What this calculator does
A cylinder is a circle extruded in a straight line, so its volume is simply the base area, πr², multiplied by the height. That makes it one of the most predictable shapes to size: double the height and volume doubles exactly, no more and no less.
Radius behaves very differently, because it feeds into the base area as a square. Doubling the radius while keeping the height fixed quadruples the volume, which is a common source of error when scaling up a tank or pipe design from a smaller prototype.
The formula
Total surface area has two parts: the curved side, which unrolls into a rectangle of width equal to the circumference and height equal to the cylinder’s height, and the two circular ends. Adding 2πrh for the curved part to 2πr² for both ends gives the total.
| Term | Meaning |
|---|---|
| r | The radius of the circular base. |
| h | The height, or length, of the cylinder. |
| V | Volume, equal to πr²h. |
| Curved surface | The side wall only, equal to 2πrh: excludes the two circular ends. |
The inputs explained
| Field | What to enter |
|---|---|
| Radius | The radius of the circular cross-section. |
| Height | The height or length along the axis. |
When to use it
Sizing a tank, drum or pipe
Volume gives the capacity directly, and the litres figure converts it for you if the radius and height were measured in centimetres: the standard way to size a water tank or fuel drum.
Ordering material to wrap or clad a cylinder
The curved surface area, without the two end caps, is what a label, a lagging wrap or a can’s side panel needs to cover.
Comparing tank proportions at equal volume
A short, wide cylinder and a tall, narrow one can hold the same volume with very different surface areas: the wider one usually has less total surface for the same capacity, which matters for material cost and heat loss.
Concrete or liquid volume in a round column or post hole
Fence post holes, concrete piers and round columns are all cylinders. Volume here converts straight into the concrete or fill needed once the units are consistent.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How volume and surface area scale with radius, height fixed at 20
A constant height with the radius widening.
| Radius | Volume | Total surface area | Curved surface only |
|---|---|---|---|
| 1 | 62.832 | 131.947 | 125.664 |
| 5 | 1,570.80 | 785.398 | 628.319 |
| 10 | 6,283.19 | 1,884.96 | 1,256.64 |
| 20 | 25,132.74 | 5,026.55 | 2,513.27 |
How volume scales with height, radius fixed at 5
A constant radius with the height stretching out.
| Height | Volume | Total surface area | Base area |
|---|---|---|---|
| 5 | 392.699 | 314.159 | 78.540 |
| 10 | 785.398 | 471.239 | 78.540 |
| 20 | 1,570.80 | 785.398 | 78.540 |
| 50 | 3,926.99 | 1,727.88 | 78.540 |
| 100 | 7,853.98 | 3,298.67 | 78.540 |
Questions
How do I find the volume of a cylinder?
Multiply the base area, πr², by the height. Radius and height must be in the same unit, and the result comes out in that unit cubed.
What is the difference between curved surface area and total surface area?
Curved surface area is the side wall alone, the shape you would get unrolling the label off a can. Total surface area adds the two flat circular ends. Use curved-only for wrapping or cladding, total for full material or paint estimates.
Does radius or height affect volume more?
Radius, because it enters the formula squared while height enters only linearly. Doubling the radius quadruples the volume; doubling the height merely doubles it.
How do I convert a cylinder’s volume to litres?
If radius and height are both in centimetres, the volume in cubic centimetres divides by 1,000 to give litres. This calculator applies that conversion automatically.
How is a cylinder’s volume related to a cone of the same base and height?
A cone with the same radius and height holds exactly one third of the cylinder’s volume: a relationship you can check against the cone calculator.
For a tapering version of this shape, see the cone calculator. For a sphere, use the sphere calculator.