How to find a cylinder's surface area
A cylinder's total surface area is the two circular ends plus the curved side: SA = 2 × π × r × (r + h). This equals 2πr² (the two caps) plus 2πrh (the wrap). For r = 3 and h = 5, SA = 2 × π × 3 × 8 = about 150.80 square units.
The factored form is just the two-part version tidied up: 2πr² + 2πrh both share 2πr, so pulling it out leaves 2πr(r + h). With r = 3 and h = 5 the caps contribute 2π × 9 ≈ 56.55 and the wrap 2π × 3 × 5 ≈ 94.25, and those two add to the same 150.80. For what the cylinder holds rather than what wraps around it, use the cylinder volume calculator.
How to use this calculator
Enter the radius and the height. If you only have the diameter, halve it for the radius. The result is in square units of your length unit. To exclude the ends, the curved part alone is 2πrh. The two flat ends are plain discs, so the area of a circle calculator checks that part of the total.
- Use one unit throughout. Mixing centimetres and metres is the most frequent mistake; convert first.
- Diameter, not radius, is the other classic slip — entering 6 instead of 3 here more than doubles the answer.
- Surface area is not volume. Volume uses πr²h and comes out in cubic units.
Caps and curved side
The 2πr² term is the area of both flat circles; the 2πrh term is the side rolled flat into a rectangle. The circumference 2πr that forms that rectangle's width comes from the circle circumference calculator.
Frequently asked questions
- What is the formula for cylinder surface area?
- SA = 2 × π × r × (r + h), which is 2πr² for the two ends plus 2πrh for the curved side.
- What is the surface area of a cylinder with radius 3 and height 5?
- About 150.80 square units.
- How do I get just the curved side?
- Use 2 × π × r × h, leaving out the two circular ends.
- What units is the surface area in?
- Square units of whatever length unit you used for radius and height.
- What about a tube or a can with only one end?
- Add one cap instead of two: use 2πrh + πr² for an open-topped can, and just 2πrh for an open pipe. Subtracting one πr² term from the full formula each time gives the same result.