About

Miscalculating sphere volume propagates errors through every downstream engineering step: material cost estimates, fluid capacity, buoyancy analysis, and thermal calculations all depend on an accurate V. The formula V = 43πr³ is cubic in radius, meaning a 2% measurement error in r compounds to roughly 6% error in volume. This tool calculates volume, surface area, diameter, and great-circle circumference from a single radius input across six unit systems. It uses native 15-digit IEEE 754 precision for π and applies exact conversion factors between metric and imperial units.

This calculator assumes a geometrically perfect sphere. Real objects deviate from true sphericity. For critical applications (pressure vessels, optical lenses), measure effective radius at multiple points and average. The tool does not account for wall thickness. If computing internal volume of a hollow sphere, subtract the inner sphere volume from the outer.

Formulas

The volume of a sphere is derived by integrating the area of infinitesimally thin circular cross-sections (disks) along the diameter. The primary formula relates volume to the cube of the radius:

V = 43 π r³

The surface area of a sphere is exactly four times the area of its great circle:

A = 4 π r²

The diameter and great-circle circumference follow directly from the radius:

d = 2r C = 2πr

Where V = volume, A = surface area, d = diameter, C = circumference (great circle), r = radius, and π ≈ 3.141592653589793. Because volume scales with r³, the sensitivity of volume to radius error is dVV = 3 drr, meaning a 1% error in radius produces approximately 3% error in volume.

Reference Data

Radius	Diameter	Volume	Surface Area	Circumference	Common Object
1.1 cm	2.2 cm	5.575 cm³	15.205 cm²	6.912 cm	Marble
2.0 cm	4.0 cm	33.510 cm³	50.265 cm²	12.566 cm	Golf ball
3.5 cm	7.0 cm	179.594 cm³	153.938 cm²	21.991 cm	Tennis ball
3.81 cm	7.62 cm	231.847 cm³	182.415 cm²	23.939 cm	Billiard ball
5.0 cm	10.0 cm	523.599 cm³	314.159 cm²	31.416 cm	Softball
11.0 cm	22.0 cm	5,575.28 cm³	1,520.53 cm²	69.115 cm	Soccer ball
12.0 cm	24.0 cm	7,238.23 cm³	1,809.56 cm²	75.398 cm	Basketball
15.0 cm	30.0 cm	14,137.17 cm³	2,827.43 cm²	94.248 cm	Bowling ball
0.5 m	1.0 m	0.5236 m³	3.1416 m²	3.1416 m	Exercise ball
1.0 m	2.0 m	4.1888 m³	12.5664 m²	6.2832 m	Weather balloon
5.0 m	10.0 m	523.599 m³	314.159 m²	31.416 m	Small storage tank
6,371 km	12,742 km	1.083 × 10¹² km³	5.101 × 10⁸ km²	40,030 km	Earth (mean)
1,737 km	3,474 km	2.197 × 10¹⁰ km³	3.793 × 10⁷ km²	10,917 km	Moon (mean)
69,911 km	139,822 km	1.431 × 10¹⁵ km³	6.142 × 10¹⁰ km²	439,264 km	Jupiter (mean)

Frequently Asked Questions

Volume scales as r³, so relative error is amplified threefold. A 1% error in radius produces approximately 3% error in volume. For a sphere of radius 10 cm measured as 10.1 cm, the volume error is about 12.6 cm³ out of 4,188.79 cm³. Always use calipers or micrometers for precision-critical work.

Yes. This calculator accepts radius directly, but you can divide your diameter measurement by 2 before entering it. The relationship is r = d2. Substituting into the volume formula gives V = π6d³.

The calculator uses JavaScript's native Math.PI constant, which provides 15 significant digits: 3.141592653589793. This is IEEE 754 double-precision, sufficient for all practical engineering and scientific applications. Errors from floating-point representation are below 1 part in 10¹⁵.

Compute the volume of the outer sphere using the outer radius R, then subtract the volume of the inner sphere using the inner radius r: V_shell = 43π(R³ − r³). Run this calculator twice with each radius and subtract the results.

No. The formula V = 43πr³ applies only to perfect spheres where all three semi-axes are equal. For an ellipsoid with semi-axes a, b, c, use V = 43πabc. Earth, for instance, is an oblate spheroid with equatorial radius 6,378 km and polar radius 6,357 km.

This calculator uses exact conversion factors defined by international standards. For example, 1 in = 25.4 mm exactly (by definition since 1959). Converting between metric units (mm, cm, m) uses powers of 10, which are exact. No rounding is introduced during conversion. Results are displayed to 6 significant figures.