Volume Calculator

How to use Volume Calculator

1. Choose the shape.
2. Enter its dimensions — all in the same unit.
3. Read the volume and the formula applied.
4. All dimensions must use the same unit; the result is in that unit cubed.
5. 1 litre = 1,000 cm³, and 1 m³ = 1,000 litres.
6. A cone is one third of its cylinder; a sphere is two thirds of the cylinder that encloses it.

The relationships worth remembering instead of the formulas

A cone is exactly one third of the cylinder that contains it, and a pyramid is one third of its prism — the same factor, for the same reason. A sphere is two thirds of the cylinder it fits inside exactly, which Archimedes considered his finest result and had carved on his tomb. Knowing those three relationships means you can derive most of the formulas from the cylinder, and it gives you a sanity check: if your cone comes out bigger than a third of the cylinder, something is wrong.

Units are cubed, which is where the errors are

Volume scales with the cube of the length ratio. A metre is 100 centimetres, so a cubic metre is a million cubic centimetres, not a hundred. Double every dimension of a box and the volume increases eightfold. This catches people out constantly in aquarium capacities, concrete orders and shipping quotes — and it is the same trap as squared units for area, one power worse. Convert all dimensions to the same unit before calculating, never after.

Litres, cubic centimetres and the useful coincidence

One litre is exactly 1,000 cubic centimetres, and one cubic metre is exactly 1,000 litres. That makes tank and container arithmetic easy in metric: a box 20 × 30 × 40 cm is 24,000 cm³, so 24 litres. One cubic centimetre of water weighs almost exactly one gram, which is how the metric system was designed and why these conversions are clean rather than coincidental.

Real containers hold less than the maths says

Wall thickness, rounded internal corners, the fill line, and whatever is already inside all reduce usable capacity. An aquarium’s stated volume is typically its external dimensions, and the water it actually holds once gravel and the gap below the rim are accounted for is noticeably less — often 10–15%. Calculate from internal dimensions where you can, and leave headroom where you cannot.