Sphere Volume Calculator
V = (4/3)πr³. Surface area = 4πr².
Result
General calculation reads
Amazon affiliateAs an Amazon Associate we may earn from qualifying purchases. This does not add cost for you.
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 · r³The 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.
Worked examples
- Inputs:
- r = 3.4 cm
- Output:
- V = (4/3)π(3.4)³ ≈ 164.6 cm³
- Inputs:
- r = 6,371 km
- Output:
- V ≈ 1.083 × 10¹² km³ — matches NASA's published value within 0.1%
- 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.
Frequently asked
Why (4/3) for the constant?+
Why are bubbles spherical?+
Sphere vs. ball?+
Hemisphere?+
Earth as sphere?+
Related calculators
More tools you might like
Hand-picked tools that pair well with this one — same audience, same intent.
V = πr²h. Surface area = 2πr² + 2πrh (top + bottom + side).
V = s³. Six equal square faces.
V = l × w × h. Box / cuboid volume.
V = (1/3)πr²h. One-third of the cylinder of same base and height.
C = 2πr (or πd). Area = πr². The fundamental circle formulas.
Estimate body surface area in m² using Mosteller and Du Bois formulas — for clinical reference, anesthesia dosing, and physiologic indexing.