Circumference of a Cylinder Calculator
Enter a radius (or diameter) and height to instantly find the circumference of the circular cross-section, the lateral surface area, the total surface area, and the volume of the cylinder. Switch freely between metric and imperial units. The "Show your work" panel displays every step of the calculation so you can follow the arithmetic yourself.
What is the circumference of a cylinder?
A cylinder is a three-dimensional solid with two parallel, congruent circular faces (called bases) connected by a curved lateral surface. The circumference of a cylinder is simply the circumference of one of those circular faces - the distance around the edge of the circle. It is identical to the width of the cylinder's label if you unrolled the curved surface into a flat rectangle. Because both circular ends are identical, the circumference is the same at every height along the axis.
Circumference formula
The circumference C of a circle (and therefore of a cylinder's circular face) is C = 2 x pi x r, where r is the radius and pi is approximately 3.14159. If you know the diameter d instead of the radius, use C = pi x d, because d = 2r. If you only know the circumference and want to find the radius, rearrange to get r = C / (2 x pi). All three versions are equivalent - this calculator handles all three automatically based on which measurement you provide.
Surface area and volume
Knowing the circumference immediately gives you the lateral surface area: unroll the curved side and you get a rectangle with width equal to the circumference and height equal to the cylinder height, so Lateral area = C x h = 2 x pi x r x h. Add the two circular end caps (each with area pi x r^2) and you have the total surface area: A = 2 x pi x r x h + 2 x pi x r^2, which simplifies to A = 2 x pi x r x (h + r). The volume is V = pi x r^2 x h. These formulas share the same radius, so once you know one value you can derive all the others - which is exactly what this calculator does.
Practical uses
Cylinder geometry comes up in everyday situations. Wrapping a label around a can: the label width must equal the circumference. Insulating a pipe: the insulation area is the lateral surface. Filling a tank: volume tells you capacity. Painting a column: total surface area determines how much paint you need. Metal fabrication and 3D printing: all dimensions are needed to spec a part. The reverse-solve mode (enter a circumference to find the radius) is handy when you can measure around an object but cannot easily measure straight across it - for example, measuring around a tree trunk or a pipe with a tape measure.
Common cylinder sizes and their circumferences
| Object | Approx. diameter (cm) | Approx. circumference (cm) |
|---|---|---|
| Standard coin (25 mm) | 2.5 | 7.85 |
| Soda can | 6.6 | 20.7 |
| Tennis ball | 6.7 | 21.0 |
| Basketball | 24.0 | 75.4 |
| Standard pipe (1 in nominal) | 3.3 | 10.4 |
| Large tree trunk (30 cm dia) | 30.0 | 94.2 |
| Oil drum (standard 55 gal) | 57.2 | 179.6 |
Approximate values for familiar cylindrical objects. Circumference = 2 x pi x radius.
Frequently asked questions
What is the circumference of a cylinder?
The circumference of a cylinder is the perimeter of its circular cross-section - the distance all the way around the edge of either circular face. It is calculated as 2 x pi x radius, or equivalently as pi x diameter. Both circular ends have the same circumference because they are congruent.
What is the formula for the circumference of a cylinder?
C = 2 x pi x r, where r is the radius of the circular face and pi is approximately 3.14159. If you know the diameter (d = 2r), you can use C = pi x d instead. To reverse-solve for the radius from a known circumference, use r = C / (2 x pi).
How is circumference different from lateral surface area?
Circumference is a one-dimensional length - the perimeter of a single circular face. Lateral surface area is a two-dimensional area - the total area of the curved side of the cylinder. You calculate lateral area by multiplying the circumference by the cylinder height: Lateral area = C x h. Both quantities share the same formula base (2 x pi x r), but lateral area adds the height dimension.
How do I find the circumference if I only know the diameter?
Multiply the diameter by pi: C = pi x d. For example, a cylinder with a diameter of 10 cm has a circumference of pi x 10 = 31.42 cm. You can also use this calculator by selecting "Diameter" in the "Give me" dropdown.
Can I find the radius if I only have the circumference?
Yes. Divide the circumference by (2 x pi): r = C / (2 x pi). For example, a circumference of 31.42 cm gives r = 31.42 / (2 x 3.14159) = 5 cm. Select "Circumference (reverse-solve)" in the input mode to have this calculator do it for you automatically.
What is the total surface area of a cylinder?
The total surface area combines the curved lateral surface and both circular end caps. The formula is A = 2 x pi x r x h + 2 x pi x r^2, which simplifies to A = 2 x pi x r x (h + r). If you unroll the lateral surface you get a rectangle of width C (circumference) and height h, so the lateral portion is C x h. Each circular base has area pi x r^2, and there are two of them.
Does the height of the cylinder affect its circumference?
No. Circumference depends only on the radius (or diameter) of the circular face, not on the height of the cylinder. Two cylinders with the same radius but different heights will have exactly the same circumference. Height does affect lateral surface area, total surface area, and volume.