How much material covers the outside of a cylinder — both circular ends plus the curved side.
How it works
The two circular ends contribute 2πr², and the curved side (unrolled into a rectangle) contributes 2πrh; adding them gives the total surface area.
What this does not include
This does not include volume — for how much a cylinder holds, use this site’s cylinder volume calculator instead. These are two different questions about the same shape.
How to use this calculator
- Enter the radius and height.
A worked example
A cylinder with radius 3, height 5: surface area = 2πr² + 2πrh = 150.796447.
A cylinder with radius 2, height 10: surface area is also 150.796447 — a shorter, wider cylinder and a taller, narrower one can share the same total surface area.
What the variables mean
| Variable | Meaning |
|---|---|
| Radius | Radius of the circular top and bottom |
| Height | Distance between the top and bottom |
Edge cases worth knowing
Different radius/height combinations can produce identical surface areas, as the two examples above show — surface area alone doesn’t uniquely determine a cylinder’s shape.
A radius of zero collapses the cylinder to a line with no surface, so the calculator declines to show a result.
Frequently asked questions
Why does the formula have two separate terms?
One term (2πr²) covers the flat top and bottom circles; the other (2πrh) covers the curved side wrapped around, unrolled flat as a rectangle whose width equals the circumference.
What’s a practical use for this?
Estimating the material needed to wrap or paint a cylindrical tank, can, or pipe.
Does a taller cylinder always have more surface area than a wider one?
Not necessarily — a short, wide cylinder and a tall, narrow one can have very different surface areas even with similar volumes, since the two terms scale differently with radius and height.
