Math & Science
Cylinder Circumference Calculator
Work from a radius, a diameter, or a tape measure around the outside — whichever you actually have.
Cylinder Circumference Calculator
About the Cylinder Circumference Calculator
The circumference of a cylinder is the distance around its circular face: C = 2πr, or πd if you have the diameter. This calculator works from a radius, a diameter, or a circumference — whichever you actually managed to measure.
That third option matters more than it sounds. On a pipe, a tree or a tank in situ, getting a tape around the outside is often the only measurement you can take. The tool reverses the formula to give you the radius and diameter from it.
Add a height and you also get the curved (lateral) surface area, the total surface area including both ends, and the volume — which covers most of what anyone needs a cylinder calculation for.
How to use the Cylinder Circumference Calculator
- Choose what you know — radius, diameter or circumference.
- Enter that measurement.
- Optionally add the height for surface area and volume.
- Select Calculate.
- All results share whatever unit you entered.
How to calculate circumference of a cylinder: the formulas
C = 2πr = πd (circumference)
r = C ÷ 2π (radius, working backwards)
Lateral area = C × h = 2πrh
Total area = 2πrh + 2πr²
Volume = πr²h
Worked example
You put a tape around a pipe and read 22 cm. It is 150 cm long. What is the diameter, and how much paint covers it?
Radius: 22 ÷ (2π) = 3.50 cm, so the diameter is 7.00 cm.
Curved surface: 22 × 150 = 3,300 cm² = 0.33 m².
Volume: π × 3.50² × 150 = 5,773 cm³
7 cm diameter — 0.33 m² to paint — 5.77 litres capacity
Why measuring the circumference beats measuring the diameter
Getting a tape across the exact centre of a circle by eye is hard, and any miss reads short. Wrapping a tape around is easy and self-correcting. Then divide by π.
There is a precision bonus too. Because C = πd, a circumference reading is about 3.14 times larger than the diameter it represents, so the same 1 mm reading error becomes roughly three times less significant. This is exactly why foresters measure tree girth and machinists use pi tapes calibrated to read diameter directly.
Curved area or total area?
- Lateral (curved) area — just the tube, no ends. Use it for painting a pipe, wrapping a label round a tin, or lagging a duct.
- Total surface area — the tube plus both circular ends. Use it for a sealed tank, a closed drum, or anything where the ends need coating too.
The gap is 2πr². On a short, fat cylinder the ends dominate; on a long, thin one they barely register. For a pipe 3.5 cm in radius and 150 cm long, the ends add only 77 cm² to 3,300 — about 2%. Halve the length and they matter twice as much.
| Circumference | Diameter | Radius | Base area |
|---|---|---|---|
| 10 cm | 3.18 cm | 1.59 cm | 7.96 cm² |
| 20 cm | 6.37 cm | 3.18 cm | 31.8 cm² |
| 30 cm | 9.55 cm | 4.77 cm | 71.6 cm² |
| 50 cm | 15.9 cm | 7.96 cm | 199 cm² |
| 100 cm | 31.8 cm | 15.9 cm | 796 cm² |
| 200 cm | 63.7 cm | 31.8 cm | 3,183 cm² |
Notice that doubling the circumference quadruples the base area. Area scales with the square of any linear dimension, which is why a pipe of twice the girth carries roughly four times the flow.
Measuring a pipe accurately
- Wrap the tape square to the axis. A tape at a slight angle traces an ellipse and reads long.
- Pull it snug, not tight. Overtightening on lagged or soft pipe compresses it and reads short.
- Take the reading at the overlap, and repeat in two or three places along the length.
- Know which diameter you need. A tape gives the outside diameter. For flow capacity you need the inside — subtract twice the wall thickness.
Plumbing sizes are often nominal rather than actual. A "half-inch" pipe measures neither 0.5 in inside nor outside in most standards. Measure the real thing rather than trusting the label.
For tanks including partly filled ones, use the tank area calculator. For other solids, the volume calculator covers seven shapes.
Related guides
Other ways to use this calculator
- Circumference formula — C = 2 pi r, or pi times the diameter.
- Pipe circumference — measure the outside diameter, or wrap a tape around the pipe.
- Cylinder surface area — the curved area is circumference × height.
- Circumference of a cylinder calculator — the cylinder circumference formula is C = πd, the same as for its circular end.
Frequently asked questions
The circumference of a cylinder is the distance around its circular face: C = 2πr, or πd from the diameter. A pipe of radius 3.5 cm has a circumference of 2 × π × 3.5 = 22 cm. This is the circumference of the circle at either end — the cylinder's height plays no part in it. Multiply the circumference by the height to get the curved surface area.
Divide the circumference by 2π, which is about 6.283. A tape reading 22 cm gives 22 ÷ 6.283 = 3.50 cm radius, and double that for a 7 cm diameter. Measuring the circumference is often more accurate than measuring across the middle, because a tape wrapped round is easy to place and a diameter measured by eye tends to miss the centre.
Curved (lateral) surface area is just the tube: 2πrh. Total surface area adds both circular ends, giving 2πrh + 2πr². Use curved area for painting a pipe or wrapping a label, and total area for a sealed tank or drum. On a long thin cylinder the ends add almost nothing; on a short fat one they dominate.
Wrap a tape around it square to the axis, pull snug rather than tight, and read at the overlap — then divide by π for the diameter. Repeat in two or three places. Remember a tape gives the outside diameter; for flow capacity subtract twice the wall thickness. Be aware that plumbing sizes are often nominal, so a "half-inch" pipe rarely measures half an inch anywhere.
Use C = 2πr, or C = πd if you know the diameter. A cylinder with a 5 cm radius has a circumference of 2 × 3.1416 × 5 = 31.4 cm. The height does not change the circumference.
Sources and further reading
- NIST — Guide for the Use of the International System of Units — length and area units used throughout
- Circumference — Encyclopaedia Britannica — the relationship between circumference, diameter and π
- NIST — Fundamental physical constants — reference values used in the conversions