Volume calculator for geometric solids
Volume and surface area of cubes, spheres, cylinders, cones, prisms and pyramids.
Calculator inputs
Results
Enter your values and press “Calculate” to see the result.
In short
- What it calculates
- Volume and surface area of cubes, spheres, cylinders, cones, prisms and pyramids.
- Formula used
Cube: V = a³- Example
- Cylinder with radius 2 dm and height 5 dm:
Volume calculator
Choose the solid and enter its dimensions. Along with the volume you get the total surface area, useful for working out paint or cladding.
If you work in decimetres, the volume matches the capacity in litres exactly.
How it works
Sphere, cone and cylinder formulas involve π. The cone surface adds the base and the lateral area, which needs the slant height, obtained from Pythagoras' theorem.
Formula
Cube: V = a³
Prism: V = a × b × c
Sphere: V = (4/3)·π·r³
Cylinder: V = π·r²·h
Cone: V = π·r²·h / 3
Square pyramid: V = a²·h / 3
Worked example
Cylinder with radius 2 dm and height 5 dm:
V = π × 2² × 5 = 62.8319 dm³
That is 62.83 litres of capacity.
Explanation
Volume grows with the cube
Doubling a body's dimensions multiplies its volume by eight, not two. It is why a slightly larger suitcase holds much more, and why large animals have different proportions: weight grows with the cube while bone strength grows with the square of their cross-section.
A litre is a cubic decimetre
The equivalence is exact by definition, and it makes moving between geometry and capacity very convenient. A cubic metre is a thousand litres; a cubic centimetre is a millilitre. With those two references almost any conversion can be done without a table.
Volume and capacity are not the same
Volume is the space a body occupies; capacity is what fits inside a container. A thick-walled tank has a greater external volume than internal capacity, and in calculations for tanks, pipes or packaging that difference matters.
Practical cases
Working out how much water a pool holds, how much soil a planter needs, how much concrete for a slab, or whether a piece of furniture fits in a boot. All are volume problems solved with the same formulas.
Frequently asked questions
How do I convert volume to litres?
One cubic decimetre is exactly one litre. If you measured in metres, multiply by 1000 to get litres.
Does the surface area include the bases?
Yes. For cubes, prisms, cylinders and cones the total surface area including the bases is calculated.
How many litres in a cubic metre?
Exactly a thousand. And a cubic centimetre is exactly a millilitre, both defined rather than approximate equivalences.
Why does doubling size multiply volume so much?
Because volume depends on three dimensions. Doubling each multiplies the result by two three times, that is by eight.
Need to calculate something else?
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The four most common percentage calculations in a single tool.