Surface Area of a Cylinder Formula

Geometry Formulas: Area, Volume, Perimeter
Formula:

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

Answer

Surface area of a cylinder
S = 2 · π · r² + 2 · π · r · h

Here r is the radius, h is the height, perpendicular to the base. The result comes out in square units.

Where the formula comes from

S = 2 · π · r² + 2 · π · r · h

Unroll the can. The side becomes a rectangle whose width is the circumference 2πr and whose height is h; the two ends are discs of πr² each. Add them: 2πr² + 2πrh.

Worked examples

Let r = 3, h = 10. Then the surface area of a cylinder ≈ 245.04 square units.

Let r = 1.5, h = 2.4. Then the surface area of a cylinder ≈ 36.76 square units.

The common mistake

Counting one end instead of two, or none. An open pipe has only the 2πrh; a tin can has both discs. Decide what the object actually is before adding.

Other quantities: Cylinder

Related Calculations

See Also

Geometry Formulas: Area, Volume, Perimeter

These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the surface area of a cylinder? (The answer is: S = 2 · π · r² + 2 · π · r · h). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter
Formula:

Values from the Formula (h = 10)

If r =Surface area
1≈ 69.12 square units
2≈ 150.8 square units
3≈ 245.04 square units
4≈ 351.86 square units
5≈ 471.24 square units
10≈ 1,256.64 square units

FAQ

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

Surface area of a cylinder S = 2 · π · r² + 2 · π · r · h

Where does this formula come from?

Unroll the can. The side becomes a rectangle whose width is the circumference 2πr and whose height is h; the two ends are discs of πr² each. Add them: 2πr² + 2πrh.

What is the most common mistake here?

Counting one end instead of two, or none. An open pipe has only the 2πrh; a tin can has both discs. Decide what the object actually is before adding.

How do I use this formula?

Put your own numbers in place of the letters. With r = 1.5, h = 2.4, for instance, the formula S = 2 · π · r² + 2 · π · r · h gives ≈ 36.76 square units.

See Also