How do I calculate the surface area of a cylinder?

A cylinder has three measurable surfaces: the circular top, the circular bottom, and the curved lateral surface. Use these formulas depending on what you need to paint, wrap, or cover:

Base Area (ft²) = π × r² | Lateral Area (ft²) = 2π × r × h | Total Surface Area (ft²) = 2π × r² + 2π × r × h

For volume: Volume (ft³) = π × r² × h. Divide by 7.48 to convert to gallons, or by 27 for cubic yards.

When to Use Each Formula

Painting a cylinder: Use lateral area (the curved side only)
Covering top and bottom lids: Add 2 × base area
Filling with liquid or material: Use volume

How to Measure a Cylinder

Measure the radius or diameter: Measure across the circular top or bottom at the widest point. Divide by 2 for the radius.
Measure the height: The vertical distance from the base to the top.
Select what to calculate: Base area, lateral area, total surface area, or volume.

Common Cylinder Calculations

Object	Typical Diameter	Use Case
Round pillar	1–2 ft	Paint coverage
Water tank	4–8 ft	Volume (gallons)
Grain silo	20–30 ft	Storage capacity
Round pool	15–24 ft	Water volume
Tree trunk	1–4 ft	Wrapping material

Frequently Asked Questions

Total Surface Area = 2π × r² + 2π × r × h. Add the two circular ends (2πr²) to the curved side (2πrh). For a cylinder 3 ft in radius and 10 ft tall: 2π(9) + 2π(3)(10) = 56.55 + 188.50 = 245.04 sq ft.

The lateral area is the curved side only: 2π × r × h. Think of it as the area of a rectangle rolled into a tube — width = circumference (2πr), height = h.

Volume = π × r² × h. A cylinder 5 ft in radius and 8 ft tall holds π × 25 × 8 = 628.32 cu ft (about 4,699 gallons).

Calculate the lateral surface area (2πrh). One gallon of paint covers roughly 350–400 sq ft. Divide the lateral area by the coverage rate to get the number of gallons needed.

Yes. Calculate the full cylinder surface area and divide by 2 for the curved part, then add the rectangular flat face (diameter × height) and one semicircle base if needed.