Cylinder Volume Calculator
Find the volume of a cylinder from its radius or diameter and height, with the capacity in litres and gallons, the lateral and total surface area and the answer in terms of π. It also solves for the height or radius from the volume or surface area, and handles hollow cylinders such as pipes and tubes.
How it works
V = πr²h · lateral area L = 2πrh · total area A = 2πr² + 2πrh · h = V ÷ (πr²) · r = √(V ÷ πh) · h = (A − 2πr²) ÷ 2πr · hollow: V = π(R² − r²)h · 1 L = 1,000 cm³
A cylinder is a circle pushed straight up, so its volume is the base area πr² multiplied by the height. The surface splits into two parts: the two circular ends, which add up to 2πr², and the curved side, which unrolls into a rectangle of width 2πr (the circumference) and height h, giving the lateral area 2πrh. Adding them gives the total surface area. You can enter the radius or the diameter, and pick a length unit to see the capacity in litres, US gallons and other volume units. Each formula can also be turned around, so you can find the height from the radius and a volume (in cubic units, litres or gallons), or the radius from the height and the volume or lateral area. For a hollow cylinder such as a pipe, enter the outer radius and the wall thickness. You get the volume of the wall material, π(R² − r²)h, as well as how much the pipe holds inside. Results are also shown in terms of π, such as 72π, when the numbers allow it.
Worked example
For radius 3 in and height 8 in: volume = π × 3² × 8 = 72π ≈ 226.1947 in³, which is about 3.7067 litres or 0.9792 US gallons. The lateral area is 2π × 3 × 8 = 48π ≈ 150.7964 in², and the total surface area adds the two ends, 2π × 3² = 18π, giving 66π ≈ 207.3451 in². Working backwards, a 1-litre can with a 4 cm radius needs a height of 1,000 ÷ (π × 4²) ≈ 19.89 cm. A pipe 100 cm long with a 5 cm outer radius and a 0.5 cm wall has π × (25 − 20.25) × 100 ≈ 1,492.26 cm³ of material and holds about 6.36 litres.
Sources: Cylinder — Wikipedia · NIST Handbook 44, Appendix C — unit conversion factors
Frequently asked questions
How do I find the capacity in litres?
Pick cm as the length unit and the calculator does it for you: it computes the volume in cm³ and divides by 1,000, since 1 litre = 1,000 cm³. A cylinder of 5 cm radius and 20 cm height holds π × 25 × 20 ≈ 1,570.8 cm³ ≈ 1.57 litres. In inches, 1 US gallon = 231 in³.
What if I know the diameter instead of the radius?
Choose “Diameter” and type it in. The radius is half the diameter, so a 10 cm wide jar has a 5 cm radius. Using the diameter as if it were the radius makes the volume four times too large.
How do I find the height for a given volume?
Choose “Height (from radius and volume)”. The calculator rearranges V = πr²h into h = V ÷ (πr²). For 2 litres in a 6 cm radius container: 2,000 cm³ ÷ (π × 36) ≈ 17.68 cm.
How do I calculate the volume of a pipe or tube?
Choose “Hollow cylinder” and enter the outer radius (or diameter), the wall thickness and the length. The wall material is π(R² − r²) × length. The space inside is πr² × length, using the inner radius r = R − wall.
What is lateral surface area used for?
The lateral area 2πrh is the curved side without the top and bottom — the label wrapping a can, or the paint on a pipe’s outside. Add the two ends only when they are also covered.
Does a tilted (oblique) cylinder have the same volume?
Yes. By Cavalieri’s principle, an oblique cylinder with the same base and the same perpendicular height has the same volume, πr²h. Only the area of the slanted side is different.
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This calculator is for educational purposes. Double-check important results before acting on them.