sphere volume calculator
A sphere volume calculator uses V = (4/3) × π × r³ from diameter alone: a 4 ft sphere holds 33.51 ft³, 1.24 yd³, or about 250.7 gallons.
Sphere volume calculator: cubic feet, yards, gallons, and liters
A sphere volume calculator needs just one number, the diameter. Halve it for the radius, cube that, and multiply by 4/3 and π. A sphere 4 feet across has a 2 ft radius, so its volume is (4/3) × π × 2³ = 33.51 cubic feet, which is 1.24 cubic yards, or about 250.7 US gallons.
The result appears in four units, because tank capacity is quoted in gallons while concrete or stone for a cast sphere is ordered in yards.
The formula in plain words
Picture a basketball inside a square cardboard box that hugs it on all sides. The sphere fills a bit over half the box. The exact share is π ÷ 6, about 52.4 percent.
- Cubic feet = (4/3) × π × (diameter ÷ 2)³
- Shortcut = 0.5236 × diameter³
- Cubic yards = cubic feet ÷ 27
- Gallons = cubic feet × 7.48052
- Liters = gallons × 3.78541
Because the diameter is cubed, a small increase in diameter raises the volume sharply.
Worked examples
- Spherical water tank, 4 ft across
- Radius: 4 ÷ 2 = 2 ft
- Cubic feet: (4/3) × π × 2³ = 33.51 ft³
- Cubic yards: 33.51 ÷ 27 = 1.241 yd³
- Gallons: 33.51 × 7.48052 = 250.7 gal
- Liters: 948.9 L
- Large sphere, 8 ft across
- Radius: 4 ft
- Cubic feet: (4/3) × π × 4³ = 268.08 ft³
- Cubic yards: 9.929 yd³
- Gallons: 2,005.4 gal
The second sphere is twice as wide as the first and holds exactly 8 times as much (33.51 × 8 = 268.08).
Sphere volume by diameter
| Diameter | Cubic feet | Cubic yards | Gallons |
|---|---|---|---|
| 2 ft | 4.19 | 0.155 | 31.3 |
| 4 ft | 33.51 | 1.241 | 250.7 |
| 6 ft | 113.10 | 4.189 | 846.0 |
| 8 ft | 268.08 | 9.929 | 2,005.4 |
| 10 ft | 523.60 | 19.393 | 3,916.8 |
| 12 ft | 904.78 | 33.510 | 6,768.2 |
How to measure
- Diameter through the center. Use calipers or a straight tape across the widest point.
- Circumference option. Wrap a tape around the equator, then divide by π to find the diameter.
- Inside or outside. For a tank’s capacity, use the inside diameter. For a solid cast sphere, use the outside diameter.
- Wall thickness. A hollow sphere holds less than the outer diameter suggests. Subtract twice the wall thickness to get the inside diameter.
- Convert units. If your measurement is in inches, divide by 12 before entering it.
Common mistakes
- Entering the radius. The calculator wants diameter, so a radius of 3 ft means a diameter of 6 ft. Entering 3 gives an answer one-eighth of the correct one.
- Using a sphere formula for a tank with flat ends. Many tanks are cylinders with domed ends, not full spheres.
- Forgetting the unit. Volume is cubic feet, so an error in feet gets cubed.
- Counting solid material as capacity. A cast sphere’s volume is the concrete you pour, not the water it holds.
- Ignoring fill level. A tank is never completely filled, so plan for usable volume somewhat below the full figure.
From volume to weight
Volume alone does not tell you the load. A 4 ft sphere holds 250.7 gallons of water, and at 8.34 lb per gallon that is about 2,091 lb of water. A solid concrete sphere of the same size holds 33.51 ft³, which is about 5,027 lb at the 150 lb per ft³ used on this site.
Hollow spheres and shells
For a shell, such as a cast hollow ball, subtract the inside from the outside. A 4 ft sphere with 3 in walls has a 3.5 ft inner diameter. The inner volume is 22.45 ft³, so the shell is 33.51 − 22.45 = 11.06 ft³ of material.
Related calculators
For half a sphere, such as a dome, use the hemisphere volume calculator. A stretched sphere is covered by the ellipsoid volume calculator, and upright tanks by the cylinder volume calculator. To compare against a box, use the volume calculator.
Frequently asked questions
What's the formula for sphere volume?
Volume equals four-thirds pi times the radius cubed: V = (4/3) × π × r³. Radius is half the diameter, so only one measurement, the diameter, is needed. A shortcut is V ≈ 0.5236 × d³.
Why does volume grow so fast as diameter increases?
Because radius is cubed. Doubling the diameter multiplies volume by 8, not 2. A 4 ft sphere holds 33.5 ft³ while an 8 ft sphere holds 268.1 ft³. Small measurement errors on a large sphere translate into big volume differences.
Where would I actually need a sphere's volume in construction?
Spherical water storage tanks, some propane and pressure vessels, and decorative spheres cast in concrete or carved from stone all need this calculation. It is less common than box or cylinder volume but shows up in tank and vessel sizing.
How do I measure the diameter of a large sphere accurately?
Measure straight across the widest point, through the center, not around the curve. If you can only measure the circumference, divide it by π (3.1416) to get the diameter. For a tank, the manufacturer's spec sheet usually lists the diameter directly.
Is a sphere ever used as a rough estimate for a rounded pile or mound?
Rarely. Piles sit on the ground and are closer to a cone or dome (hemisphere) than a full sphere. Use the Hemisphere Volume Calculator for a dome-shaped mound instead.
How does gallon capacity compare between a sphere and a same-diameter cylinder?
A sphere holds two-thirds of the volume of a cylinder with the same diameter and a height equal to that diameter. A 4 ft sphere holds 33.5 ft³, while a 4 ft by 4 ft cylinder holds 50.3 ft³.
Estimates only. Verify quantities with your supplier before purchasing.