Volume calculator

Cubic metres, litres and centimetres

Volume units differ by a factor of 1000, not 10 or 100, because length is multiplied three times. 1 m = 10 dm, so 1 m³ = 10 × 10 × 10 = 1000 dm³. And since 1 dm³ is exactly 1 litre, one cubic metre holds 1000 litres.

The calculator works in whatever unit you enter. Type an aquarium's size in centimetres, 100 × 40 × 50, and you get 200,000, which is cm³. Divide by 1000 for 200 litres. For small objects it is convenient to measure in decimetres, because the answer is then directly in litres.

• 1 m³ = 1000 dm³ = 1000 l
• 1 dm³ = 1 l = 1000 cm³
• 1 cm³ = 1 ml
• 1 m³ = 1,000,000 cm³

Raised garden bed: how many bags of soil?

A raised bed is a box. A frame 2 m long, 1 m wide and 30 cm high: 2 × 1 × 0.3 = 0.6 m³, or 600 litres. With 50 l bags of soil you need 600 ÷ 50 = 12 bags. Loose soil settles after watering, so a couple of extra bags save a second trip later.

Make sure the 30 cm goes in as metres (0.3), not 30. Otherwise you get 60 m³, a hundred times too much. The calculator's surface area of 5.8 m² includes the bottom and the top of the box (2 m² each). The correct area for the side boards is 2 × (2 × 0.3 + 1 × 0.3) = 1.8 m².

Concrete for a foundation and post holes

A 6 × 8 m slab foundation 15 cm thick: 6 × 8 × 0.15 = 7.2 m³. For a strip foundation take the length along the centre line, for example 28 m, and multiply by the cross-section: 28 × 0.4 × 0.8 = 8.96 m³. Using the centre line avoids counting the corners twice, which happens when you add up the outside wall lengths.

Fence post holes are cylinders. A hole 30 cm across and 1 m deep: radius 0.15 m, volume π × 0.15² × 1 ≈ 0.0707 m³, about 71 litres. Ten holes need ≈ 0.71 m³ of concrete. Concrete is ordered in cubic metres, so convert everything before you call the supplier.

Cylinders, cones and spheres in practice

A rain barrel with a 30 cm radius and 90 cm height: π × 0.3² × 0.9 ≈ 0.2545 m³, about 254 litres. A sand pile is roughly a cone: a 1.5 m base radius and 1 m height give (1/3) × π × 2.25 × 1 ≈ 2.36 m³. A cone holds exactly one third of a cylinder with the same base and height.

A school cone problem: r = 3, h = 4. Volume (1/3) × π × 9 × 4 = 12π ≈ 37.70. The slant height by Pythagoras is √(9 + 16) = 5 and the total surface π × 3 × (3 + 5) = 24π ≈ 75.40.

A football with an 11 cm radius would show only 0.0056 m³ in metres, because the calculator rounds to four decimals. Enter the radius in decimetres (1.1) and you get 5.5753 dm³, or ≈ 5.58 litres.

Why a small measuring error makes a big difference

In a sphere's volume the radius is cubed. Double the radius and the volume grows 2³ = 8 times. In a cylinder the radius is squared: doubling it quadruples the volume, while doubling the height only doubles it. So measure the radius or diameter with extra care.

Note that the cylinder and cone fields take the radius. Measure a barrel's diameter of 60 cm and enter it as the radius, and the result is four times too big. The calculator's cylinder surface includes both ends; for an open barrel subtract the lid area π × r².