Volume is the space a solid occupies; capacity is what fits inside it. A box measuring 30 by 20 by 15 centimetres has a volume of 9,000 cubic centimetres, which is exactly 9 litres or 2.3775 US gallons — and if those are its external dimensions, its capacity is smaller by whatever the walls take up.
Most volume mistakes are not arithmetic. They are measuring the outside of something and then filling the inside of it.
How much do the walls actually cost?
More than their thickness suggests, because the loss applies on both sides of all three dimensions. A 5 mm wall on that 30 × 20 × 15 cm box leaves an interior of 29 × 19 × 14 cm, which is 7,714 cubic centimetres — 7.71 litres against 9. The walls are 3.3 per cent of the smallest dimension and they took 14.3 per cent of the capacity.
The effect is worst on small containers and on anything with thick walls relative to its size. It is why a "20 litre" storage crate holds noticeably less than 20 litres of anything, and why the figure on the label is usually the nominal external volume.
Which formulas cover most cases?
Four shapes and one relationship handle nearly everything.
| Shape | Volume |
|---|---|
| Box | length × width × height |
| Cylinder | π × radius² × height |
| Sphere | 4/3 × π × radius³ |
| Cone | 1/3 × π × radius² × height |
The relationship worth memorising is that a cone is exactly one third of the cylinder that would contain it, and a pyramid is exactly one third of its box. A cylinder of radius 15 cm and height 40 cm holds 28,274.33 cm³, or 28.27 litres; the cone of the same radius and height holds 9,424.78 cm³, which is 9.42 litres and precisely a third.
That is not an approximation. It falls out of the same integral, and it turns two formulas into one you can check in your head.
Which radius do you use for a cylinder?
Half the diameter, which is where most cylinder errors start. A tank described as 60 cm across has a radius of 30 cm, and using 60 as the radius overstates the volume by a factor of four — because the radius is squared.
The squaring is what makes the error so large. Getting the height wrong by a factor of two doubles the answer; getting the radius wrong by a factor of two quadruples it. Any volume figure that looks implausibly large is worth checking against the radius first.
How do you go from volume to capacity in the units people use?
By fixed conversions, once the cubic figure is in hand.
- 1 litre = 1,000 cubic centimetres. So cubic centimetres divide by a thousand.
- 1 cubic metre = 1,000 litres. A cubic metre of water is a tonne.
- 1 US gallon = 3.785411784 litres. Litres × 0.264172 gives US gallons.
- 1 imperial gallon = 4.54609 litres, about 20 per cent larger than the US one.
- 1 cubic foot = 28.3168 litres. Common on tanks and shipping.
Mixing units inside a single calculation is the other frequent failure. A tank measured in feet and reported in litres needs the dimensions converted first or the answer multiplied by 28.3168 — never both, and never neither.
Partly filled containers need a different calculation entirely. A cylinder standing upright is easy — the volume scales with the fill height — but one lying on its side is not, because the cross-section of the liquid is a circular segment rather than a rectangle. A horizontal tank half full holds exactly half, and a horizontal tank a quarter full by depth holds about 19.6 per cent of its capacity rather than 25.
What about surface area?
It answers a different question and scales differently. Doubling every dimension of a box multiplies its volume by eight and its surface area by four, which is why large containers are more material-efficient per litre than small ones and why heat is lost faster from small objects.
For that 30 × 20 × 15 cm box the surface area is 2,700 cm². It is the figure you need for paint, wrapping or insulation, and it has no direct relationship to the 9 litres inside.
Questions people ask
How do I work out a tank in gallons? Get the volume in litres first, then convert once at the end. Converting the dimensions to gallons is not a thing that can be done — gallons are a volume, not a length.
What is a capsule? A cylinder with a hemisphere on each end, which is the shape of most propane and compressed-gas tanks. Its volume is the cylinder plus one whole sphere, because two hemispheres make one.
Is the surface area of a pyramid the whole thing? It includes the base unless stated otherwise. For a roof you want the lateral area only, which is the total less the base.
Why does my tank hold less than the calculation says? Usually fill level rather than walls. Tanks are rarely filled to the brim, and many have a stated usable capacity below the geometric one.
Measure the inside if you are filling it and the outside if you are moving it. The volume calculator reports litres and gallons alongside the cubic figure for every shape, litres to gallons handles the two-gallon problem, and the slope calculator covers the geometry that comes next on the same job.