Cylinder Surface Area Calculator
Compute cylinder surface area from radius and height.
For can labels, paint estimation on columns, and sheet metal cylinder fabrication.
SA = 2 × π × r² + 2 × π × r × h = 2 × π × r × (r + h)
Two circular ends plus the curved side. The curved side is a rectangle when unrolled — its width is the circumference (2πr) and its height is h, so its area is 2πr × h.
Worked example — soda can label: A standard 12 oz aluminum can has r = 1.3 in, h = 4.83 in. Label area (curved side only, no top or bottom): 2π × 1.3 × 4.83 ≈ 39.45 sq in. That’s the printed wrapper area. Total cylinder surface: 39.45 + 2π × 1.69 = 39.45 + 10.62 = 50.07 sq in.
Why labels exclude top and bottom: the can lid is stamped separately (different metal alloy, different printing equipment), and the can bottom doesn’t get labeled because it sits on store shelves.
Worked example — painting a round column: A 12-inch-diameter porch column 8 feet tall. r = 6 in = 0.5 ft. Side area = 2π × 0.5 × 8 = 25.13 sq ft. You skip the bottom (sits on floor) and the top (capital or beam attachment). Just the curved side.
A quart of exterior paint covers ~100 sq ft per coat. One quart paints 4 such columns per coat — two coats = 2 quarts per 4 columns.
Where cylinder surface area matters in practice:
- Can and bottle labels. Printed wrapper area for cans, bottles, jars, tubes.
- Round column painting. Porch columns, lamp posts, sign poles.
- Tank painting. Industrial tanks for water, fuel, chemicals. Paint estimates rely on surface area, not volume.
- Pipe wrap and insulation. Length of pipe × circumference = surface area for foam pipe sleeves or heat tape.
- Drum exterior decals. 55-gallon drums, oil drums, rain barrels — decal area for branding or hazard labels.
- Heat exchanger surface. Heat-transfer efficiency depends on contact surface area between fluid and wall.
Lateral surface vs. total surface:
People often want just the lateral (curved side) surface — the printable label area. The two ends are separate considerations.
| Quantity | Formula |
|---|---|
| Lateral surface | 2πrh |
| One circular end | πr² |
| Total surface | 2πr(r + h) |
Conversion shortcuts for paint coverage:
- Latex flat: ~400 sq ft/gallon, 2 coats
- Exterior acrylic: ~350 sq ft/gallon, 2 coats
- Industrial epoxy: ~150-250 sq ft/gallon depending on viscosity
- Most coatings need 1.2-1.5× the geometric SA to account for irregularities, drips, and proper film build
Sphere vs. cylinder of the same diameter:
A cylinder of diameter d and height d has SA = 2π(d/2)² + 2π(d/2) × d = πd²/2 + πd² = 3πd²/2 ≈ 4.71 × d². A sphere of diameter d has SA = 4π(d/2)² = πd² ≈ 3.14 × d². So the sphere has about 67% of the cylinder’s surface — same proportion as the volume ratio. Archimedes was thorough.