Surface Area of a Cylinder Calculator
Enter radius and height to find lateral area, base area, total surface area, and volume.
What Is a Cylinder?
A right circular cylinder is a three-dimensional solid with two parallel circular bases connected by a curved lateral surface. The axis (line connecting the centers of the two bases) is perpendicular to the bases. The radius r is the radius of each circular base, and the height h is the perpendicular distance between the bases. Cylinders are among the most common shapes in engineering and everyday life, prized for their structural strength, ease of manufacture, and efficient volume-to-surface-area ratio.
Lateral Surface Area: Unrolling the Cylinder
The lateral surface area (also called the curved surface area) is the area of the curved side, excluding the top and bottom circles. The key insight is to imagine cutting the cylinder along a vertical line and unrolling it flat — the result is a rectangle. The width of this rectangle equals the circumference of the base circle (2πr), and the height equals h. Therefore:
Lateral Area = 2Ï€rh
Total Surface Area Formula
The total surface area of a closed cylinder (with both circular caps) adds the lateral area to the area of both circles:
SA = 2πr² + 2πrh = 2πr(r + h)
Two bases (2πr²) + Lateral area (2πrh)
For example, a cylinder with radius 5 cm and height 10 cm: SA = 2π(25) + 2π(5)(10) = 50π + 100π = 150π ≈ 471.24 cm².
Volume Formula
The volume of a cylinder is the area of the circular base multiplied by the height: V = πr²h. For the example above: V = π(25)(10) = 250π ≈ 785.40 cm³. Volume grows with the square of the radius, which is why doubling the radius quadruples the volume even without changing the height.
Open vs Closed Cylinders
Not all cylinders are closed. An open cylinder (such as a pipe or tube) has no circular caps and only the lateral surface area applies: SA = 2πrh. A half-open cylinder (like a cup or tin can open at the top) includes one base: SA = πr² + 2πrh. The fully closed cylinder formula SA = 2πr² + 2πrh applies to sealed containers like canned goods. Choosing the right formula depends on the real-world object you're measuring. This calculator lets you see all three values simultaneously.
Real-World Applications
Cylinder surface area calculations are essential across many fields. In packaging design, engineers calculate how much sheet metal is needed to make a can — minimizing material while maximizing volume. A 330 ml beverage can (roughly r = 3.3 cm, h = 11.5 cm) has a total surface area of about 310 cm². In construction, cylindrical concrete pillars require surface area calculations for waterproofing or painting. Pipe manufacturers use lateral surface area to determine how much coating material is needed per meter of pipe. In engine design, the lateral surface area of cylinders affects heat transfer and cooling requirements. Understanding surface area also helps in insulating storage tanks and determining paint coverage for cylindrical water towers.
Cylinder vs Prism
A cylinder is the circular analog of a prism. Both have two congruent parallel bases connected by a lateral surface. For a prism, the bases are polygons and the lateral faces are rectangles; for a cylinder, the bases are circles and the lateral surface is curved but can be unrolled into a rectangle. The formulas are analogous: prism lateral area = perimeter of base × height; cylinder lateral area = circumference of base × height (2πr × h). As the number of sides of a regular prism increases toward infinity, it approaches a cylinder.