Volume Calculator: Cube, Cylinder, Sphere, Cone
The volume of a box, cube, cylinder, sphere, cone or pyramid, in litres too.
Good to know. A cone holds exactly a third of the cylinder it fits in. Ice cream shops know this very well.
How it works
In plain words
A box is length × width × height. A cylinder is the area of its circle times its height. A cone or pyramid holds a third of the cylinder or box around it. A sphere is four thirds of π times the radius cubed.
The formula
box = l × w × h · cube = s³ cylinder = π r² h · cone = π r² h ÷ 3 sphere = 4/3 π r³ · pyramid = s² h ÷ 3
Worked example
A cylinder 10 cm high with a radius of 5 cm holds π × 5² × 10 = 785.3982 cm³, which is 0.785 litres.
Sources
No outside data or rates: this is plain arithmetic.
4 automated tests check its answers on every change.
About the volume calculator: cube, cylinder, sphere, cone
Volume is how much space a shape takes up, or how much it holds: water in a tank, soil in a planter, concrete in a post hole, air in a room. Pick the shape, enter its measurements in one unit, and the calculator gives the volume in that unit cubed, in litres and in US gallons, plus the surface area.
The formulas follow a pattern. A box or cylinder is the area of its base times its height. A cone or a pyramid, which tapers to a point, holds exactly a third of the cylinder or box that fits around it. A sphere holds two thirds of the cylinder it fits inside, which Archimedes considered his finest discovery.
For containers, measure the inside, not the outside, or the result includes the walls. A litre is 1,000 cm³, the volume of a 10 cm cube, and a cubic metre is 1,000 litres. A US gallon is 3.785 litres; a UK gallon, 4.546 litres, is bigger.
For a room, use the room volume calculator. For concrete, soil or gravel, the dedicated calculators add waste and bag counts.
Questions people ask
How do I calculate the volume of a cylinder?
Multiply π by the radius squared and by the height. A radius of 5 cm and a height of 10 cm give 785.4 cm³.
How do I calculate the volume of a sphere?
Multiply 4/3 by π by the radius cubed. A ball with a 10 cm radius holds about 4,189 cm³, or 4.19 litres.
How many litres are in a cubic metre?
1,000. A litre is 1,000 cubic centimetres.