sphere volume calculator
Calculate a sphere's volume in cubic feet, cubic yards, gallons, and liters from diameter alone — for spherical tanks and storage vessels.
A sphere’s volume matters when you’re sizing a spherical tank, pressure vessel, or decorative concrete or stone ball. Enter the diameter and get volume in cubic feet, cubic yards, gallons, and liters.
How this calculator works
Sphere volume is four-thirds pi times the radius cubed. Radius is half the diameter.
Formula: Cubic feet = (4/3) × π × (diameter ÷ 2)³. Cubic yards = ft³ ÷ 27. Gallons = ft³ × 7.48052. Liters = ft³ × 28.3168.
Worked example
A sphere 4 ft in diameter:
- 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: 33.51 × 28.3168 ≈ 948.9 L
Reference
| Diameter (ft) | Cubic feet |
|---|---|
| 2 | 4.19 ft³ |
| 4 | 33.51 ft³ |
| 6 | 113.10 ft³ |
How to measure
Measure the diameter straight through the center of the sphere, at its widest point. This applies to spherical storage tanks, pressure vessels, and cast concrete or stone spheres used as decorative elements. For half a sphere — a dome shape sitting flat-side-down — use the Hemisphere Volume Calculator instead.
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 — diameter — is needed.
Why does volume grow so fast as diameter increases?
Because radius is cubed, doubling the diameter multiplies volume by 8, not 2. A sphere twice as wide holds eight times as much, which is why 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 (concrete or stone) all need this calculation. It's 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. For a tank, the manufacturer's spec sheet usually lists this 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) shape 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 less than a cylinder of the same diameter and height equal to that diameter — a sphere is two-thirds the volume of its bounding cylinder. Check the Cylinder Volume Calculator to compare directly.
Estimates only. Verify quantities with your supplier before purchasing.