Right Cylinder Calculator (A, V, A_l, A

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A right circular cylinder — think of a soup can, a pipe, or a storage tank — has its volume and every part of its surface area follow directly from just two measurements: its radius and its height. It's one of the most common 3D shapes encountered in packaging design, plumbing and HVAC (pipe volume and surface area for insulation), and manufacturing (calculating material for cylindrical tanks, rollers, or containers).

How it works

Enter the radius (r) and height (h). The base area is that of a plain circle, A_base = πr². The lateral (side) surface area — imagine unrolling the curved wall into a flat rectangle — has width equal to the circle's circumference (2πr) and height h, giving A_lateral = 2πrh. Total surface area adds both circular ends (top and bottom) to the lateral surface: A_total = 2A_base + A_lateral. Volume is simply the base area times the height, V = πr²h, the same "area × height" logic used for any prism-like solid.

Enter radius.
Enter height.
Click Calculate to see your results.

Examples

Radius = 3, height = 7

V = π(9)(7) ≈ 197.92. Lateral area = 2π(3)(7) ≈ 131.95. Total area = 2π(9) + 131.95 ≈ 56.55 + 131.95 ≈ 188.50.

Radius = 4, height = 10

V = π(16)(10) ≈ 502.65. Lateral area = 2π(4)(10) ≈ 251.33. Total area = 2π(16) + 251.33 ≈ 100.53 + 251.33 ≈ 351.86.

Common mistakes to avoid

Forgetting to double the base area when computing total surface area — a cylinder has two circular ends, not one.
Using the diameter where the radius is expected (or vice versa), which throws off every formula by a factor of 2 or 4.
Confusing the lateral area (just the curved side) with the total area (which also includes both circular ends).

Frequently asked questions

A cylinder has two circular faces (top and bottom), each with area πr², so both must be counted separately before adding the curved lateral surface.

If you cut the curved wall of a cylinder along a vertical line and flatten it out, it forms a flat rectangle whose width equals the circle's circumference (2πr) and whose height equals the cylinder's height — multiplying those gives the lateral area.

A cylinder's volume (πr²h) is exactly three times a cone's volume ((1/3)πr²h) when they share the same radius and height — a classic geometric relationship.

You can ignore the area outputs entirely — V = πr²h stands on its own and doesn't depend on any of the surface-area calculations.

Doubling the height only doubles the volume, but doubling the radius quadruples it — since volume depends on r² but only on h to the first power.

A right cylinder has its two circular ends stacked directly above one another, with the lateral surface perpendicular to the bases; an oblique cylinder is tilted, so these same simple formulas no longer directly apply without additional adjustments.

Free Right Cylinder Calculator