Volume of a cylinder, formula and calculator.

The volume of a cylinder is V = π × r² × h. Take a radius of 4 cm and a height of 10 cm. The base area is π × 4 × 4 = 50.2655 cm². Multiply by the height: 50.2655 × 10 = 502.6548 cm³. That is 0.5027 liters. The tool writes out these steps for any size.

How to use the converter

1. Choose Find: volume from radius and height, the material in a hollow cylinder (a pipe), or the height needed for a volume.
2. Pick Radius or Diameter under I know the, type it and the Height, and choose a Unit of length.
3. Read the big result and The working under it.
4. The cards give the base area, the side area, the total surface area, liters and US gallons. Use Copy result or Copy link to keep it.

Why it is area times height

Stack thin discs, each with the area of the base, π × r². The volume is the area of one disc times the number of discs, which is the height. That is also true for a box: base area times height. A cylinder is a box with a round base. If you know the diameter d, use r = d ÷ 2, so V = π × d² ÷ 4 × h.

What changes when you double a size

The radius is squared and the height is not. Doubling the height doubles the volume. Doubling the radius makes it four times as big. For r = 4 cm and h = 10 cm the volume is 502.65 cm³. Doubling the height gives 1,005.31 cm³. Doubling the radius gives 2,010.62 cm³, which is four times the first.

Volume per 10 cm of height

Worked examples

• Liters in each meter of pipe. A pipe with an inside diameter of 50 mm has r = 25 mm. For a length of 1 m = 1,000 mm, V = π × 25² × 1,000 = 1,963,495 mm³. A liter is 1,000,000 mm³, so that is 1.9635 liters per meter.
• A round tank, r = 1.5 m, h = 3 m. V = π × 1.5² × 3 = 21.2058 m³, which is 21,205.8 liters, or 5,602.0 US gallons.
• The height for 1 liter. A cylinder of radius 5 cm has a base of π × 25 = 78.5398 cm². One liter is 1,000 cm³, so the height is 1,000 ÷ 78.5398 = 12.7324 cm.
• A drum in inches. Diameter 22 in, height 34 in. r = 11. V = π × 121 × 34 = 12,924.5 in³. Divide by 231 for US gallons: 55.95.

The liter and gallon figures

A liter is 1,000 cm³ (NIST Special Publication 811, Appendix B.8 gives 1 L = 1.0 E-03 m³ as exact, checked 24 Oct 2026). A US gallon is 231 cubic inches exactly (NIST Handbook 44 (2026), Appendix C, checked 24 Oct 2026), which the tool uses to turn any unit into gallons.

Hollow cylinder: a pipe or a tube

A hollow cylinder is a big cylinder with a smaller one taken out of the middle. The material is π × (R² − r²) × h, where R is the outer radius and r the inner radius. The inner radius is the outer radius minus the wall thickness. Take a pipe with an outer diameter of 60 mm, a wall of 5 mm and a length of 2 m (2,000 mm). R = 30 mm and r = 25 mm. The wall ring has an area of π × (900 − 625) = 863.9380 mm², so the material is 863.9380 × 2,000 = 1,727,876 mm³, or 1,727.876 cm³. The space inside is π × 625 × 2,000 = 3,926,991 mm³, which is 3.927 liters. The converter has a Hollow cylinder choice under Find, with outer size, wall thickness and length.

A tank that is only partly full

For an upright cylinder the liquid is itself a cylinder, so use the depth of the liquid as the height. A tank 80 cm across, filled to a depth of 35 cm, holds π × 40² × 35 = 175,929 cm³, which is 175.93 liters. Enter 80 as the diameter and 35 as the height. A cylinder lying on its side is different, because the liquid surface cuts the circle, and the simple formula does not apply.

Liters for each centimeter of height

For a round upright tank, every centimeter of height holds the base area times 1 cm. That makes a handy dip-stick table.

A can in inches and gallons

Take a drum 12 in across and 20 in tall. The radius is 6 in, so V = π × 6² × 20 = 2,261.95 cubic inches. A US gallon is 231 cubic inches, so the drum holds 9.792 US gallons. In liters, with 1 in³ = 0.016387064 L, that is 37.067 L. Set the unit to inches and the cards show the same figures.

Mistakes to avoid

• Using the diameter as the radius. The result is 4 times too big. A 8 cm wide can has r = 4.
• Forgetting to square the radius. π × 4 × 10 is not the volume. It needs π × 4 × 4 × 10.
• Mixing units. Radius in cm and height in m gives nonsense. Use one unit for both sizes.
• Using the outside size of a pipe or a tank wall. Capacity needs the inside radius.

For a ball, see the volume of a sphere page. For boxes and other solids the area and volume calculator has more shapes.