Sphere Volume Calculator

Volume of a sphere is V = (4/3) × π × r³. The cube on the radius is what makes sphere volume grow so dramatically with size — double the radius and the volume increases by a factor of 8 (2³). Triple the radius and volume goes up 27×. This is why a small change in a planet's radius corresponds to an enormous change in mass and gravity, and why bagged ice melts so much faster as cube size drops.

Surface area follows A = 4 × π × r² — exactly four times the area of a great-circle cross-section. The ratio of surface area to volume is 3/r, which falls as the sphere grows. That ratio is the reason small mammals have to eat more relative to their body weight to stay warm and why building heat-loss is dominated by surface area.

An NBA basketball has a diameter of 9.55 in (24.26 cm), so the radius is 4.775 in. V = (4/3) × π × 4.775³ ≈ 456 in³ ≈ 7.47 liters. That is the volume of air at rest inside the ball. At the regulation inflation of 7.5–8.5 psi above atmospheric, the air mass inside is about 9 grams — meaningful because a deflated ball that gains a gram in a humid arena measurably changes its bounce.

A spherical hot-water tank with an inside radius of 18 inches holds (4/3) × π × 18³ ≈ 24,429 in³, which is 105.8 US gallons. That capacity per square foot of surface area is why spherical tanks are favored for industrial cryogenics: less surface means less heat transfer. Most home water heaters are cylindrical only because cylinders are easier to manufacture and stack — they pay an efficiency penalty for that convenience.

Confusing radius and diameter. Always halve the diameter before plugging into the formula. Failing to do so makes the volume eight times too large.

Mixing units. Cubing magnifies unit errors. If you measured the radius in inches but plug into a meters-based formula somewhere downstream, your volume will be off by a factor of 16,387 (1 m³ = 61,024 in³).

Ignoring wall thickness. The formulas above apply to the inner surface only. For a tank or container with significant wall thickness, decide whether you need internal capacity (use inner radius) or material volume (compute the difference between outer and inner sphere volumes).

Assuming a sphere is the most efficient shape for storage of a non-fluid. For solids, cylinders pack more efficiently and avoid wasted corner space.