Sphere Volume Calculator

V = (4/3) × π × r³

The classic formula. Volume scales with the cube of the radius, so doubling the radius makes the sphere hold 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 water balloon filled out to a 6-inch diameter, so r = 3 in. V = (4/3) × π × 27 ≈ 113 in³. One cubic inch is 16.39 cm³, so that is about 1.85 liters, near enough 3.9 US pints.

Water weighs a kilogram per liter, so the filled balloon is 1.85 kg, a bit over four pounds. That is the real limit on a water-balloon launcher: the pouch and your grip give out long before the tubing does, which is why the fun sizes top out around a 5-inch fill.

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. Watch the naming trap on bearings: the 608 in a skateboard wheel is an 8 mm bore, not an 8 mm ball. The balls inside are closer to 4 mm, and each one holds about 0.002 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:

That is why babies are not just small adults. Volume falls away faster than surface does, so a newborn carries far more skin per kilogram than you do and sheds heat through it much faster. It is also why an elephant has those enormous ears: a big animal has too little surface to dump heat through, so it grows extra surface on purpose. Geometry drives biology in both directions.

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 holds the most volume for a given surface area. Soap bubbles and water droplets in free fall take this form because surface tension is pulling the film to the smallest area that can still contain what is inside.