hemisphere volume calculator
A hemisphere volume calculator turns a diameter into volume: a 6 ft dome holds 56.55 ft³, which is 2.094 yd³ or 423 gallons. Enter diameter, read four units.
Hemisphere volume calculator: what it does
A hemisphere volume calculator finds the space inside half a ball. Type the diameter across the flat base, and it returns cubic feet, cubic yards, US gallons and liters. The formula is volume = (2/3) × π × r³, where r is half the diameter.
A hemisphere is half a sphere, so it holds exactly half as much as a full sphere of the same width.
The formula in plain words
Half the diameter gives the radius. Multiply the radius by itself three times. Multiply that by π, then by 2/3. The result is cubic feet. Divide by 27 for cubic yards. Multiply by 7.48052 for gallons. Multiply the gallons by 3.78541 for liters.
Worked example, a 6 ft dome
A bowl-shaped basin is 6 ft across at the rim.
- Radius: 6 ÷ 2 = 3 ft
- Cubed: 3 × 3 × 3 = 27
- Cubic feet: (2/3) × π × 27 = 56.55
- Cubic yards: 56.55 ÷ 27 = 2.094
- Gallons: 56.55 × 7.48052 = 423.0
- Liters: 423.0 × 3.78541 = 1,601.3
Worked example, a soil mound
You want to build a rounded berm 10 ft across the base and need to know how much fill to order.
- Radius: 5 ft, cubed is 125
- Cubic feet: (2/3) × π × 125 = 261.80
- Cubic yards: 261.80 ÷ 27 = 9.696
That is about 9.7 yards of soil, and a real mound that slopes gently will hold less than a perfect dome. If the mound is taller than a hemisphere or lower than one, a cone or a flat-topped shape fits better.
Volume by diameter
| Diameter | Cubic feet | Cubic yards | Gallons |
|---|---|---|---|
| 2 ft | 2.09 | 0.078 | 15.7 |
| 4 ft | 16.76 | 0.621 | 125.3 |
| 6 ft | 56.55 | 2.094 | 423.0 |
| 8 ft | 134.04 | 4.964 | 1,002.7 |
| 10 ft | 261.80 | 9.696 | 1,958.4 |
| 12 ft | 452.39 | 16.755 | 3,384.1 |
Doubling the diameter multiplies the volume by eight, since the radius is cubed.
How to measure
- Measure the diameter across the flat top of the bowl or the flat base of the dome, through the middle.
- If the base is not a clean circle, take two measurements at right angles and average them.
- For a basin you plan to fill with liquid, measure inside the walls.
- For a mound, check the height too. A true hemisphere is as tall as its radius, so a 10 ft base should be 5 ft high.
Common mistakes
- Entering the radius as if it were the diameter. That cuts the answer to one eighth.
- Using the outside of a tank or basin. Wall thickness shrinks the inside volume.
- Treating a low, flat mound as a hemisphere. If the height is well under the radius, the real volume is a good deal smaller.
- Mixing up US gallons with imperial gallons if you work from a British supplier. This page uses US gallons.
Weight and partial fills
Water weighs about 8.34 pounds per US gallon, so the 6 ft bowl holds roughly 423 × 8.34 = 3,528 pounds when full. That matters if the basin sits on a deck or a platform.
A bowl rarely stays full. A hemisphere filled to a depth h holds π × h² × (3r − h) ÷ 3. For the 6 ft bowl (r = 3 ft) filled 1.5 ft deep, that is π × 2.25 × 7.5 ÷ 3 = 17.67 cubic feet, about 132 gallons. It is far less than half of 56.55, because the bottom of a round bowl is narrow. This calculator only does the full hemisphere, so use the formula above for a partial fill.
Related pages
The full ball is covered by the sphere volume calculator. For a tall pile with a point, use the cone volume calculator, and for a straight-sided tank use the cylinder volume calculator.
Frequently asked questions
What is the formula for hemisphere volume?
Volume = (2/3) × π × r³, where r is the radius. It is exactly half the volume of a sphere with the same diameter. For a 6 ft hemisphere, r is 3 ft and the volume is (2/3) × π × 27 = 56.55 cubic feet.
Do I enter the diameter or the radius?
The diameter. This calculator halves it for you. Measure straight across the flat base of the dome, through the center, and type that number in.
Where do hemispheres show up on a job?
Domed tank lids, half-round basins and planters, rounded fire pits, and smooth soil mounds or berms. Real mounds are rarely perfect, so treat the answer as a close estimate.
How does a hemisphere compare with a cone for a pile of material?
A cone has a sharp peak and holds less. For the same base diameter, a hemisphere as tall as its radius holds (2π/3) × r³, while a cone with that same radius and height holds (π/3) × r³, so the dome holds twice as much. A steep, freely dumped pile is closer to a cone.
Is the gallon figure for water?
It converts cubic feet to US gallons at 7.48052 gallons per cubic foot. That works for any liquid. Water weighs about 8.34 pounds per gallon, so the 6 ft bowl holds roughly 3,500 pounds of water.
How accurate is it for a bowl measured from the outside?
It overstates capacity, because wall thickness takes up space. Measure the inside diameter at the rim for the working volume.
Estimates only. Verify quantities with your supplier before purchasing.