Cylinder Calculator — Radius, Height, Surface Area, Volume

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)

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.).