How to Calculate Volume: Box, Cylinder, Sphere and Cone (and Convert to Litres)
Volume questions usually come up for a practical reason: how much water a tank holds, how much soil to order for a garden bed, whether a box will fit in the car. The maths is simple once you know which formula matches the shape, and most mistakes come from units rather than from the formula itself.
The four shapes that cover most real objects
Box (rectangular prism): length × width × height. Rooms, fish tanks, planters, shipping boxes and concrete slabs are all boxes.
Cylinder: π × r² × h, where r is the radius (half the diameter) and h is the height. Water tanks, pipes, cans and round planters.
Sphere: (4 ÷ 3) × π × r³. Balls, globe lights, spherical tanks.
Cone: (1 ÷ 3) × π × r² × h. Funnels, piles of sand or gravel, ice cream cones.
A useful check: a cone holds exactly one third of a cylinder with the same base and height. If your cone answer is not a third of the cylinder answer, something has gone wrong.
Worked example: a fish tank
A tank is 36 × 18 × 18 inches. Its volume is 36 × 18 × 18 = 11,664 cubic inches.
A US gallon is 231 cubic inches, so the tank holds 11,664 ÷ 231 = 50.5 US gallons, or about 191 litres. In practice you will fill it a little short of the rim and gravel takes up space, so the real water volume will be somewhat lower.
Worked example: a round water tank
A cylindrical tank is 1 metre across and 1.5 metres tall. The radius is 0.5 m, so the volume is:
π × 0.5² × 1.5 = 1.18 cubic metres
One cubic metre is 1,000 litres, so the tank holds about 1,178 litres, or roughly 311 US gallons.
The most common mistake here is using the diameter instead of the radius. That multiplies the answer by four, which would make this tank look like it holds about 4,700 litres.
Worked example: soil for a raised bed
A raised bed is 2.4 m long, 1.2 m wide and 0.3 m deep: 2.4 × 1.2 × 0.3 = 0.864 cubic metres, which is 864 litres or about 30.5 cubic feet.
Bagged compost is sold in litres, so that is roughly eleven 80-litre bags. Soil settles once watered, so add around 10% to the order.
Keep every measurement in the same unit
Mixing units is where most volume answers go wrong. If the length is in metres and the depth in centimetres, convert first: 30 cm is 0.3 m. Multiplying 2.4 × 1.2 × 30 gives 86.4, which is wrong by a factor of 100.
Conversions worth remembering:
- 1 cubic metre = 1,000 litres = 35.3 cubic feet = 264.2 US gallons
- 1 litre = 1,000 cubic centimetres
- 1 cubic foot = 28.3 litres = 7.48 US gallons
- 1 US gallon = 231 cubic inches = 3.785 litres
- 1 UK (imperial) gallon = 4.546 litres, which is larger than a US gallon
Odd shapes: split them up
An L-shaped planter is two boxes. A tank with a domed top is a cylinder plus half a sphere. Work out each piece and add them together. For a pile of gravel, a cone is a reasonable model: measure the width at the base and the height at the peak.
Do it in one step
The volume calculator handles all four shapes and gives the answer in litres, US gallons and cubic feet at once. For slabs and footings, the concrete calculator adds the waste allowance, and the volume converter switches between any two units.