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Math

Cylinder Volume & Surface Area Calculator

Enter the base radius r and height h of a right circular cylinder to instantly get the volume V = πr²h, lateral (curved) surface area 2πrh, base area πr², total surface area, diameter and base circumference — handy for tank / can / pipe capacity and geometry homework.

Volume V

785.3982

Lateral area A_l

314.1593

Base area A_b

78.5398

Total surface area A_t

471.2389

Diameter d

10

Base circumference C

31.4159

Formula

V = πr²h ; A_l = 2πrh ; A_b = πr² ; A_t = 2πr(h + r)

Units are up to you (cm, m, in, ft, m all fine). Radius and height share one linear unit; areas use that unit squared; volume uses that unit cubed. 1 litre = 1000 cubic centimetres.

Formula

V = π r² h | lateral A_l = 2π r h | base A_b = π r² | total A_t = 2π r (h + r)

Frequently asked

How big is a 330 ml soda can?

A standard Euro 330 ml can is roughly 66 mm outer diameter (r ≈ 3.3 cm) and 11.5 cm tall. Plug it in: V = π × 3.3² × 11.5 ≈ 393 cm³. The ~60 cm³ overhead above 330 ml is head-space — gas room left between the liquid and the lid for thermal expansion.

A pipe 25 mm in diameter and 3 m long holds how many litres?

Convert first: r = 12.5 mm = 1.25 cm, length 300 cm. V = π × 1.25² × 300 ≈ 1473 cm³ ≈ 1.47 L. In the tool, enter r = 1.25 and h = 300 (cm) and you’ll get the same 1473 cm³.

What happens to the volume if I double the height? Or the radius?

Volume scales linearly with height: double h, double V. Radius is different — the formula has r squared (V = πr²h), so doubling r quadruples the volume (2² = 4). That is why "making the cup wider" affects capacity far more than "making it taller" by the same factor.

Why does the total surface area count the base TWICE?

A closed cylinder has TWO circular ends — one top, one bottom — so A_t = lateral + 2 × base. For an open-top container (a tumbler, an open tank) use A_l + 1 × A_b instead; for an open-ended pipe wall just A_l = 2πrh. The tool reports the closed-cylinder total — adjust by hand if your shape is open.

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