r = 6 cm and a volume of about 452 cm³, which is 0.45 liters.
Why does doubling the size multiply volume by 8?
Because the radius appears cubed: (2r)³ = 8r³. Volume grows with the cube of any length measurement, which is why a slightly bigger bowl holds dramatically more.
Is a hemisphere half the volume of a sphere exactly?
Yes — cutting a sphere through its center gives two identical halves, each (2/3)πr³. The page shows the full-sphere number too so you can check either way.
How many gallons does a hemispherical tank end hold?
Compute in feet and multiply cubic feet by 7.48. A tank head with a 2-ft radius adds (2/3)π(8) ≈ 16.76 ft³, roughly 125 gallons beyond the cylindrical body.