Transparent method
The formula
Worked example
Example inputs
How to interpret the result
Surface area on a cylinder is easy to shortchange, because it's tempting to picture only the curved side and forget the two flat circular ends sitting on top and bottom. Leave those out of a materials estimate, paint, wrapping, sheet metal, and the real total comes in noticeably short of what actually gets used.
Before you rely on it
What to check
Confirm whether the figure you need is volume, what fits inside, or total surface area, what covers the outside: the two use different parts of the same formula and answer different questions.
The common error
Where people go wrong with cylinder volume & surface area calculator
Computing only the curved lateral surface and calling it total surface area. The two circular ends add real area, more of the total the shorter and wider the cylinder is.
Sensitivity evidence
How radius changes the volume
| Radius | Volume | Surface area |
|---|---|---|
| 2.4 | 181 | 187 |
| 2.7 | 229 | 215.5 |
| 3worked example | 282.7 | 245 |
| 3.3 | 342.1 | 275.8 |
| 3.6 | 407.2 | 307.6 |
Every input, tested
Which input moves the volume most
| Input | Tested from | To | Volume at each end | Swing |
|---|---|---|---|---|
| Radius | 2.7 | 3.3 | 229 to 342.1 | 113.1 (40%) |
| Height | 9 | 11 | 254.5 to 311 | 56.5 (20%) |
Two variables at once
Volume by radius and height
| Radius \ Height | 8 | 10 | 12 |
|---|---|---|---|
| 2.4 | 144.8 | 181 | 217.1 |
| 2.7 | 183.2 | 229 | 274.8 |
| 3 | 226.2 | 282.7 | 339.3 |
| 3.3 | 273.7 | 342.1 | 410.5 |
| 3.6 | 325.7 | 407.2 | 488.6 |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Radius | 3 |
| Height | 10 |
| Volume | 282.7 |
| Surface area | 245 |
Where the inputs come from
Enter the radius of the circular base and the height of the cylinder in the same unit. If you have the diameter, halve it. For a tank lying on its side, use its length as the height. The calculator returns volume, pi r squared times height, and total surface area including both ends. For an open container without a lid, subtract one circle's area from the surface figure.
When the result stops applying
A partly filled horizontal tank needs a different calculation. Rounding and unit errors, particularly mixing diameter and radius, are the usual mistakes.
What to compare it with
See the circle area calculator for the base, the cone, sphere and capsule pages for related solids, and the pipe and tank tools in the trades categories. The unit conversion calculators convert volume to gallons and liters, and the annulus page handles hollow tubes.
People also ask
Frequently asked questions
What is the volume formula for a cylinder?
Pi times the radius squared times the height, the area of the base multiplied by the height.
How do I convert cylinder volume to gallons?
For inches, divide the volume in cubic inches by 231 to get US gallons, since one gallon holds 231 cubic inches, or multiply cubic feet by 7.48.
Does the surface area include the ends?
Yes, total surface area adds the two circular ends to the curved side. For an open can without a lid, subtract the area of one end.