📦 Volume Calculator
Calculate the volume of eight common solids. The result comes back in cubic units plus litres and gallons, which is what you need for tanks, pools and anything you have to fill.
Volume of eight solids, and converting to something useful
Volume is how much space a solid occupies, or how much it holds. Most practical questions are the second kind: how many litres in that tank, how much water in the pool, how much soil for the raised bed. The arithmetic is straightforward; the units are where things go wrong.
The eight formulas
| Solid | Formula | You need |
|---|---|---|
| Rectangular box | l × w × h | Three dimensions |
| Cube | edge³ | One edge |
| Cylinder | πr²h | Radius and height |
| Sphere | 4/3 πr³ | Radius |
| Cone | ⅓ πr²h | Radius and height |
| Rectangular pyramid | ⅓ × base area × h | Base dimensions and height |
| Capsule | πr²(4r/3 + h) | Radius and the straight side height |
| Ellipsoid | 4/3 πabc | Three semi-axes |
Two patterns are worth noticing. Anything that comes to a point, a cone or a pyramid, is exactly one third of the prism with the same base and height. And a sphere is exactly two thirds of the cylinder that just contains it, a result Archimedes considered his finest and had carved on his tomb.
The conversion that matters
One cubic metre holds exactly 1,000 litres. That single fact handles most capacity questions in metric. In imperial, a cubic foot is 7.48 US gallons, which is less memorable and more often looked up.
| Volume | Litres | US gallons | Imperial gallons |
|---|---|---|---|
| 1 cubic metre | 1,000 | 264.17 | 219.97 |
| 1 cubic foot | 28.32 | 7.48 | 6.23 |
| 1 cubic yard | 764.55 | 201.97 | 168.18 |
| 1 cubic inch | 0.0164 | 0.00433 | 0.00360 |
Volume scales as the cube
Doubling every dimension multiplies volume by eight. A tank twice as tall, twice as wide and twice as long holds eight times as much, not twice. This catches people out when scaling up a design, and it is why large animals have proportionally thicker legs: mass grows with the cube of size while bone cross-section grows with the square.
The same square-cube relationship explains why a 12-inch pizza is not twice a 9-inch one. It is 1.78 times the area, so the larger pizza is usually the better value even at a meaningfully higher price.
Partially filled containers
A cylinder standing upright and filled to depth d holds πr²d, which is simple. A cylinder lying on its side is considerably harder, because the cross-section is a circular segment rather than a rectangle, and it needs an inverse cosine. This is why fuel gauges on horizontal tanks are non-linear and why the last quarter of an oil tank seems to disappear faster than the first.
Displacement for awkward shapes
For a solid with no formula, measure the water it displaces. Submerge it in a container of known cross-section and multiply the rise in level by that area. It is exact, it needs no geometry, and it is the method Archimedes is supposed to have discovered in the bath.
A worked example
A cylindrical water tank 1.2 m in diameter and 1.8 m tall. The radius is 0.6 m, so the volume is π × 0.36 × 1.8 = 2.036 m³, which is 2,036 litres or 538 US gallons. Filled to 1.4 m rather than the brim, it holds π × 0.36 × 1.4 = 1,583 litres.
Frequently Asked Questions (FAQs)
How many litres are in a cubic metre?
Exactly 1,000. A cubic metre is a cube one metre on each side, and a litre is defined as a cubic decimetre, so a thousand of them fit. It is the single most useful conversion in capacity calculations.
How do I calculate the volume of a tank?
For an upright cylinder, πr²h using the internal radius. For a rectangular tank, length times width times height. Measure the inside, not the outside, since wall thickness can account for several per cent on a small tank.
Why is a cone exactly one third of a cylinder?
It falls out of integration, and it holds for any pyramid-like solid: a shape tapering to a point has one third the volume of the prism with the same base and height. The result predates calculus, having been proved by Eudoxus and used by Archimedes.
How do I find the volume of an irregular object?
By displacement. Submerge it in a container of known cross-section and multiply the rise in water level by that area. For objects that float or absorb water, wrap them or use a sand equivalent.
What is the volume of a half-full horizontal cylinder?
Exactly half the total, by symmetry. Any other fill level needs the circular segment formula, which involves an inverse cosine, because the cross-section of the liquid is not a simple shape.
Does doubling a container's size double its capacity?
Only if you doubled one dimension. Doubling all three multiplies capacity by eight. This is the most expensive misunderstanding when scaling up tanks, ponds or any container built to a plan.