How to find a cylinder's volume
The volume of a cylinder is the area of its circular base times its height: V = π × r² × h. For a radius of 3 and height of 10, that's π × 9 × 10 = about 282.74 cubic units. It's the same idea as stacking circles of area πr² to the full height.
Any solid with a constant cross-section has volume equal to cross-sectional area × length, and for a cylinder the cross-section is a circle of area πr². Because the radius is squared, doubling it quadruples the volume while doubling the height only doubles it. If you are buying paint or sheet metal rather than filling the tank, the cylinder surface area calculator is the one you want.
How to use this calculator
Enter the radius of the circular end and the height (or length) of the cylinder, in the same unit. The result is in cubic units. For a tank or pipe given the diameter, halve it to get the radius first.
Both measurements must share a unit — mixing centimetres with metres is the most common error. A horizontal pipe works the same way: its "height" is simply its length along the axis.
Capacity in litres or gallons
To convert cubic units to capacity: 1 litre = 1,000 cm³, and 1 US gallon ≈ 231 cubic inches. For a concrete column form, the Sonotube calculator does the same math in construction units; for a plain box, see the volume calculator.
Use the internal radius when you care about what fits inside a vessel, and the external radius when you care about the space it occupies.
Frequently asked questions
- What is the formula for cylinder volume?
- V = π × r² × h: square the radius, multiply by pi, then multiply by the height.
- How do I find cylinder volume from the diameter?
- Halve the diameter to get the radius, then use V = π × r² × h.
- What is the volume of a cylinder with radius 3 and height 10?
- About 282.74 cubic units (π × 9 × 10).
- How do I convert to litres?
- If your measurements are in centimetres, divide the cubic-cm result by 1,000 to get litres.
- Does this work for a pipe or a hollow tube?
- Not directly — this gives the volume of a solid cylinder. For a hollow pipe, calculate the volume using the outer radius, then subtract the volume calculated with the inner radius; the difference is the material in the wall, while the inner figure alone is the fluid capacity.