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.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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