Sphere Volume Calculator
Compute sphere volume from radius or diameter.
For balls, planets, water spheres, and balloon capacity.
With unit conversion to liters.
V = (4/3) × π × r³
The classic formula. Volume scales with the cube of the radius — double the radius and the sphere holds 8× as much.
Worked example — basketball volume: A regulation NBA basketball has a circumference of 29.5 in, so r = 29.5 / (2π) ≈ 4.696 in. V = (4/3) × π × 103.5 ≈ 433.6 cubic inches ≈ 7.10 liters of air at atmospheric pressure.
Worked example — water-balloon capacity: A standard 11-inch water balloon (when filled to 6-inch diameter): r = 3 in. V = (4/3) × π × 27 ≈ 113 in³ ≈ 1.96 US pints ≈ 0.93 liters of water. Most water-balloon launchers struggle past this size because the balloon weighs about 1 kg — enough that grip strength matters more than launcher tension.
Where sphere volumes show up:
- Sports balls. Soccer ball (22 cm dia, 5.6 L), tennis ball (6.5 cm dia, 144 cm³), golf ball (4.27 cm dia, 40.7 cm³), bowling ball (21.6 cm dia, 5.27 L).
- Planets. Earth has r ≈ 6,371 km, so V ≈ 1.08 × 10¹² km³ = 1.08 sextillion m³.
- Marbles and ball bearings. A standard 5/8" marble (r = 5/16") has V ≈ 0.128 in³. Steel ball bearings used in skateboard wheels (608 size) are 8 mm = 0.31 in dia, V ≈ 0.016 in³.
- Water tank capacity for spherical reservoirs. Some industrial liquid storage uses spherical tanks (typically 50,000-1,000,000 gal capacity).
- Christmas ornament volume. A 4" diameter glass ornament has V ≈ 33 cubic inches.
Why volume grows so fast with size:
Volume scales with r³. Here’s a feel for it:
| Radius | Volume |
|---|---|
| 1 cm | 4.19 cm³ |
| 2 cm | 33.5 cm³ (×8) |
| 5 cm | 524 cm³ (×125 from r=1) |
| 10 cm | 4,189 cm³ (×1,000) |
That’s why babies aren’t just “small adults” — they have much less heat-loss surface relative to body volume. Same reason elephants have skinny ears: less surface-to-volume for cooling. Geometry drives biology.
Comparing to other shapes:
A sphere of radius r holds (4/3)πr³ ≈ 4.19r³. A cube of side 2r (bounding the sphere) holds 8r³. Ratio: sphere fits about 52.4% of bounding cube. A cylinder of radius r and height 2r holds 2πr³ ≈ 6.28r³. Ratio: sphere fits exactly 2/3 of the cylinder (Archimedes’ result).
Sanity check:
- r = 0: V = 0. ✓
- r = 1 (unit sphere): V = 4π/3 ≈ 4.189. ✓
- Doubling r: V scales by 2³ = 8.
The sphere is the shape that maximises volume for a given surface area — soap bubbles and water droplets in zero gravity take this form because surface tension minimises surface area.