How this calculator works
A right cylinder has two parallel circular bases and a curved side that meets them at right angles. The base area is πr², and because there are two identical bases the total surface adds them twice. The curved side, unrolled, is a rectangle of width 2πr and height h, so its area is 2πrh. Volume is the base area multiplied by the height. If you know the volume and one of the other measurements, dividing reconstructs the missing one.
Formula
V = πr²h; base area A_b = πr²; lateral area A_l = 2πrh; total area A = 2πr² + 2πrh; r = √(V/(πh)); h = V/(πr²).
Worked example
A cylinder with a radius of 3 m and a height of 5 m has a base area of 9π ≈ 28.274 m², a lateral area of 30π ≈ 94.248 m² and a total surface area of 48π ≈ 150.796 m². Its volume is 45π ≈ 141.372 m³.
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Frequently asked questions
Is the lateral area the same as the total area?
No. The lateral area covers only the curved side. The total area also includes the two circular bases, which add 2πr².
Why is the curved side 2πrh?
Cut the curved surface down one side and unroll it. It becomes a flat rectangle whose width equals the circumference 2πr and whose height is the cylinder height h.
Can a cylinder have a negative height?
No. A physical cylinder needs positive dimensions. Negative and zero measurements are rejected because they cannot form a solid or would make the division in solve mode undefined.