Compute the volume of eleven common solids — sphere, cone, cube, cylinder, rectangular tank, capsule, spherical cap, conical frustum, ellipsoid, square pyramid, and tube. Lengths can be miles, yards, feet, inches, or metric units down to ångströms. Mixed units produce a cubic result in each unit you used.
Common cubic units
Factors use the international foot (1 ft = 0.3048 m exactly), consistent with NIST conversion tables.
| Unit | Cubic metres |
|---|---|
| 1 cubic inch | 0.000016387064 m³ |
| 1 cubic foot | 0.028316846592 m³ |
| 1 cubic yard | 0.764554857984 m³ |
| 1 cubic metre | 1 m³ |
| 1 litre | 0.001 m³ |
Examples
Sphere of radius 3 ft
Volume is (4/3) π × 27 = 36π = 113.09733552923 ft³. The same formula with radius 1 m is 4.1887902047864 m³.
Cone with mixed units
Radius 12 in and height 1 ft. In inches both dimensions are 12, so the volume is 1809.5573684677 in³. In feet both are 1, so it is also 1.0471975511966 ft³.
Cube, tank, and pyramid
A 2 ft cube is 2³ = 8 ft³. A 2 × 3 × 4 ft tank is 24 ft³. A square pyramid with base edge 5 ft and height 12 ft is 100 ft³.
Spherical cap from r and R
Base radius 3 ft and ball radius 5 ft give heights 1 ft and 9 ft, so two volumes: 14.660765716752 ft³ and 508.93800988155 ft³. From r = 3 ft and h = 4 ft the ball radius is 3.125 ft and the volume is 90.058989402907 ft³.
Tube of concrete
Outer diameter 3 ft, inner diameter 2.5 ft, length 10 ft is (9 − 6.25) × 10 / 4 = 6.875π = 21.59844949343 ft³.
Formula
Each length is converted into a common unit, the shape formula is applied, and the volume is printed to 14 significant digits. Zero dimensions are allowed and give zero volume; empty or negative values are rejected.
sphere V = (4/3) π r³
cone V = (1/3) π r² h
cube V = a³
cylinder V = π r² h
rectangular tank V = l × w × h
capsule V = (4/3) π r³ + π r² h
spherical cap V = (1/3) π h² (3R − h)
conical frustum V = (1/3) π h (r² + rR + R²)
ellipsoid V = (4/3) π a b c
square pyramid V = (1/3) a² h
tube V = π (d1² − d2²) l / 4
Spherical-cap conversions when two of the three values are known:
r and R: h = R ± √(R² − r²)
r and h: R = (h² + r²) / (2h)
R and h: r = √(2 R h − h²)
What this result does not include
The result is ideal geometric volume from the dimensions entered. Real tanks can have rounded corners, wall thickness, fittings, headspace, or stated usable capacity that differs from outside geometry. Excavation and material purchases also need separate allowances for compaction, spillage, uneven surfaces, and supplier package sizes. Use measured internal dimensions for capacity and the appropriate material calculator for an order estimate.
For a related calculation, use our density calculator.
Measure packed cargo
For repeated cartons or several package sizes, use the CBM Calculator. It totals external package volumes and compares gross with dimensional weight using your chosen divisor. Space estimates remain volume-based and do not guarantee a container fit.