Cylinder volume formula:
π × radius² × height

Cylinder volume formula

The volume of a cylinder is π times the radius squared times the height. A cylinder with a radius of 3 and a height of 10 holds 3.14159 × 9 × 10 = 282.74 cubic units.

The idea is simple: the circular base has an area of π × r², and stacking that base up to the full height multiplies it by the height. Use the same length unit for both measurements, and the answer is in cubic units of that length.

Worked example in metres and litres

A water drum with a 1 metre diameter and 1.2 metres of height therefore holds about 942 litres. Always halve a diameter before squaring it.

Here is a second case, a round concrete column. With a radius of 0.15 m and a height of 3 m, the volume is π × 0.0225 × 3 = 0.2121 cubic metres. Ordering concrete in whole cubic metres, that column needs a little over a fifth of one, so builders add a margin for spillage and uneven moulds.

The shape also explains why tall, thin and short, wide containers can hold the same amount. Doubling the radius multiplies the volume by four, but doubling the height only doubles it, so a small change in radius matters far more than the same change in height.

Cylinder, cone and sphere side by side

A cone with the same base and height as a cylinder holds exactly one third of its volume. A sphere of radius r holds 4 ÷ 3 × π × r³, which is two thirds of the cylinder that just fits around it (height equal to 2r).

The sphere row uses only the radius, because a sphere has no separate height. This comparison is why a scoop-shaped cone holds less than the matching tub, a point handy in packaging and tank design.

Where cylinder volume is used

• Sizing a round water tank or drum and converting the result to litres.
• Estimating concrete for a round pier or column footing.
• Checking how much liquid a pipe holds per metre of length.
• Working out the capacity of a tin or cooking pot.

For a pipe, treat its inside radius as the radius and its length as the height. Remember that the result is a volume of the empty space, not of the wall material.

Common mistakes with cylinder volume

• Using the diameter as the radius. This inflates the answer by four times.
• Mixing units, such as a radius in centimetres and a height in metres.
• Forgetting that the answer is in cubic units. 0.9425 m³ is not 0.9425 litres.
• Forgetting to subtract the wall thickness when you want the inside volume of a thick-walled tank.