hemisphere volume calculator
Calculate a hemisphere's (half-sphere) volume in cubic feet, cubic yards, gallons, and liters from diameter — for domes, basins, and mounds.
A hemisphere is half a sphere — the shape of a dome, a rounded basin, or a smooth mound. Enter the diameter and get volume in cubic feet, cubic yards, gallons, and liters.
How this calculator works
Hemisphere volume is two-thirds pi times the radius cubed — half of a full sphere’s volume.
Formula: Cubic feet = (2/3) × π × (diameter ÷ 2)³. Cubic yards = ft³ ÷ 27. Gallons = ft³ × 7.48052. Liters = ft³ × 28.3168.
Worked example
A hemisphere 6 ft in diameter:
- Radius: 6 ÷ 2 = 3 ft
- Cubic feet: (2/3) × π × 3³ ≈ 56.55 ft³
- Cubic yards: 56.55 ÷ 27 ≈ 2.094 yd³
- Gallons: 56.55 × 7.48052 ≈ 423.0 gal
- Liters: 56.55 × 28.3168 ≈ 1601.3 L
Reference
| Diameter (ft) | Cubic feet |
|---|---|
| 4 | 16.76 ft³ |
| 6 | 56.55 ft³ |
| 8 | 134.04 ft³ |
How to measure
Measure diameter across the flat base of the dome or bowl shape. This applies to dome-roofed structures, half-round basins and planters, and dome-bottomed tanks. For the full sphere this shape was cut from, see the Sphere Volume Calculator.
Frequently asked questions
What's the formula for hemisphere volume?
Volume equals two-thirds pi times the radius cubed: V = (2/3) × π × r³ — exactly half of a full sphere with the same diameter.
Where does a hemisphere shape actually show up in construction?
Dome-topped structures, half-round basins and planters, dome-bottomed or dome-topped tanks, and rounded mound or berm shapes are all close approximations of a hemisphere.
How is a hemisphere different from a cone for estimating a pile?
A cone comes to a sharp point; a hemisphere is a smooth, rounded dome. A loosely poured, low mound sits closer to a flattened dome shape, while a steep, freely dumped pile behaves more like a cone — pick whichever shape the actual pile resembles.
Do I measure diameter at the base or somewhere else?
Measure diameter at the flat base — the widest circular edge where the dome meets the ground or the flat side of the tank. That's the diameter the formula uses.
How does hemisphere volume compare to a full sphere of the same diameter?
It's exactly half. If you already know a full sphere's volume for that diameter, divide by two to get the hemisphere's volume — no need to recalculate from scratch.
Can I use this for a rounded planter or basin's water capacity?
Yes — for a bowl-shaped planter or basin, this gives the maximum volume when filled level to the rim. Real fill capacity is slightly less once you account for wall thickness if measuring from the outside.
Estimates only. Verify quantities with your supplier before purchasing.