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Cylinder Volume Calculator

How do I find the volume of a cylinder?

How it is calculated

The tool uses V = π × r² × h for volume and A = 2π × r × (r + h) for total surface area, where r is the radius of the circular base and h is the height, both in the same length unit. Volume comes out in that unit cubed and area in that unit squared. The surface area includes both circular ends plus the curved side. Both radius and height must be greater than zero, otherwise no result is shown. Results are rounded to two decimals. The tool takes the radius, not the diameter, and does not convert units.

Worked example

A can has a radius of 3 and a height of 10 (say, centimetres). Radius squared is 9, so the base area is π × 9 ≈ 28.274. Multiply by the height: the volume is 282.74 cubic units. For the surface, r + h = 13, so 2π × 3 × 13 = 78π, which gives 245.04 square units including the lid and the bottom.

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Common mistakes

  • Entering the diameter as the radius. Volume depends on the radius squared, so the volume ends up four times too large.
  • Mixing units, such as a radius in centimetres and a height in metres.
  • Reading the volume in cubic centimetres as litres. 1,000 cm³ is 1 litre, so divide by 1,000.
  • Using the total surface area to cover an open-top container or a pipe. The ends are included, so subtract them if they are absent.
  • Forgetting that doubling the radius quadruples the volume, while doubling the height only doubles it.

About this calculator

This calculator finds a cylinder's volume (π × r² × h) and surface area (the two circular ends plus the curved side, 2πr² + 2πrh) from its radius and height. Volume tells you how much the cylinder can hold or how much material fills it, while surface area tells you how much material is needed to build or cover its outside — two different questions that both come up constantly when working with cylindrical shapes.

It's used for practical jobs like figuring out how much water a cylindrical tank holds, how much paint or metal sheeting is needed to coat or build a pipe or drum, or how much concrete a cylindrical column requires — as well as in geometry classes to teach the derivation and application of the volume and surface area formulas.

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Comments (1)

  • Editorial team

    For a tank, use inside dimensions for capacity and outside dimensions for paint or insulation, since wall thickness separates the two. To find the liquid in an upright tank at a given level, enter the liquid height as the height. That fails for a tank lying on its side, where the liquid forms a partial circle. Remember the litre step too: with centimetres, divide the volume by 1,000. What are you measuring, a tank, a pipe or a drum?

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