Cylinder Volume Calculator
Calculate the volume of a cylinder from its radius and height. Free cylinder volume calculator that also returns total surface area with the formula and steps shown.
Updated 2026-06-14 · Free · No sign-up · Runs privately in your browser
Show the formula & steps
How the Cylinder Volume Calculator Works
Enter the radius of the circular base and the height of the cylinder, and this calculator returns the volume and the total surface area. The full working is shown so you can follow each step.
The Formulas
Volume = π × r² × h Total surface area = 2πr² + 2πrh
The volume is the area of the circular base (πr²) stretched through the height. The surface area adds the two circular ends to the curved side.
Worked Example
For a cylinder with radius 3 and height 10:
- Volume = π × 3² × 10 = π × 9 × 10 = π × 90 ≈ 282.74 cubic units
- Surface area = 2π(3²) + 2π(3)(10) = 56.55 + 188.50 ≈ 245.04 square units
Volume by Size
| Radius | Height | Volume (πr²h) |
|---|---|---|
| 2 | 5 | 62.83 |
| 3 | 10 | 282.74 |
| 5 | 12 | 942.48 |
| 10 | 20 | 6,283.19 |
Where Cylinder Volume Is Used
Cylinder volume is essential for sizing tanks, pipes, cans, drums and silos. It tells you how much liquid a container holds, how much concrete fills a cylindrical form, and the displacement of a piston. Because volume scales with the radius squared, a small increase in radius adds far more capacity than the same increase in height.
Frequently asked questions
What is the formula for the volume of a cylinder?+
The volume of a cylinder is V = π × r² × h, where r is the base radius and h is the height. You find the area of the circular base (πr²) and multiply by the height. For a cylinder with radius 3 and height 10, the volume is π × 9 × 10 ≈ 282.74 cubic units.
How do I calculate the volume of a tank?+
A cylindrical tank uses the same formula: V = π × r² × h. Measure the inside radius and the height of the liquid (or the full tank), then multiply. To convert cubic feet to US gallons, multiply by 7.48052; to convert cubic metres to litres, multiply by 1,000.
What is the surface area of a cylinder?+
Total surface area is 2πr² + 2πrh: the two circular ends (2πr²) plus the curved side wall (2πrh). For radius 3 and height 10 that is about 56.55 + 188.50 ≈ 245.04 square units. This calculator shows the total surface area alongside the volume.
Does the calculator use radius or diameter?+
It uses the radius — half the diameter. If you measured the diameter across the circular base, divide it by 2 before entering it, or measure straight from the center to the edge to get the radius directly.
What units does the cylinder volume use?+
The calculator is unit-agnostic: enter the radius and height in the same unit and the volume comes out in that unit cubed. Inches give cubic inches, centimetres give cubic centimetres, and so on. Keep both measurements in the same unit for a correct result.