Volume is area's three-dimensional sibling, and it turns up in all sorts of practical situations — filling a fish tank, ordering concrete, calculating how much soil a planter holds, or working out whether a storage unit is big enough for your furniture. The formulas vary by shape, but none of them are particularly frightening once you see them in context. Let's work through the key ones.
What Is Volume?
Volume is the amount of three-dimensional space that an object or container occupies. It's measured in cubic units — cubic centimetres (cm³), cubic metres (m³), or litres (1 litre = 1,000 cm³ = 0.001 m³). When you buy a 2-litre bottle of water, you're buying 2,000 cubic centimetres of liquid.
Our concrete calculator calculates the volume of concrete you need for slabs and foundations — one of the most practically useful applications of volume maths.
Cube and Cuboid (Box Shape)
Volume = Length × Width × Height
A room-sized storage box measuring 2m × 1.5m × 1m has a volume of 3 cubic metres (m³). If you're wondering whether a removal van is large enough for your furniture, add up the approximate volumes of your major items.
Real-world use: calculating the capacity of containers, rooms, raised garden beds, rectangular tanks. Our square footage calculator can help you establish the base area first.
Cylinder
Volume = π × r² × h
Where r is the radius of the circular end and h is the height (length) of the cylinder.
A cylindrical water butt with a diameter of 60cm and a height of 1m: radius = 0.3m, so Volume = 3.14159 × 0.09 × 1 = 0.283 m³ = 283 litres. Knowing your water butt capacity is useful for planning how long a single filling will last your garden.
Other uses: wine barrels, circular pillars, pipes, swimming pools (above-ground pools are often cylinders).
Sphere
Volume = (4/3) × π × r³
A sphere with a 20cm radius: Volume = (4/3) × 3.14159 × 8,000 = 33,510 cm³ ≈ 33.5 litres
Uses: calculating the volume of spherical tanks, decorative garden spheres, balls, or — more oddly — Earth (which is approximately a sphere of radius 6,371km, giving a volume of about 1.08 trillion km³).
Cone
Volume = (1/3) × π × r² × h
A traffic cone with a base radius of 15cm and height of 70cm: Volume = (1/3) × 3.14159 × 225 × 70 = 16,493 cm³ ≈ 16.5 litres. Useful for estimating soil or sand in conical piles, or calculating the capacity of funnel-shaped containers.
Pyramid
Volume = (1/3) × Base Area × Height
If the base is a rectangle 4m × 3m and the pyramid height is 5m: Volume = (1/3) × 12 × 5 = 20 m³. The "one third" factor is the same as for cones — both shapes taper to a point.
Converting Volume Units
- 1 m³ = 1,000 litres
- 1 litre = 1,000 millilitres (ml) = 1,000 cm³
- 1 m³ = 35.31 ft³
- 1 gallon (UK) = 4.546 litres
Practical Volume Calculations: Concrete
One of the most common real-world volume calculations is ordering ready-mix concrete for a slab. A patio that is 4m × 3m and 100mm (0.1m) deep requires:
4 × 3 × 0.1 = 1.2 m³ of concrete
Most suppliers sell by the cubic metre. Order slightly more than calculated (10% extra) to account for spillage and slight unevenness in the sub-base.
Irregular Volumes
For complex or irregular shapes, the technique is the same as for area: break the shape into simpler components, calculate each volume separately, and add them together. A swimming pool that has a shallow end and a deep end is essentially two cuboids of different depths.
Volume maths is beautifully practical. Once you can reliably calculate it for the common shapes, you'll be surprised how often it comes in handy.
Further reading: Khan Academy's geometry section covers volume calculations with interactive exercises. Practice volume calculations at Khan Academy.