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.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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