Circumference of a Cylinder Calculator
This calculator works out the circumference of a cylinder, the distance around its circular base, along with related measurements you often need alongside it. Enter either the radius or the diameter of the cylinder, whichever you know, then add the height if you also want the surface areas worked out. Choose your unit of measurement from millimetres through to feet, and pick how many decimal places of pi to use for the calculation. The calculator instantly returns the circumference (C = 2 x pi x r), the diameter, the lateral surface area (the curved side wrapped flat, equal to circumference multiplied by height), and the total surface area, which adds both circular ends. A full breakdown underneath shows the radius, diameter, height and pi value used, plus the base area and combined area of both ends. This is useful for working out how far a wheel, roller or pipe travels in one rotation, sizing a label or wrap to fit around a can or tube, or checking pipe insulation and flange lengths. Because the circumference of a cylinder depends only on the radius of its circular base, changing the height alters the surface area but never the circumference itself. Results are only as accurate as the measurements you enter, so use a tape measure or callipers for anything beyond rough estimates.
1. Enter Dimensions
2. Unit of Measurement
Worked Example (defaults)
Radius = 5 cm, Height = 10 cm
C = 2 × π × 5 = 31.416 cm
Lateral surface area = C × h = 31.416 × 10 = 314.159 cm²
Circumference Breakdown
Surface Areas
What is the Circumference of a Cylinder?
A cylinder has two circular bases and a curved lateral surface. The circumference of a cylinder refers to the perimeter of one of its circular bases. Because the base is a circle, the formula is the same as any circle: C = 2 x pi x r, where r is the radius. You can also write this as C = pi x d, where d is the diameter.
The circumference is important when working out how far one rotation of a cylindrical object (such as a wheel, roller, or pipe) covers, and when "unrolling" the lateral surface into a flat rectangle for cutting or wrapping purposes.
The Formula
| What to find | Formula | Notes |
|---|---|---|
| Circumference from radius | C = 2 x pi x r | pi = 3.14159... |
| Circumference from diameter | C = pi x d | d = 2r |
| Radius from circumference | r = C / (2 x pi) | Inverse formula |
| Lateral surface area | LSA = 2 x pi x r x h | = C x h |
| Total surface area | TSA = 2 x pi x r x (r + h) | Includes both circular bases |
Worked Example
A cylinder has a radius of 5 cm and a height of 10 cm.
- Circumference = 2 x pi x 5 = 31.416 cm
- Diameter = 2 x 5 = 10 cm
- Base area = pi x 5 x 5 = 78.540 cm²
- Both bases = 2 x 78.540 = 157.080 cm²
- Lateral surface area = 31.416 x 10 = 314.159 cm²
- Total surface area = 157.080 + 314.159 = 471.239 cm²
Circumference vs Perimeter vs Arc Length
The circumference of a cylinder is the circumference of its circular cross-section. If you were to cut a label off a tin can and lay it flat, the width of that label equals the circumference. The height of the label would equal the height of the cylinder. This is why the lateral surface area formula is simply circumference multiplied by height (C x h): it is the area of a rectangle with those two dimensions.
The term "arc length" is sometimes used for a portion of the circle's perimeter. The full arc length around the circle equals the full circumference.
Practical Uses
- Pipes and tubes: The circumference tells you the outer perimeter for wrapping insulation or calculating flange seal lengths.
- Wheels and rollers: One rotation of a cylinder covers a distance equal to its circumference. A wheel with a radius of 30 cm travels 2 x pi x 30 = 188.5 cm per full rotation.
- Packaging and labels: When designing a label for a cylindrical container, the label width must match the circumference.
- Engineering: Gear pitch circles, hydraulic cylinders, and shafts all rely on circumference calculations.
Related Calculators
- Maths and Stats Calculators: all geometry and maths tools.
- Circumference Calculator: circumference from any radius or diameter.
- Cylinder Volume Calculator: volume from radius and height.
- Cylinder Surface Area Calculator: full lateral and total surface areas.
- Area of a Circle Calculator: base circle area from radius.
Method: Standard Euclidean geometry formula C = 2πr. Pi taken to 5 decimal places (3.14159) by default, configurable in the calculator above.
Results are mathematical calculations based on your inputs. Precision depends on the accuracy of your measurements. For engineering or manufacturing use, verify measurements with appropriate instruments.