Cylinder Surface Area Calculator
Cylinder total surface, volume, and side area.
What it does
Cans, pipes, tanks, and rolls share one shape. Total surface adds three parts: top circle, bottom circle, and the side that unrolls into a rectangle. Volume multiplies the base circle by height. One radius and one height fix all three numbers.
The tool above runs the full set. With radius 6 cm and height 10 cm, surface is 603.19 cm2, volume is 1131 cm3, and the side alone is 376.99 cm2. The imperial mirror at 2.4 in by 3.9 in gives 95 in2, 70.6 in3, and 58.81 in2. Paint shops read surface and side, while capacity planning reads volume.
The side rectangle is the key picture. Cut the label off a can and it flattens to length equal to the circumference, 2 pi r, by height h. Adding the two base circles, pi r squared each, completes the total. That is why surface uses both r squared and r times h, while volume uses r squared times h.
This page assumes a right circular cylinder with flat ends. It does not cover open tops, dished ends, wall thickness, or oval sections. For an open tank, subtract one base circle from the total shown.
How to use
- Pick metric (cm) or imperial (in).
- Enter the base radius, not the diameter.
- Enter the height between bases.
- Read total surface first, then volume.
- Read side area for paint or labels.
- Halve the radius entry if you measured across.
Formula
- r
- Radius of the circular base, in cm or in.
- h
- Height between the two bases, in the same unit.
- pi
- 3.14159..., used for circles and sides.
Right circular cylinder with flat ends. At height zero the solid flattens to two disks; at radius zero there is no solid. Open tanks drop one base circle from the total.
Worked example
Example: radius 6 cm, height 10 cm
Defaults: metric radius 6 cm with height 10 cm. Imperial mirror is 2.4 in by 3.9 in.
- Inputs (metric default): radius 6 cm, height 10 cm.
- Surface: 2 pi times 6 times 16 is 603.19 cm2.
- Volume: pi times 36 times 10 is 1131 cm3.
- Side: 2 pi times 6 times 10 is 376.99 cm2.
- Imperial mirror (2.4 in, 3.9 in) gives 95 in2, 70.6 in3, 58.81 in2. Tool shows the same.
Reference table
| Size | Surface | Volume |
|---|---|---|
| 6 cm by 10 cm | 603.19 cm2 | 1131 cm3 |
| 3 cm by 5 cm | 150.8 cm2 | 141.4 cm3 |
| 5 cm by 12 cm | 534.07 cm2 | 942.5 cm3 |
| 2.4 in by 3.9 in | 95 in2 | 70.6 in3 |
| 5 in by 12 in | 534.07 in2 | 942.5 in3 |
Limits
- Right circular cylinders only. Tapers need cone math.
- Thin wall assumed. Thick walls need inner and outer passes.
- Flat ends. Dished or domed ends add area.
- No waste or seams. Sheet work needs extra.
Common mistakes
- Entering diameter as radius, which quadruples circles.
- Mixing radius units with height units.
- Forgetting the second base on a closed tank.
- Using surface when capacity needs volume.
- Rounding pi early and drifting on large tanks.
Try it yourself
Quick checks. Answers sit tucked under each question.
Radius 3 cm, height 5 cm?
Surface is 2 pi times 3 times 8 is 150.8 cm2. Volume is pi times 9 times 5 is 141.4 cm3. Side is 94.25 cm2.
Radius 5 cm, height 12 cm?
Surface is 2 pi times 5 times 17 is 534.07 cm2. Volume is pi times 25 times 12 is 942.5 cm3. Side is 376.99 cm2.
Questions
What is the surface formula?
SA = 2 pi r squared plus 2 pi r h, or 2 pi r (h plus r). Here 2 pi times 6 times 16 is 603.19 cm2.
How is volume figured?
V = pi r squared h. Here pi times 36 times 10 is 1131 cm3.
What is the side area alone?
Side = 2 pi r h. Here 2 pi times 6 times 10 is 376.99 cm2.
Does this work for oval tanks?
No. This is a right circular cylinder. Elliptical or tapered tanks need other formulas.
Can I mix cm and inches?
Use one unit per calculation. Convert first if radius is in cm and height is in inches.
What happens if I double the size?
Surface grows with the square, volume with the cube. Double both and surface quadruples while volume grows eightfold.
Sources
- OpenStax Contemporary Math: Volume and Surface Area
- LibreTexts K12: Surface Area and Volume of Cylinders