How to Calculate Volume: Tanks, Pools and Shipping Boxes

Volume questions rarely fail at the formula. They fail at the units, or at the moment somebody measures a cylinder's diameter and uses it as the radius. Both mistakes are quiet, and both produce a plausible looking answer.

The three shapes that cover most jobs

A rectangular box is length times width times height. A 4 m by 2 m garden pool filled to 1.2 m is 4 times 2 times 1.2, which is 9.6 cubic metres. A shipping box at 24 by 18 by 12 inches is 5,184 cubic inches, which divided by 1,728 gives exactly 3 cubic feet.

A cylinder is the circle area times the height: pi times radius squared times height. A water butt with a radius of 0.5 m standing 1.5 m tall holds 3.1416 times 0.25 times 1.5, which is 1.18 cubic metres. A sphere is four thirds pi r cubed.

Cylinders trip people up

Radius is squared, so it dominates. Keep the water butt at 1.5 m tall but widen the radius from 0.5 m to 1.0 m and the volume goes from 1.18 to 4.71 cubic metres. Doubling the width quadrupled the capacity. Doubling the height would only have doubled it.

This is also why entering diameter instead of radius is so destructive. A tank measured at 1 m across, entered as a 1 m radius, comes out four times too big. If the answer feels generous, check that first.

Getting the units right

Cubic units scale by the cube of the linear factor, which nobody's intuition handles well. There are 100 cm in a metre, so there are 1,000,000 cubic centimetres in a cubic metre, not 10,000. A cubic foot is 1,728 cubic inches because 12 cubed is 1,728.

The conversions worth memorising

One cubic metre is 1,000 litres. One litre is 1,000 cubic centimetres. One cubic foot is about 28.3 litres, or 7.48 US gallons. So that 9.6 cubic metre pool is 9,600 litres, or about 2,536 US gallons.

The other rule is to convert before you multiply, never after. Measure the pool as 4 m by 2 m by 120 cm, multiply as it stands, and you get 960 rather than 9.6. Turn the 120 cm into 1.2 m first and the problem disappears.

Weight is often the real question, and that needs density. Water is a convenient 1 kg per litre, so 9,600 litres is 9.6 tonnes sitting on your patio. Other materials need a lookup, which our note on calculating density works through.

Using the volume calculator

Pick the shape first, because the input boxes change with it. Then set the unit before you type anything. Fields left on metres while you enter centimetres give a number a million times too large with no warning.

For a tank or pool, measure the internal dimensions. A pool with 150 mm walls loses 300 mm across each direction, so a 4 m by 2 m shell measures 3.7 m by 1.7 m inside. At 1.2 m deep that is 7.5 cubic metres rather than 9.6, so more than a fifth of the water you were expecting has vanished into the walls. For a cylinder, measure the diameter and halve it rather than guessing the centre.

Irregular shapes get broken into pieces. An L shaped room is two rectangles added together, and a tank with a domed top is a cylinder plus half a sphere. The area calculator guide covers splitting awkward footprints into shapes you can actually measure.

Common questions

How many litres are in my fish tank? Measure the internal length, width and water depth in centimetres, multiply, then divide by 1,000. A 90 by 45 cm tank filled to 40 cm depth gives 162,000 cubic centimetres, so 162 litres. Do not use the full height unless you fill to the rim.

How do I find the volume of an odd shape? Displacement, if it fits in water. Note the level in a measuring jug, drop the object in, note the new level, and the difference is the volume. It beats any attempt to approximate a garden gnome as a cylinder.

Is a cubic metre the same as a tonne? Only for water. A cubic metre of dry sand is nearer 1.6 tonnes, and a cubic metre of polystyrene weighs almost nothing. Volume and mass need a density figure between them.

Why does the builder's quote use different numbers? Trades quote in loose volume, allowing for waste and compaction. Concrete and aggregate are usually ordered with 5 to 10 per cent on top of the calculated figure.