About the Volume Calculator
Volume is how much space something occupies, or how much it can hold. It is the number behind every question about capacity: how many litres a tank takes, how much concrete to order, whether a box will fit what you want to put in it.
This page carries eight solids — box, cube, sphere, hemisphere, cylinder, cone, square pyramid and triangular prism. Eight formulas, which sounds like a lot to learn, except that they come down to two ideas.
Idea one: constant cross-section. If a solid is the same shape all the way along, its volume is that cross-section times its length. A box is a rectangle extruded. A cylinder is a circle extruded. A prism is a triangle extruded. Same rule, three shapes.
Idea two: tapering to a point. If a solid narrows to a single point, it holds exactly one third of the straight-sided solid on the same base and height. A cone is a third of its cylinder. A pyramid is a third of its box. Any pointed solid, any base shape — always a third.
That leaves only the sphere outside both patterns, and Archimedes handled that one: it is two thirds of the cylinder that just contains it.
How to Use the Volume Calculator
Choose the solid, enter its dimensions, press Calculate.
All measurements must share a unit. Centimetres in gives cubic centimetres out; metres in gives cubic metres.
For a cone or pyramid, the height is the vertical height — straight up from the centre of the base to the tip, not up the slope.
The Formulas
Look at the pairs and the pattern shows itself:
The third is not a coincidence between two formulas; it is one fact appearing twice.
Why a third?
Measure down from the tip of a cone. At distance x the cross-section is a circle whose radius grows in proportion to x — so its area grows as x². The solid is therefore very thin near the tip for a surprisingly long way down.
Integrating x² from 0 to h gives h³/3, and that 3 in the denominator is the whole explanation. It works for any base shape, which is why pyramids and cones share it.
You can check it with water: a cone and a cylinder of matching base and height take exactly three cone-loads to fill.
Cubes: the Scaling That Catches People Out
Volume depends on three dimensions, so it scales with the cube of the size.
| Scale each length by | Volume becomes | |----------------------|----------------| | ×½ | an eighth | | ×2 | eight times | | ×3 | twenty-seven times | | ×10 | a thousand times |
This is a bigger effect than most people's intuition allows, and it shows up everywhere:
- A pizza box twice as wide, deep and tall holds eight pizzas, not two.
- A tank 25% larger in each dimension holds 95% more — nearly double.
- A hailstone twice the diameter has eight times the mass.
- Halving a recipe's tin dimensions leaves an eighth of the capacity, not half.
Paired with the surface-area rule — which scales only with the square — it explains why large containers are cheaper per litre, why big animals overheat and small ones freeze, and why a stock pot takes so much longer to cool than a mug.
Volume in Litres
Volume becomes capacity once you attach a unit, and the metric system is built to make this easy:
1 litre = 1000 cm³ (a cube 10 cm on a side)
1 cubic metre = 1000 litres
1 millilitre = 1 cm³A millilitre and a cubic centimetre are the same thing, exactly. That is not a convenient approximation — the litre was defined that way.
This calculator reports both readings, because it cannot know which unit you typed. If your numbers were centimetres, take the first; if metres, take the second. US and imperial gallons are given too, and they genuinely differ: a US gallon is 3.785 litres, an imperial one is 4.546 — about 20% larger.
Step-by-Step Example
A fish tank, 80 × 35 × 45 cm.
V = 80 × 35 × 45 = 126,000 cm³
In litres: 126,000 / 1000 = 126 litresFilled to 5 cm below the rim it holds about 112 litres, which is what matters for stocking.
Concrete for a post hole, 30 cm across and 60 cm deep.
r = 15 cm
V = π × 15² × 60 = 42,412 cm³ = 42.4 litres = 0.042 m³A conical heap, 3 m radius and 2.2 m high.
Note how modest that is: the cylinder of the same footprint and height would be 62.2 m³. The cone holds a third.
A grain silo — a cylinder with a hemispherical top. Cylinder 4 m across and 10 m tall, dome the same radius.
Composite shapes are handled exactly like this: split, calculate, add.
Understanding Your Result
The volume is in cubic units of your input unit.
The formula used names the rule applied, so you can confirm it is the one you wanted.
The shape line describes what the calculator understood from your numbers.
The capacity gives litres and gallons under both unit readings.
The scaling line shows the volume at double, triple and half the size.
When Should You Use This Calculator?
Tanks, aquariums and water butts. Capacity in litres.
Concrete, gravel and topsoil. Ordered by the cubic metre.
Shipping and storage. Whether something fits, and volumetric weight for freight.
Cooking and brewing. Tin and vessel capacity, and scaling a recipe to a different tin.
Pools and ponds. Volume drives the chemical dosing and the pump sizing.
Excavation. Spoil volume from a trench or a hole, and how many skip loads.
Packaging. Box volume against contents.
Homework. All eight solids are standard exercises, with the working shown.
Common Mistakes
Using the diameter as the radius. The radius is squared or cubed, so this gives four times the volume for a cylinder and eight times for a sphere. Halve it first.
Forgetting the one third. A cone or pyramid without it comes out three times too large.
Using a cone's slant height. The volume needs the vertical height. The slant belongs to the surface area and is always longer.
Confusing cm³ with litres. Divide by 1000. A 126,000 cm³ tank is 126 litres.
Converting cubic units linearly. A cubic metre is 1,000,000 cubic centimetres, not 100. The factor is cubed along with the unit.
Mixing units mid-calculation. All three dimensions must share one unit before you multiply.
Confusing volume with capacity. For thick-walled vessels, capacity uses the internal dimensions. Outside measurements overstate what fits inside.
Assuming a taller container holds more. A short wide one often wins. Compare volumes, not heights.