Cylinder Calculator
Compute volume, total and lateral surface area, circumference, and aspect ratio of a cylinder from radius, diameter, circumference or a target metric.
Dimensions
Updates as you typeShape · unrolled lateral
The lateral surface of a cylinder unrolls into a flat rectangle — its area is the product of circumference (2πr) and height (h). That's why lateral surface equals 2πrh.
Scale comparison · finding the optimal can
varying h · fixed r| h / d | Height | Volume | Lateral | Total SA | SA vs. minimum |
|---|---|---|---|---|---|
| Enter radius and height to see the comparison. | |||||
For a fixed radius, surface area is minimised when h = 2r (one diameter tall). Below that the extra cap area dominates; above it the lateral surface grows faster than the height saves.
Formula
- V
- Volume — space enclosed by the cylinder
- SA
- Total surface area — side + both circular caps
- L
- Lateral area — just the side, equal to the unrolled rectangle's area
- r, h
- Radius and height — the two free parameters
- d
- Diameter — 2r
- C
- Circumference — 2πr, the perimeter of the circular cap
- r = —, h = —
- Base area = πr² = —
- Volume = πr²h = —
- Circumference = 2πr = —
- Lateral area = 2πr·h = —
- Total SA = 2πr(r+h) = —
The lateral area is the one that trips people up — it's not πr·h, it's 2πr·h, because the side "unrolls" into a rectangle whose width is the full circumference (2πr), not the radius. Fun fact: for a given volume, SA is minimised when h = 2r — the reason real cans are roughly as tall as they are wide.