What is the formula for the lateral surface area of a cylinder?

The lateral (curved) surface area of a cylinder is 2 x pi x radius x height. If you unroll the curved surface it becomes a rectangle with width equal to the circumference and height equal to the cylinder height. For r=5 and h=10: lateral SA = 2 x pi x 5 x 10 = 314.16 square units.

How do you find the total surface area of a cylinder?

Add the lateral surface area to the two circular ends: total SA = 2 x pi x r x h + 2 x pi x r squared = 2 x pi x r x (r + h). For r=5 and h=10: total SA = 2 x pi x 5 x 15 = 471.24 square units.

What is the difference between lateral and total surface area?

The lateral surface area covers only the curved side of the cylinder, without the top and bottom circles. The total surface area includes both circular ends as well. Use lateral area when calculating material for a tube or pipe with open ends, and total area when the cylinder is a closed can or tank.

Cylinder Surface Area Calculator

A cylinder has two circular ends and a curved side that connects them, and its surface area breaks into two parts: the lateral (curved) surface and the two circular caps. This calculator focuses on surface area because that is what you need for coating, painting, wrapping, or specifying sheet material, and returns three values from just two inputs: the radius and the height. The lateral surface area is the curved side only, the part that would unroll into a flat rectangle with width equal to the circumference of the circle. The two end circles each have an area of pi times the radius squared. The total surface area adds all three pieces together. Why separate them? Because many real objects are open at one or both ends. A pipe or a chimney flue has no circular caps, so you only need the lateral area. A tin can needs both ends too, so the total is what matters. Similarly, a painted pipe might need only the outside curved surface, while a closed water tank needs the complete total. This calculator therefore gives you both so you can pick the right one for your purpose. Enter the radius and height in any consistent unit. The results update as you type. The formulas involve pi, so you will get exact decimal values to two places, suitable for quoting to a supplier or checking homework. A site calculator for cylinder volume already exists separately; this tool is dedicated to the surface area problem.

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Radius (r)

units

Height (h)

units

471.24

total surface area (square units)

Lateral (curved) SA314.16

Each circular end78.54

How it works

The lateral surface area is 2 × π × r × h, which is the circumference of the circle multiplied by the height. Each circular end cap has area π × r². The total surface area is lateral SA plus two end caps: 2πr h + 2πr² = 2πr(h + r). If one end is open, add just one end cap to the lateral area instead of two.

Worked example

For a cylinder with radius 5 and height 10: lateral surface area = 2 × π × 5 × 10 = 100π ≈ 314.16 square units. Each circular end = π × 25 ≈ 78.54 square units. Total surface area = 2 × π × 5 × (10 + 5) = 150π ≈ 471.24 square units. These match the pre-filled defaults above.

Related calculators

Cone Surface Area Calculator: lateral and total surface area of a cone.
Sphere Surface Area Calculator: surface area and volume of a sphere.
Surface Area Calculator: multi-solid surface area chooser.
Cube Calculator: volume and surface area of a cube.

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