Sphere Volume Calculator

V = (4/3)πr³. Surface area = 4πr².

Result

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How to use this calculator

Enter radius.
Read volume + surface area.

About this calculator

A sphere is the most symmetric 3D shape. Volume V = (4/3)πr³; surface area = 4πr². Doubling the radius multiplies volume by 8 and surface area by 4. Of all closed surfaces enclosing a given volume, the sphere has the smallest surface area — why bubbles, droplets, and stars are spherical. Earth's radius ≈ 6371 km; volume ≈ 1.083 × 10¹² km³.

How it works — the formula

V = (4/3) · π · r³

The volume of a sphere is four-thirds π times the cube of its radius. Archimedes proved this ratio in On the Sphere and Cylinder (~225 BC) by showing the sphere fills two-thirds of its circumscribing cylinder. The modern derivation integrates the area of circular cross-sections, A(z) = π(r² − z²), from −r to r — yielding (4/3)πr³.

Sources: NIST DLMF §1.10 — Pi and elementary constants · Wolfram MathWorld — Sphere volume · NASA — planetary volume reference (uses 4/3·π·r³ throughout fact sheets)

Worked examples

Example 1

Tennis ball

Inputs:: r = 3.4 cm
Output:: V = (4/3)π(3.4)³ ≈ 164.6 cm³

Example 2

Earth approximation

Inputs:: r = 6,371 km
Output:: V ≈ 1.083 × 10¹² km³ — matches NASA's published value within 0.1%

Example 3

Doubling the radius

Inputs:: r = 1 → r = 2
Output:: Volume scales by 2³ = 8× (volume scales with the cube of linear size)

Limitations

Formula assumes a perfect sphere — real objects are oblate spheroids or irregular and need surface integrals or 3D meshes.
For very small radii, accuracy is bounded by double-precision; for radii beyond ~10⁹ km, IEEE 754 limits show.
A "displacement volume" (water-displacement test) and a "geometric volume" can differ for porous or hollow objects.
Sphere caps and segments use distinct formulas — see related calculators for partial-sphere geometries.

Volume is exact arithmetic within floating-point precision; rounding shown is cosmetic.