Key takeaways
- The surface area of a cylinder is SA = 2πr² + 2πrh.
- 2πr² covers the two flat circular ends; 2πrh covers the curved side.
- The curved side, unrolled flat, is just a rectangle with width 2πr and height h.
- Surface area covers the outside; volume measures what fits inside.
In this guide
What is the surface area of a cylinder?
Surface area is the total area of every outer surface of the cylinder: the top circle, the bottom circle, and the curved side wrapped around them. It's measured in square units such as cm² or m². This is different from volume, which measures what fits inside, not what covers the outside.
Why does the surface area of a cylinder matter?
It tells you exactly how much metal sheet, paper, or paint is needed to build or cover a can-shaped object.
A soup can's paper label wraps only around the curved side, using2πrhof paper. The can itself needs two extraπr²metal discs on top of that for the lid and base — which is exactly why the full formula has two separate parts added together.
The formula
| Symbol | What it means | Example |
|---|---|---|
| SA | The total surface area you want to find | 207.35 m² |
| π (pi) | A fixed number, about 3.14159 | 3.14159 |
| r | The radius of the circular base | 3 m |
| h | The height of the cylinder | 8 m |
How to find the surface area step by step
- 1Measure the radius and height.
- 2Find the area of the two circular ends.
2 × π × r². - 3Find the area of the curved side.
2 × π × r × h. - 4Add the two results together.
- 5Add square units. Such as cm² or m².
Now try it yourself. Change the radius and height in the calculator below and watch the surface area update, with every step shown.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Confusing surface area with volume. Surface area is the outer covering, in square units; use the volume of a cylinder calculator instead if you need how much it holds.
- Skipping the curved side. Some people only calculate the two circles and forget the
2πrhpart that wraps around the middle, like the paper label on a can. - Using the diameter instead of the radius. Always halve the diameter before squaring.
Tips and tricks
- Calculate the two parts separately (end caps, then curved side) and add them at the end — it's easier to check for mistakes that way.
- Comparing to a similar shape with a pointed top? See the surface area of a cone calculator.
Where you'll use it in real life
- Manufacturing: figuring out how much metal sheet is needed to make a can.
- Packaging: working out how much paper wraps a label around a jar.
- Construction: estimating how much paint covers a cylindrical pillar.
- Industrial design: calculating material for pipes and cylindrical containers.
Quick summary
To find the surface area of a cylinder, add the area of the two circular ends (2πr²) to the area of the curved side (2πrh). Unrolled flat, the curved side is just a rectangle. Use the calculator above to check your own cylinder instantly.
Worked example
A cylindrical grain silo has a radius of 3 meters and a height of 8 meters. How much sheet metal is needed to build the silo, including the top and bottom?
- 01SA = 2πr² + 2πrh
- 02SA = 2π(3)² + 2π(3)(8)
- 03SA = 2π(9) + 2π(24)
- 04SA = 56.55 + 150.8
- 05SA = 207.35 m²
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I find just the curved (lateral) surface area, without the top and bottom?
Use only the 2πrh part of the formula, leaving out the 2πr² for the two circular ends. This is useful for a label that wraps around a can without covering the top or bottom.
What's the difference between surface area and volume of a cylinder?
Surface area (2πr² + 2πrh) is the material needed to cover the outside, in square units. Volume (πr²h) is how much fits inside, in cubic units. Use the [volume of a cylinder calculator](/calculator/volume-cylinder) for what it holds.
How do I find the surface area of a cylinder from the diameter?
Divide the diameter by 2 to get the radius, then use SA = 2πr² + 2πrh as usual.
Why does the formula have two separate parts?
Because a cylinder's surface is made of two different shapes: two flat circles (the ends) and one curved rectangle wrapped into a tube (the side), so each part is calculated separately and added together.
