Cylinder Calculator — Radius, Height, Surface Area, Volume

Enter any two values. Private by design — runs locally in your browser.

Diagram & Inputs

Tip: Enter any two values (r/d, h, S, L, or V). The calculator checks consistency if you provide more.

Results

How the Cylinder Calculator Works

A right circular cylinder is defined by its radius r and height h. From those, the key measures are:

  • Lateral surface area (side): L = 2πrh
  • Total surface area: S = L + 2πr² = 2πr(r + h)
  • Volume: V = πr²h

Provide any two values—such as r & h, r & S, h & V, L & V, or S & L. The tool solves for r and h (using exact formulas or a quick numerical method when needed), then derives the rest. If you enter more than two values, it checks for consistency within a small numerical tolerance.

Units: r, d, and h use a length unit (e.g., cm); L and S use squared units (e.g., cm²); V uses cubed units (e.g., cm³). Choose your preferred decimal places and π precision to match classroom or lab conventions.

Formulas & Solvable Pairs (Quick Reference)

  • Given r and h: L=2πrh, S=L+2πr², V=πr²h
  • Given r and S: h = S/(2πr) − r
  • Given r and V: h = V/(πr²)
  • Given h and S: r = (−h + √(h² + 2S/π))/2
  • Given h and V: r = √(V/(πh))
  • Given L and S: r = √((S − L)/(2π)), then h = L/(2πr)
  • Given L and V: r = 2V/L, then h = L/(2πr)
  • Given S and V: equation 2πr² + 2V/r − S = 0 (usually two solutions; the tool finds them numerically)

5 Fun Facts about Cylinders

Lateral area is a rectangle

Unroll a cylinder’s side and you get a rectangle of width 2πr and height h. That’s why L = 2πrh is just “perimeter × height.”

Unwrap trick

Volume scales fast

Double the radius and volume jumps by 4×; double the height and volume doubles. Radius changes dominate because of the r² term.

Scaling intuition

Pi choice matters

Using π = 22/7 overshoots true π by ~0.04%. On a 10 cm radius, that’s about 0.25 cm² error in area—tiny for homework, big for machining.

Precision check

Soap-film minimal

A soap film spanning two circles forms a “catenoid,” not a cylinder. Cylinders have constant radius; catenoids shrink in the middle to minimize surface area.

Physics twist

Capsule math

A pill shape is a cylinder plus two hemispheres. Its volume is πr²h + 4/3 πr³—useful for bottle or tank capacity estimates.

Beyond basic

Cylinder Calculator: FAQs

Which inputs are valid?

Any two of radius r (or diameter d), height h, total surface area S, lateral area L, or volume V. More values are fine; the tool checks consistency.

What formulas are used?

L = 2πrh, S = 2πr(r + h), V = πr²h. Closed-form rearrangements are used where possible; otherwise a brief numerical solve is applied.

Does the calculator keep my data private?

Yes. Computation is entirely client-side; nothing is uploaded.

Can I change units, decimals, or π?

Yes. Choose a length unit, set decimal places, and pick a π approximation (native precision, 22/7, etc.).

Explore more tools