How to Calculate the Surface Area of a Cylinder
A cylinder has three surfaces: two circular bases (top and bottom) and one curved lateral surface (the side). To find the total surface area, you calculate the area of all three parts and add them together.
The Formula
Total Surface Area = 2πr² + 2πrh
Where:
- r = radius of the circular base
- h = height of the cylinder
- π ≈ 3.14159
You can factor this as: SA = 2πr(r + h)
The two parts:
- 2πr² — area of both circular bases
- 2πrh — lateral (side) surface area
Step-by-Step Example
Find the surface area of a cylinder with radius 5 cm and height 10 cm.
- Calculate the base areas: 2 × π × 5² = 2 × 3.14159 × 25 = 157.08 cm²
- Calculate the lateral area: 2 × π × 5 × 10 = 314.16 cm²
- Add: 157.08 + 314.16 = 471.24 cm²
Real-World Applications
- Manufacturing: Calculating material needed to make cans, pipes, or drums
- Painting: Estimating paint coverage for cylindrical tanks or pillars
- Packaging design: Determining label area for a cylindrical container
Lateral Surface Area Only
If you only need the side area (no caps, like a pipe or tube):
Lateral SA = 2πrh
For a pipe with r = 3 cm and h = 50 cm: 2 × π × 3 × 50 = 942.48 cm²
Use our cylinder surface area calculator to solve any cylinder dimensions instantly.