Cylinder volume formula:
πr²h for tanks, pipes and cans

A stack of circles

Think of a cylinder as a pile of identical circular discs. The area of each disc is π × r², and the height of the pile is h. The volume is therefore the area of one disc times the number of discs, or in the continuous case, the height.

The formula is the same for a tall silo and a short tin. It is also the same for a pipe lying on its side, where the height is the length of the pipe. Whichever way up it is, the base is the circle and h is the distance between the two circular ends.

Worked example: a water tank

A plastic tank is 1.2 m in diameter and 1.5 m tall. You want to know its capacity in litres.

The most common slip is using 1.2 as the radius. That would quadruple the base area and give 6.79 m³, which is clearly too large for a tank of that size.

Rated capacity is often lower than the geometric volume because of the inlet height, the lid and the overflow level. Check the manufacturer's usable volume when it matters.

How much is in a partly filled tank?

For a vertical cylinder, the volume of liquid depends only on the depth. Use the same base area with the liquid height in place of h.

A tank on its side is different. The volume is not proportional to the depth, because the width of the liquid surface changes with depth. For a horizontal tank you need a special formula or a dipstick chart.

Units: from cubic centimetres to litres

Because 1 litre is 1,000 cm³, a can with an inside radius of 3.3 cm and a height of 11.5 cm has a volume of π × 10.89 × 11.5 = 393.4 cm³, or 0.393 litres. A 330 ml drink fills it only to about 84% of its depth, which leaves the headspace needed for the lid and for fizz.

A paint tin 15 cm across and 25 cm tall has a radius of 7.5 cm, so its volume is π × 56.25 × 25 = 4,417.9 cm³, about 4.4 litres. A 4 litre tin therefore has a little headroom, and that is deliberate so that it can be stirred.

Pipes and how changes scale

A 100 mm inner-diameter pipe of 50 m length holds π × 0.05² × 50 = 0.3927 m³, which is 393 litres. This number helps when you flush a line, estimate chemical dosing or size a header tank.

Radius enters as a square, so small changes in width matter more than the same proportional changes in height. If you need more capacity and have a choice, widening gives more for each percent than raising.

Sizing a tank for a target capacity

Often the volume is known and the height is the unknown. Rearrange the formula: h = V ÷ (π × r²). Suppose a roof can take a tank 1.5 m across, and you want 5,000 litres, which is 5 m³.

If 2.83 m is too tall for the space, widen the tank rather than shorten it. A 2 m diameter needs only 5 ÷ π = 1.59 m of height. The solution space is a trade-off between footprint and height, and the formula lets you try each pair in seconds.

Hollow cylinders: pipes and tubes

A pipe is a big cylinder with a smaller one removed, so its material volume is π × (R² − r²) × length, with R the outer radius and r the inner one. A steel tube with 60 mm outside and 50 mm inside diameter has radii of 30 and 25 mm.

This is a good example of why the inner radius matters for capacity but the outer one matters for weight and for fitting into a space.

Rolling a sheet into a cylinder

Roll a rectangular sheet without overlap and the side that curls round becomes the circumference, while the other side becomes the height. The choice changes the volume, which surprises many people. Take a sheet 30 cm by 20 cm.

The squat, wide roll holds 50% more. The reason is that the radius is squared in the formula while the height enters once, so stretching the rim is rewarded. The same logic explains why cans and tanks tend to be shorter and wider than you would guess when volume is the aim.

Slips and checks

• Diameter used as radius, giving four times the real volume.
• Mixed units, such as radius in cm and height in m.
• Forgetting to convert cubic units to litres.
• Using the outer diameter for a thick-walled tank. Use the inside radius for capacity.
• Rounding π to 3 for convenience; it understates the volume by 4.5%.

A cylinder volume calculator can handle the conversion from diameter, check a partly filled depth, and give both cubic metres and litres in one go.