Lateral Surface Area Cylinder Calculator

Background.

Peel the label off a tin can and flatten it, and you are holding a rectangle. One side is the height of the can; the other is the distance around it. That rectangle is the can's lateral surface area, the curved side alone without the top and bottom, and the unrolling trick is the entire formula: circumference times height, or 2πrh.

Plenty of real jobs want exactly this part of a cylinder and nothing else. A painter quoting for round columns, a fabricator rolling a steel tank shell, someone wrapping insulation around a hot-water cylinder or printing a label for a jar: none of them need the end discs. Add the ends and you have the total surface area, 2πrh + 2πr², the figure for a closed can made from sheet metal.

Because the formula multiplies radius by height, quite different cylinders can share a curved area. One 3 units in radius and 5 tall has the same lateral area as one 5 in radius and 3 tall, 30π or about 94.25 square units, even though the wider one holds two-thirds more.

A common slip is entering a diameter where the radius belongs, which doubles the answer. If you measured the width straight across, halve it first; if you taped around the outside, divide by 2π.

For pipes and tanks, decide which surface you mean. Paint and outer insulation follow the outside radius; an internal lining follows the inside one, and on a thick-walled pipe the two differ noticeably. The page assumes a right cylinder, with the side square to the ends, and treats the surface as smooth.

What is lateral surface area cylinder calculator?

The lateral surface of a cylinder is its curved side: every point at distance r from the central axis, between the two flat ends. Its area equals that of the rectangle you get by slitting the side straight along its length and unrolling it, with one edge equal to the circumference 2πr and the other to the height h. It leaves out the two circular ends, each of area πr², which together with the curved side make up the total surface area.

How to use this calculator.

1. 01Enter the cylinder radius, the distance from the centre of a round end to its edge. If you measured a diameter, halve it; if you taped the girth, divide by 2π, about 6.283.
2. 02Enter the height, the length of the cylinder along its axis. For a pipe lying on its side, this is simply the pipe's length.
3. 03Use the same unit for both. Radius and height in metres give square metres; in inches, square inches.
4. 04Add the ends yourself if you need them: each is πr², so a closed cylinder's total is the result plus 2πr², and an open-topped tank's is the result plus πr².

The formula.

A = 2πrh, where r is the radius, h the height and π about 3.14159. The factor 2πr is the circumference of the circular end, and multiplying by h sweeps that circumference along the length of the cylinder. Written with the diameter d, the same formula is A = πdh. The area is proportional to each input on its own, so doubling either the radius or the height doubles the lateral area, and doubling both makes it four times larger. Volume behaves differently, rising with the square of the radius: curved area per unit of volume works out to 2 ÷ r, which is why a wide, squat tank needs less wall per litre than a tall, narrow one of the same capacity. Both inputs must be positive. The formula holds for a right circular cylinder only; an oblique cylinder, whose side leans, has a larger curved surface than 2πr times its vertical height.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. Precalculus 2e, 2021. Trigonometry and analytic geometry chapters. Retrieved 2026-08-06.
2. [2]OpenStax, Rice University. College Algebra 2e, 2021. Algebra and function chapters. Retrieved 2026-08-06.
3. [3]NIST/SEMATECH. e-Handbook of Statistical Methods, 2012. Chapter 1.3 and Chapter 4. Retrieved 2026-08-06.