What Is the Lateral Surface Area of a Cylinder?
The lateral surface area of a cylinder is the area of its curved side — the part you would see if you removed the top and bottom circular caps. For an open cylinder (a tube), this is the only surface there is. If you unroll the curved side, it forms a rectangle whose width equals the base circumference and whose height equals the cylinder height. This calculator computes that area instantly using the formula \(A = 2\pi r h\).
How to Use This Calculator
Enter the radius (\(r\)) of the circular base and the height (\(h\)) of the cylinder, in any consistent unit (cm, m, inches, etc.). The result is the lateral surface area in square units of whatever unit you used. The tool also reports the base circumference (\(2\pi r\)) so you can see how the rectangle that wraps the cylinder is built.
The Formula Explained
The curved surface, when unrolled flat, is a rectangle. Its width is the distance around the base, which is the circumference \(2\pi r\). Its height is simply the cylinder height \(h\). Multiplying width by height gives the area: $$A = 2\pi r \times h = 2\pi r h$$ Note this excludes the two end circles; to include both caps for a closed cylinder you would add \(2\pi r^2\).
Worked Example
Suppose a cylinder has radius \(r = 5\) and height \(h = 10\). Then $$A = 2 \times \pi \times 5 \times 10 = 100\pi \approx 314.16 \text{ square units.}$$ The base circumference is \(2\pi \times 5 = 10\pi \approx 31.42\) units, and multiplying by the height of \(10\) confirms the area of about \(314.16\).
FAQ
Does this include the top and bottom? No. Lateral surface area covers only the curved side. Add \(2\pi r^2\) for both caps to get the total surface area.
What units are used? Any consistent unit. If \(r\) and \(h\) are in meters, the area is in square meters.
What's the difference between lateral and total surface area? Total surface area = lateral area + the two circular ends = \(2\pi r h + 2\pi r^2\). An open cylinder only has the lateral part.
