Quick answer: the volume of a hemisphere is V = (2/3) π r³ — half the full sphere. From a diameter, V = (π/12)d³. A true hemisphere is exactly as tall as its radius; if your dome or bowl is shallower than that, it's a spherical cap and holds less.
The hemisphere formula, step by step
where r = radius of the flat circular face (= the dome's height, if it's a true half-sphere)
Worked example — a garden dome 6 ft across:
- Radius: 6 ÷ 2 = 3 ft
- Cube it: 3³ = 27
- V = (2/3) × π × 27 = 56.55 ft³ ≈ 423 US gallons of enclosed air
A useful identity check: hemisphere = sphere ÷ 2 = exactly twice the cone with the same base and height. That last one surprises people — a cone-shaped funnel with the same mouth and depth holds precisely half of what the matching bowl does.
Hemisphere volumes by diameter — quick reference
| Diameter | If inches → volume | If feet → volume | If feet → US gal |
|---|---|---|---|
| 6 | 56.5 in³ | 56.5 ft³ | 423 |
| 8 | 134 in³ | 134 ft³ | 1,003 |
| 10 | 262 in³ | 262 ft³ | 1,959 |
| 12 | 452 in³ | 452 ft³ | 3,385 |
| 16 | 1,072 in³ | 1,072 ft³ | 8,022 |
| 20 | 2,094 in³ | 2,094 ft³ | 15,665 |
Where hemisphere volume shows up in real life
Tank end caps
Pressure vessels end in hemispherical (or shallower elliptical) heads because curves carry pressure better than flat plates. A 4-ft-diameter propane tank's two hemispherical ends together add one full 4-ft sphere: (π/6) × 64 ≈ 33.5 ft³ ≈ 251 gallons on top of the cylindrical middle — which is why the capsule calculator exists for the complete tank.
Domes and igloos
A geodesic greenhouse dome 20 ft across rising 10 ft encloses (2/3)π × 1,000 ≈ 2,094 ft³. Heating and fan sizing for dome structures starts from this number, and it's why domes are efficient: maximum floor-to-volume ratio with minimum surface losing heat.
Mixing bowls and ladles
Cookware is full of near-hemispheres. A 10-inch mixing bowl holds at most (π/12) × 1,000 ≈ 262 in³ ≈ 4.5 quarts — matching the "4.5 qt" stamped on the box, minus a little for the rim you'd never fill.
Common mistakes & pro tips
- Assuming every dome is a hemisphere. Only if height = half the span. A 20-ft-wide dome rising just 6 ft is a spherical cap and holds far less than the hemisphere formula predicts.
- Diameter as radius. 8× error here, since r is cubed. Bowl and dome widths are diameters — use Diameter mode.
- Using (4/3) instead of (2/3). That's the full sphere — double the right answer.
- Pro tip — flat-bottomed check. A hemisphere sits flat on its circular face. If your object rocks or has a foot ring, measure the inside curve, not the outside profile.
How to use this calculator
- Measure the radius or diameter. Measure across the flat circular face — that's the diameter — or from its center to the edge for the radius. Pick the matching mode.
- Let it apply V = (2/3)πr³. Cube the radius, multiply by π, then by two-thirds — exactly half the full sphere formula.
- Convert the output. Switch between cubic units, liters and gallons in the result menu.
Frequently asked questions
What is the formula for the volume of a hemisphere?
V = (2/3)πr³ — exactly half a sphere's (4/3)πr³. A hemisphere with a 3 cm radius holds (2/3)π × 27 = 56.55 cm³.
How much does a hemispherical bowl hold?
Measure the inside diameter, halve it, and apply (2/3)πr³. A salad bowl 25 cm across inside: r = 12.5 cm, V = (2/3)π × 1,953 ≈ 4,090 cm³ ≈ 4.1 liters. Real bowls are often shallower than a true half-sphere, so treat this as the upper bound.
How do I calculate dome volume?
If the dome is a full half-sphere, use (2/3)πr³ with the radius equal to both its height and half its span. A dome spanning 40 ft that rises 20 ft: V = (2/3)π × 8,000 ≈ 16,755 ft³. If the rise is less than half the span, it's a spherical cap — a shallower slice with a different formula.
What's the difference between a hemisphere and a spherical cap?
A hemisphere is exactly half a sphere — cut through the center. A spherical cap is any other horizontal slice, shallower or deeper. Caps use V = (πh²/3)(3r − h), where h is the cap height and r the sphere's radius; when h = r that formula collapses to the hemisphere's (2/3)πr³.