Volume is how much space a solid holds: a box is length × width × height, a cylinder is π × radius² × height, and a sphere is 4/3 × π × radius³.
Volume measures how much space a solid takes up, or how much a container holds, and every common shape has its own formula. A box is length times width times height; a cylinder is the area of its circular end times its length; a sphere follows a slightly stranger rule involving four-thirds of pi. This guide gives you the volume formula for every shape you are likely to meet, with worked examples, plus the two things people most often get wrong: mixing units and confusing volume with capacity in litres. The CalcRange Volume Calculator does the arithmetic once you know which solid you are dealing with.
What Volume Is
Volume is three-dimensional space, which is why its units are always cubed. A cubic metre is a cube measuring one metre along each edge, and any solid filling that much space has a volume of one cubic metre whatever its shape.
The cubing matters when you scale. Doubling every dimension of a box multiplies its volume by eight, not two, because all three dimensions grew at once. That single fact explains why a slightly larger storage tank holds far more than it looks.
Volume Formulas for Every Solid
| Solid | Formula | Notes |
|---|---|---|
| Cube | s³ | s = edge length |
| Rectangular box | l × w × h | the everyday one |
| Cylinder | π × r² × h | circular end area times length |
| Sphere | (4/3) × π × r³ | r = radius |
| Cone | (1/3) × π × r² × h | exactly a third of a cylinder |
| Square pyramid | (1/3) × base area × h | a third of the matching box |
| Triangular prism | ½ × b × h × length | triangle area times length |
Two patterns make these easier to remember. Anything that comes to a point — a cone or a pyramid — is one third of the straight-sided shape that contains it. And anything prism-shaped — a cylinder, a box, a prism — is simply the area of its end multiplied by its length. That leaves only the sphere as a genuine one-off worth memorising.
The circle-based shapes all use the radius, which is half the diameter. Measuring across a pipe gives the diameter, so halve it before squaring.
Worked Examples
Rectangular tank
2 m long, 1.5 m wide, 1 m deep: 2 × 1.5 × 1 = 3 cubic metres.
Cylinder
A water pipe 0.1 m radius, 5 m long: π × 0.1² × 5 = 3.1416 × 0.01 × 5 = 0.157 cubic metres.
Sphere
A ball of 0.3 m radius: (4/3) × π × 0.3³ = 1.3333 × 3.1416 × 0.027 = 0.113 cubic metres.
Cone
A pile of sand 1 m high with a 1.5 m base radius: (1/3) × π × 1.5² × 1 = 0.3333 × 3.1416 × 2.25 = 2.36 cubic metres.
Calculate a Volume
Choose your solid, enter the dimensions, and the CalcRange Volume Calculator returns the answer. For flat surfaces you need the area calculator instead, and for concrete pours our concrete quantity guide takes volume the last step to bags of cement.
Volume Versus Capacity in Litres
Volume in cubic metres and capacity in litres describe the same thing in different units, and the conversion is worth committing to memory.
1 cubic metre = 1,000 litres
1 litre = 1,000 cubic centimetres
The rectangular tank above holds 3 cubic metres, which is 3,000 litres. The cylinder holds 0.157 cubic metres, or 157 litres. This is the step people skip when sizing a water tank or an aquarium: they calculate a tidy volume in metres and forget to convert, then wonder why the numbers feel wrong.
A useful shortcut for tanks measured in centimetres: multiply length by width by height in centimetres, then divide by 1,000 to get litres directly.
Irregular Solids
Some shapes have no formula, and there are two honest ways around that.
Break it up. An L-shaped or stepped solid splits into boxes and prisms you can calculate separately and add. This handles most real-world objects, from oddly shaped rooms to machine parts.
Displace water. For a genuinely irregular object that fits in a container, submerge it and measure how much the water level rises. The rise, converted to litres, is the object’s volume. This is the method attributed to Archimedes, and it remains the simplest way to measure something no formula describes.
Common Mistakes
- Mixing units. Convert everything to the same unit before multiplying, never metres in one dimension and centimetres in another.
- Using diameter instead of radius in any circle-based formula, which inflates the result fourfold for a cylinder.
- Forgetting to convert cubic metres to litres when sizing a container.
- Dropping the one-third on cones and pyramids, which triples the answer.
- Cubing wrongly when scaling. A tank twice the size in every direction holds eight times as much.
Frequently Asked Questions
What is the formula for the volume of a cylinder?
Pi times the radius squared times the height, which is the area of the circular end multiplied by the length. For a pipe with a 0.1 m radius and 5 m length, that is 3.1416 times 0.01 times 5, or about 0.157 cubic metres.
How do I convert cubic metres to litres?
Multiply by 1,000, since one cubic metre holds exactly 1,000 litres. A 3 cubic metre tank therefore holds 3,000 litres. For containers measured in centimetres, multiply the three dimensions and divide by 1,000 to reach litres directly.
What is the volume of a sphere?
Four-thirds times pi times the radius cubed. It is the one common formula without an intuitive shortcut, so it is worth memorising. A sphere of 0.3 m radius holds about 0.113 cubic metres.
Why is a cone a third of a cylinder?
Because a cone with the same base and height as a cylinder fills exactly one third of it, a result from geometry. The same one-third relationship holds between any pyramid and the prism that shares its base and height.
How do I find the volume of an irregular object?
Either split it into regular solids, calculate each, and add, or submerge it in water and measure how far the level rises. The water displacement method works for any shape that fits in a container and needs no formula at all.
What is the difference between volume and capacity?
They measure the same quantity of space. Volume usually refers to how much a solid occupies and is quoted in cubic units, while capacity refers to how much a container holds and is quoted in litres or gallons. One cubic metre of volume equals 1,000 litres of capacity.
How do I calculate the volume of a tank in gallons?
Work out the volume in cubic metres or litres first, then convert. One cubic metre is about 264 US gallons or 220 imperial gallons, and one litre is about 0.264 US gallons. Always confirm which gallon a source means, since the two differ by roughly a fifth.
The Bottom Line
Most volumes come down to two ideas: a prism is its end area times its length, and a pointed shape is a third of the solid around it, leaving only the sphere to memorise on its own. Keep every dimension in the same unit, use the radius rather than the diameter, and remember that a cubic metre is a thousand litres when you are filling a tank. For irregular objects, split them up or displace water. Run your dimensions through the volume calculator, and convert to litres before you trust the number for anything you plan to fill.
Last reviewed: August 2026. Evergreen content — recommended editorial review: every 12 months.