This volume calculator computes the capacity of seven common 3D solids — a box, cube, sphere, cylinder, cone, square pyramid and ellipsoid. Pick a shape, type its dimensions, and the volume appears instantly using the correct geometric formula. It is handy for everything from sizing a tank or aquarium to checking homework.
How it works
Each solid uses its standard formula, with the result given in cubic units:
| Solid | Formula |
|---|---|
| Box (rectangular prism) | length × width × height |
| Cube | side³ |
| Sphere | (4/3) × π × radius³ |
| Cylinder | π × radius² × height |
| Cone | (1/3) × π × radius² × height |
| Square pyramid | (1/3) × base-edge² × height |
| Ellipsoid | (4/3) × π × a × b × c |
The calculator is unit-agnostic: enter every dimension in the same unit and the volume comes back in that unit cubed.
Worked examples
Cylinder with radius 3 and height 10:
V = π × 3² × 10 = π × 90 ≈ 282.74 cubic units.
If those measurements are in centimetres, that is about 282.7 cm³ (≈ 0.28 litres). Change to a cone with the same radius and height and the volume drops to a third: (1/3) × π × 9 × 10 ≈ 94.25 cm³ — this is why cone-shaped paper cups hold so much less than cylindrical mugs of the same height.
Sphere with radius 5 cm:
V = (4/3) × π × 5³ = (4/3) × π × 125 ≈ 523.6 cm³
That is just over half a litre. A basketball has a radius of roughly 12 cm, giving a volume of about 7,238 cm³ ≈ 7.2 litres.
Rectangular box 40 cm × 20 cm × 15 cm (for example, an aquarium):
V = 40 × 20 × 15 = 12,000 cm³ = 12 litres
Practical unit conversions
- cm³ to litres: divide by 1,000 (1 litre = 1,000 cm³)
- cm³ to US gallons: divide by 3,785
- m³ to litres: multiply by 1,000
- in³ to US gallons: divide by 231
To convert correctly, first make sure all three dimensions are in the same unit before plugging them in. Mixing centimetres and metres in one calculation is the most common error.
When to use each solid
- Use box for tanks, crates, room air volume, or rectangular containers.
- Use cylinder for pipes, fuel tanks, round columns, and mugs.
- Use sphere for ball tanks, globes, and hemispherical domes (halve the result).
- Use cone for funnels, hoppers, and ice-cream cones.
- Use ellipsoid for egg shapes, submarines, and oblate spheroids like an M&M sweet.
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