Sphere & Hollow Spherical Shell Volume Calculator
Archimedes' sphere volume theorem establishes that the volume V enclosed by a sphere of outer radius R (and optional hollow inner radius r) equals V = (4/3) × π × (R³ - r³).
Enclosed three-dimensional volume
Exterior radius from center to surface
Set to 0 for a solid sphere, or inner radius for a spherical tank shell
Step-by-Step Calculation
Archimedes' sphere volume theorem establishes that the volume V enclosed by a sphere of outer radius R (and optional hollow inner radius r) equals V = (4/3) × π × (R³ - r³).
Real-World Reference Values
Occupies exactly 2/3 of its circumscribed cylinder
Radial derivative dV/dR equals surface area 4πR²
Ideal geometry for LNG & high-pressure Horton spheres
20-Row Comparison Table
Sphere / Shell Volume (V) · Outer Sphere Radius (R)
| # | Outer Sphere Radius (m) | Sphere / Shell Volume (m³) | Δ % |
|---|---|---|---|
| 01 | 0.01 m | 4.1888e-6 m³ | -100.00% |
| 02 | 5 mCurrent | 523.5988 m³ | 0.00% |
| 03 | 15.0088 m | 14,162.07 m³ | +2604.76% |
| 04 | 22.5082 m | 47,765.15 m³ | +9022.47% |
| 05 | 30.0076 m | 113,183.37 m³ | +21516.43% |
| 06 | 37.507 m | 221,017.07 m³ | +42111.15% |
| 07 | 45.0064 m | 381,866.59 m³ | +72831.15% |
| 08 | 52.5058 m | 606,332.26 m³ | +115700.93% |
| 09 | 60.0052 m | 905,014.42 m³ | +172745.02% |
| 10 | 67.5046 m | 1,288,513.41 m³ | +245987.93% |
| 11 | 75.004 m | 1,767,429.56 m³ | +337454.18% |
| 12 | 82.5034 m | 2,352,363.20 m³ | +449168.28% |
| 13 | 90.0028 m | 3,053,914.68 m³ | +583154.74% |
| 14 | 97.5022 m | 3,882,684.33 m³ | +741438.08% |
| 15 | 105.0016 m | 4,849,272.49 m³ | +926042.82% |
| 16 | 112.501 m | 5,964,279.49 m³ | +1138993.47% |
| 17 | 120.0004 m | 7,238,305.67 m³ | +1382314.55% |
| 18 | 127.4998 m | 8,681,951.36 m³ | +1658030.57% |
| 19 | 134.9992 m | 10,305,816.91 m³ | +1968166.04% |
| 20 | 142.4986 m | 12,120,502.64 m³ | +2314745.49% |
Frequently Asked Questions
How do I calculate the radius of a solid sphere from its volume?+
Keep Inner Radius r = 0, click SOLVE FOR on R, and enter your volume V to evaluate R = ∛(3V / 4π).
How do I find the metal volume of a hollow spherical pressure vessel?+
Enter the outside radius as R and inside radius as r; the solved volume V is the exact shell wall material volume.
Why does doubling a sphere's radius increase its volume by 8×?+
Volume scales with the third power of linear dimension (2³ = 8), while surface area scales with the second power (2² = 4).