Volume Of a Cylinder Calculator

What this calculator does

A cylinder is a circular tube with flat ends: a can, a pipe, a water tank, a bottle. This works out its volume, the space inside, from the radius of its circular base and its height.

Type the two in, pick a unit, and you have the capacity.

Using the calculator

1. Type the base radius, the distance from the centre of the circular end to its edge.
2. Type the height.
3. Pick the unit, then press Calculate.

Both values have to be positive, and the volume comes back in cubic units of the unit you pick.

The formula | volume = π × radius² × height

The volume of a cylinder is:

volume = π × radius² × height

It is the base-times-height rule again, with a circle for the base. The base is a circle, whose area is π × radius², and the cylinder is that circle raised straight up to the height. So the volume is the circle's area times the height. A good way to picture it is as a tall stack of thin circular disks: work out one disk, then pile them up the full height.

The value of π it uses

The tool works with π set to 3.141592654, ten significant figures. That is far finer than anything you could measure on a real tank or pipe, so π is never the weak link in the answer. Your result is only ever as accurate as the radius and height you measured, so once you have it, round it back to match how carefully you measured those.

Cubic units and litres

Because the formula multiplies lengths to the third power overall, the volume comes out in cubic units, matched to the unit you chose: a cylinder measured in centimetres gives cubic centimetres, cm³. For a capacity you can pour, the bridge is that 1 litre is 1,000 cm³, so a volume in cubic centimetres divided by 1,000 gives litres, handy for tanks and bottles.

A worked example | radius 10 cm, height 20 cm

Say the radius is 10 cm and the height is 20 cm.

1. Area of the circular base: π × 10² = π × 100 = 314.159 cm².
2. Times the height: 314.159 × 20 = 6,283.19 cm³.

So the volume is about 6,283 cm³, which is roughly 6.28 litres. That is the same as 2,000π, since the radius squared times the height comes to 2,000.

A cone is a third, a sphere is two thirds

The cylinder sits at the centre of two nice relationships. A cone with the same base and height holds exactly one third as much, so three such cones fill the cylinder. And a sphere that just fits inside the cylinder takes up exactly two thirds of it, the result Archimedes was proudest of, more than two thousand years ago. For those, see the volume of a cone calculator and the volume of sphere calculator.

Questions people ask

What is the volume of a cylinder with radius 10 and height 20?

About 6,283 cm³, or 2,000π. Square the radius and multiply by π and the height: π × 10² × 20.

What value of π does it use?

It uses π as 3.141592654, ten significant figures, which is more precise than any real measurement you would feed it.

Is the volume the base area times the height?

Yes. The base is a circle of area π × radius², and multiplying that by the height gives the volume, the same base-times-height rule used for prisms.

How do I get litres?

If the volume is in cubic centimetres, divide by 1,000, since 1 litre is 1,000 cm³.

How does a cylinder relate to a cone?

A cone with the same base and height has exactly one third of the cylinder's volume, so three of those cones would fill it.

References

A note on where this comes from. The base of the cylinder is a circle, whose area π × radius² rests on the value of π tabulated by the US National Institute of Standards and Technology. That a sphere is two thirds of its circumscribing cylinder, and the geometry tying the two together, was proved by Archimedes in On the Sphere and Cylinder. For further reading, see Cylinder.

1. Archimedes, On the Sphere and Cylinder (c. 225 BCE), the relationship between a sphere and the cylinder that contains it.
2. National Institute of Standards and Technology (NIST), Digital Library of Mathematical Functions, value of π used in the circular base area. https://dlmf.nist.gov/