Cylinders are everywhere: the water tank on a roof, the can in your hand, the pipe under your sink — two identical circles joined by a curved side, all sharing the same volume formula. Learn it once and you can work out how much any of them holds. The Volume Calculator does it instantly, but the hand method takes about a minute.
Below: what a cylinder is, where the formula comes from, how to handle the diameter, five worked examples — a plain calculation, one from the diameter, and three real ones, a water tank, a drinks can and a length of pipe — and the mistakes to avoid.
What is a cylinder?
A cylinder is a solid with two flat, identical, parallel circular ends — the bases — joined by one curved surface; the distance between them is the height. A drinks can and a drainpipe are cylinders, and the formula is the same either way. Two measurements describe one: the radius of the base and the height. The radius runs from the centre of the circle to its edge; the diameter runs straight across, through the centre, and is always twice the radius — and the formula uses the radius. Volume is the space inside, in cubic units: cubic centimetres (cm³) for cans, cubic metres (m³) for tanks.
The cylinder volume formula
The cylinder volume formula is V = πr²h: multiply π (pi, 3.14159…) by the radius squared, then by the height. Read as two steps it is clearer: work out the area of the circular base, πr², then multiply by the height — a cylinder is a circle stretched out along its height, every slice the same circle, so the volume is that circle’s area times how far it stretches. A cylinder with radius 3 has a base area of π × 3² = π × 9 ≈ 28.27, and at a height of 5 its volume is 28.27 × 5 = 141.37. Use the π button on your calculator.
Radius or diameter? Halve it first
Most real cylinders are measured across, not from the centre out: measuring across is easy, finding the centre is not. So most problems hand you the diameter, and the first step is always to halve it — a cylinder 6 cm across has a radius of 3 cm, a tank 1 m across has a radius of 0.5 m, and a pipe 10 cm across has a radius of 5 cm. Skipping this step is the most common cylinder mistake: a diameter used as the radius gives an answer four times too big, because the radius is squared. Then square it: r² is the radius multiplied by itself, so for a radius of 3, r² is 3 × 3 = 9, not 6 and not 3.
Worked example 1: radius 3, height 5
A cylinder with radius 3 and height 5: square the radius, 3² = 3 × 3 = 9; multiply by the height, 9 × 5 = 45; multiply by π, 45 × 3.14159… = 141.37. The volume is 141.37 cubic units — 141.37 cm³ in centimetres, 141.37 m³ in metres — the unit is always the one you measured in, cubed. Check: it fits in a 6 × 6 × 5 box of 180, and 141.37 is about 79% of that (π/4).
Worked example 2: diameter 6, height 6
A cylinder 6 across and 6 tall. Halve the diameter first: 6 ÷ 2 = 3, so the radius is 3. Square it: 3² = 9. Multiply by the height: 9 × 6 = 54. Multiply by π: 54 × 3.14159… = 169.65 cubic units. It is taller than the first by 1, and its volume is bigger by 28.28 — exactly π × 9, the base area.
Worked example 3: a water tank
A round water tank is 1 m across and 1.2 m tall. How many litres does it hold? Halve the diameter: 1 ÷ 2 = 0.5 m radius. Square it: 0.5² = 0.25. Multiply by the height: 0.25 × 1.2 = 0.3. Multiply by π: 0.3 × 3.14159… = 0.9425 m³. Convert to litres: 1 m³ is 1,000 litres, so 0.9425 × 1,000 = 942.48. The tank holds about 942 litres. Cross-check in centimetres: radius 50 cm, height 120 cm, so 50² = 2,500, × 120 = 300,000, × π = 942,477.8 cm³ = 942.48 litres — the same answer.
Worked example 4: a drinks can
A drinks can is 7 cm across and 12 cm tall. Halve the diameter: 7 ÷ 2 = 3.5 cm radius. Square it: 3.5² = 12.25. Multiply by the height: 12.25 × 12 = 147. Multiply by π: 147 × 3.14159… = 461.81 cm³. One cubic centimetre is exactly one millilitre, so the can holds 461.81 ml — about 462 ml if it were a perfect cylinder. A real can of that size is usually labelled 330 ml: a real can is not a perfect cylinder — the top tapers in and the base is pushed up.
Worked example 5: a length of pipe
A pipe is 10 cm across and 2 m long. How much water does it hold when full? Convert first: 2 m is 200 cm, so every measurement is in centimetres. Halve the diameter: 10 ÷ 2 = 5 cm radius. Square it: 5² = 25. Multiply by the length: 25 × 200 = 5,000. Multiply by π: 5,000 × 3.14159… = 15,707.96 cm³. Convert to litres: 15,707.96 ÷ 1,000 = 15.71. Two metres of that pipe holds about 15.7 litres. Note the “height” of a pipe is its length, and the diameter that counts is the inside diameter.
Units: keep them the same, then convert the answer
Every measurement in the formula must use the same unit — all centimetres, all metres, all inches. Mix them and the answer is meaningless: a radius of 50 cm with a height of 1.2 m gives π × 2,500 × 1.2 = 9,424.78, a number with no unit at all. Convert first: 1 m = 100 cm; 1 m³ = 1,000 litres; 1 litre = 1,000 cm³; 1 cm³ = 1 ml. Convert the answer at the end.
Common mistakes
- Using the diameter as the radius. A cylinder 6 across has radius 3, not 6: π × 36 × 5 = 565.49, exactly four times the correct 141.37. Halve the diameter first.
- Forgetting to square the radius. π × 3 × 5 = 47.12, exactly a third of the correct 141.37. The radius must be multiplied by itself first — r² is 9 for a radius of 3, not 3.
- Mixing units. A radius in centimetres and a height in metres cannot go into the same formula. Convert everything to one unit first, or the answer is wrong by a factor of 10, 100 or 1,000,000.
- Rounding too early. Rounding π to 3.14 is fine for a rough answer, but rounding the radius or the base area before squaring doubles the error. Keep full precision and round only the final answer.
- Confusing volume with surface area. Volume is the space inside, in cubic units (cm³); surface area is the skin outside, in square units (cm²). Radius 3, height 5: volume 141.37 cm³, surface area 150.80 cm² — the units are the giveaway.
Related tools
For any other measurements, the Volume Calculator does the working for you: enter the radius and height and it shows the volume in cubic units, with the formula and your numbers substituted in so you can check the steps. It also covers cubes, boxes, cones, spheres and square pyramids, it is free, and it needs no sign-in. For all of ToolZana’s free tools, start at the ToolZana home page.
The short version
The cylinder volume formula is V = πr²h: π times the radius squared, times the height — base area πr² times height. Halve the diameter first: a cylinder 6 across has radius 3, so r² is 9, not 36. Radius 3 and height 5 gives 45π = 141.37; radius 3 and height 6 gives 54π = 169.65. A tank 1 m across and 1.2 m tall holds about 942 litres, a can 7 cm across and 12 cm tall holds about 462 ml, and 2 m of pipe 10 cm across holds about 15.71 litres. Doubling the height doubles the volume; doubling the radius quadruples it. Keep all measurements in the same unit and round only at the end. For any other measurements, the Volume Calculator gives the exact answer in seconds.
Frequently Asked Questions
What is a cylinder, exactly?
A cylinder is a solid with two flat, identical, parallel circular ends — the bases — joined by one curved surface. The distance between the two circles is the height, and the radius of the circles is the cylinder’s radius. A drinks can, a drainpipe and a candle are all cylinders, hollow or solid, and the formula is the same either way.
Why is the cylinder volume formula πr²h?
Because a cylinder is a circle stretched out along its height. Every slice through it is the same circle, with area πr², so the volume is that area times how far it stretches — the height. That is why the formula has two readings: π times the radius squared times the height, or base area times height.
How do I find the radius if I only know the diameter?
Halve the diameter: the radius is always half the diameter. A cylinder 6 cm across has a radius of 3 cm, a tank 1 m across has a radius of 0.5 m, and a pipe 10 cm across has a radius of 5 cm. Write the halved number down before you do anything else, because the formula needs the radius. Using the diameter as the radius gives an answer four times too big, since the radius is squared.
How do I work out the volume of a water tank?
Measure the diameter across the top and the height, in the same unit, then halve the diameter to get the radius and apply V = πr²h. A tank 1 m across and 1.2 m tall has radius 0.5 m: 0.5² = 0.25, × 1.2 = 0.3, × π = 0.9425 m³. Multiply by 1,000 to get litres: 942.48, so the tank holds about 942 litres.
How do I convert a cylinder’s volume into litres?
It depends on the unit the volume is in. If it is in cubic metres, multiply by 1,000 — 0.9425 m³ is 942.48 litres. If it is in cubic centimetres, divide by 1,000, because 1 litre is 1,000 cm³ — 15,707.96 cm³ of pipe is 15.71 litres. And 1 cm³ is exactly 1 ml, so a can of 461.81 cm³ holds 461.81 ml. Convert the answer at the end, not the measurements in the middle.
What happens to the volume if I double the radius?
It becomes four times bigger, because the radius is squared. A cylinder with radius 3 and height 5 has a volume of 141.37; doubling the radius to 6, with the same height, gives 565.49 — exactly four times as much. Doubling the height, by contrast, only doubles the volume: radius 3 and height 10 gives 282.74. That is why a slightly wider tank holds so much more than a slightly taller one.
Why is my cylinder volume four times too big?
Almost always because the diameter went into the formula instead of the radius. A cylinder 6 across has radius 3, and using 6 gives π × 36 × 5 = 565.49 instead of the correct π × 9 × 5 = 141.37 — exactly four times too big. Halve the diameter first and redo the calculation.
Can I work out a cylinder’s volume from its circumference?
Yes. The circumference is 2πr, so divide it by 2π to get the radius, then use the formula as normal. A cylinder with a circumference of 18.85 cm has a radius of 18.85 ÷ (2 × 3.14159…) = 3 cm; with a height of 5, its volume is π × 3² × 5 = 141.37 cubic units. Wrap a tape measure around the cylinder to get the circumference — often easier than measuring across it.
How do I find the height of a cylinder if I know its volume?
Rearrange the formula: height = volume ÷ (πr²). For a cylinder with a volume of 141.37 and a radius of 3, the height is 141.37 ÷ (π × 9) = 141.37 ÷ 28.27 = 5. The height version comes up most often, for example when you know a tank’s capacity and diameter and want to know how tall it must be.
What is the fastest way to check my cylinder volume answer?
Use the free Volume Calculator. Enter the radius and the height and it shows the volume in cubic units, with the formula and your numbers substituted in, so you can compare its steps with your own. It runs entirely in your browser, handles the π and the squaring for you, and needs no sign-in.