Cylinder Surface Area Calculator: total, lateral and base area
Calculate the total, lateral and base surface area of a cylinder from its radius or diameter and height, for a closed can, an open-top container or an open tube, with the answer in terms of π, the volume and steps. Or work back from the area to the height or radius.
How it works
Closed: A = 2πrh + 2πr² = 2πr(h + r) · Open top: A = 2πrh + πr² · Tube: A = 2πrh · r = d ÷ 2 · From the area: h = (A − 2πr²) ÷ (2πr), r = (−h + √(h² + 2A ÷ π)) ÷ 2 · Volume = πr²h
A cylinder’s surface has two parts: the curved side and the flat circular ends. Unrolled, the side is a rectangle whose width is the circumference 2πr and whose height is h, so the lateral area is 2πrh. Each end is a circle of area πr². A closed can has two ends, an open-top container such as a cup or tank has one, and a pipe or tube has none, so the total is 2πrh plus two, one or zero times πr². You can enter the diameter instead of the radius, and the calculator can also work backwards: from a known surface area and radius it finds the height, and from the area and height it solves the quadratic 2πr² + 2πhr = A for the radius. Results are shown as decimals and as an exact multiple of π, with the volume πr²h and circumference for reference. All lengths must be in the same unit; the area comes out in that unit squared.
Worked example
For radius 5 and height 12: lateral area = 2π × 5 × 12 = 376.9911, one base = π × 5² = 78.5398, so the two bases = 157.0796 and the total surface area = 376.9911 + 157.0796 = 534.0708 square units, which is exactly 170π. The volume is π × 5² × 12 = 942.4778 cubic units.
Sources: CalculatorSoup: Cylinder calculator (formulas and solve-for modes) · Math is Fun: Cylinder (worked example r = 2, h = 7) · Calculator.net: Surface area calculator (cylinder example)
Frequently asked questions
What is the formula for the surface area of a cylinder?
Total surface area = 2πrh + 2πr² = 2πr(h + r), where r is the radius and h is the height. For r = 2 and h = 7 that is 2π × 2 × 9 = 36π ≈ 113.097.
What is lateral surface area?
Lateral surface area is just the curved side of the cylinder, without the two end caps. It equals 2πrh, the circumference times the height, as if you unrolled the side into a rectangle.
When should I exclude the bases?
For open objects like a tube, a pipe or a label wrapped around a can, use the lateral area only. For a cup, bucket or open tank, count one base. Use the total with both ends when the cylinder is closed, like a sealed tin.
How do I find the surface area from the diameter?
Halve the diameter to get the radius, then use the formula. A cylinder 10 cm across and 12 cm tall has radius 5 cm and a total surface area of 534.07 cm². Choose “from diameter and height” above to skip the step.
How do I find the height from the surface area?
Subtract the area of the ends and divide by the circumference: h = (A − 2πr²) ÷ (2πr). For A = 534.07 and r = 5 that gives h ≈ 12.
How is this different from volume?
Surface area (square units) is the area of the outer skin; volume (cubic units) is the space inside, πr²h. The calculator shows both.
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This calculator is for educational purposes. Double-check important results before acting on them.