Surface Area of a Cylinder Calculator

Enter a cylinder's radius and height to get its total surface area, lateral (side) surface area, and base area using SA = 2πr(r + h), plus an optional material cost estimate.

Quick Facts

Total surface area formula
SA = 2πr² + 2πrh = 2πr(r + h)
Adds the two circular bases to the curved lateral surface.
Lateral surface area formula
L = 2πrh
The curved side "unrolled" into a rectangle of width 2πr and height h.
Base area formula
B = 2πr²
Combined area of the top and bottom circles.

Your Results

Calculated
Total Surface Area
-
SA = 2πr(r + h)
Lateral (Side) Surface Area
-
L = 2πrh
Area of Both Bases
-
B = 2πr²
Estimated Material Cost
-
Total surface area × cost per square unit

Ready

Enter a radius, height, and unit, then press Calculate.

Formula and Method for the Surface Area of a Cylinder

A cylinder is a solid with two parallel, congruent circular bases connected by a curved lateral surface. Its total surface area is the sum of the areas of both circular bases and the curved side: SA = 2πr² + 2πrh, which factors to SA = 2πr(r + h), where r is the radius of the base and h is the height. This calculator also reports the lateral surface area alone (the curved side only) and an optional material cost estimate.

How the calculation works

Enter the radius and height of the cylinder in the same unit, then choose that unit. The calculator multiplies the radius by itself and by 2π to get the combined area of the two circular bases (2πr²), multiplies the radius, height, and 2π to get the lateral surface area (2πrh) — the curved side "unrolled" into a rectangle whose width equals the base's circumference (2πr) and whose height is h — and adds the two together for the total surface area, SA = 2πr² + 2πrh = 2πr(r + h). If you enter a cost per square unit, the tool multiplies it by the total surface area to estimate material cost.

Common mistakes

  • Radius vs. diameter: many product listings give diameter, not radius. Divide the diameter by 2 before entering it here — using the diameter as the radius doubles it and overstates every result.
  • Units: surface area is in square units (ft², m²). A cylinder with a 5 ft radius does not have "5 ft" of surface area — the units square when you multiply lengths together.
  • Confusing lateral and total area: if you only need the wrap-around area — like a label on a can — use the lateral surface area (2πrh), not the total, since the total also counts the top and bottom circles.

Real-world applications

  • Sizing labels, wraps, and sheet metal for cans, pipes, drums, and rollers uses lateral surface area
  • Painting or coating tanks, silos, and cylindrical columns uses total surface area to estimate paint or coating needed
  • Packaging design and shipping-tube fabrication use total surface area to estimate material cost
  • Heat-transfer and insulation calculations use a cylinder's surface area to compute heat loss or exchange rates

Frequently Asked Questions

What is the formula for the surface area of a cylinder?
The total surface area of a cylinder is SA = 2πr² + 2πrh, which factors to SA = 2πr(r + h), where r is the base radius and h is the height. For example, a cylinder with r = 5 ft and h = 10 ft has SA = 2π(5)(5 + 10) = 2π(5)(15) ≈ 471.24 ft².
What is the difference between total and lateral surface area?
Lateral (curved) surface area, L = 2πrh, is only the area of the curved side — like a label wrapped around a can. Total surface area adds the area of the two circular bases, 2πr², to the lateral area: SA = L + 2πr² = 2πr(r + h).
How do I convert diameter to radius before using this calculator?
Divide the diameter by 2: r = d / 2. If a cylinder's diameter is 10 in, its radius is 5 in. Entering the diameter in place of the radius will overstate both the lateral and total surface area.
How much extra material should I budget for wrapping or coating a cylinder?
Add roughly 5–10% to the calculated surface area to allow for overlap, seams, trimming, and coating over-spray.

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