Surface Area Of A Cylinder Calculator

What this calculator does

The surface area of a cylinder is its whole outside: the two circular ends, top and bottom, plus the curved side that wraps around between them. This tool gives you both parts and the total, from the cylinder's radius and height.

Type the two in and you have the area of the outside, split into its pieces.

Using the calculator

1. Type the radius of the circular end.
2. Type the height of the cylinder.
3. Press Calculate.

Both values have to be positive. The tool reports three numbers: the area of the top and bottom together, the area of the side, and the total. There is no unit setting, so they come as plain numbers in square units of whatever unit you used.

The formula | two ends + side = 2πr² + 2πrh

The total surface area of a cylinder is the two ends plus the curved side:

total = (2 × π × radius²) + (2 × π × radius × height)

The first part is the two circular ends. Each end is a circle of area π × radius², and there are two of them, so 2 × π × radius². The second part is the curved side. The tool shows the ends and the side separately, then the total.

Why the side is 2πrh

The curved side seems hard to pin down until you peel it off, like taking the label off a tin. Unrolled, it is just a flat rectangle. Its height is the cylinder's height h. Its width is the distance all the way around the circular end, which is the circumference, 2 × π × radius. Multiply the two, width times height, and the side area is 2 × π × radius × height. A curved surface that turns out to be an ordinary rectangle once flattened.

Just the side, or the whole thing

Splitting the answer into parts is useful, because you do not always want the whole surface. To size a label that wraps around a can, or sheeting that clads a pipe, you want only the side, 2 × π × radius × height. To work out paint or material for a closed tank with its lids, you want the full total, side plus the two ends. The tool gives you both so you can take whichever you need.

Square units, and the π it uses

Surface area is an area, so the answers are in square units of whatever you measured in: a cylinder in centimetres gives cm². The tool shows plain numbers with no unit attached. For π it uses 3.141592654, ten significant figures, far finer than any real tank or pipe.

A worked example | radius 10, height 20

Say the radius is 10 and the height is 20.

1. The two ends: 2 × π × 10² = 2 × π × 100 ≈ 628.32.
2. The side: 2 × π × 10 × 20 ≈ 1,256.64.
3. Total: 628.32 + 1,256.64 ≈ 1,884.96.

So the outside comes to about 1,884.96 square units. The side's width here is the circumference, 2 × π × 10 ≈ 62.83, and its height is 20, which multiply to that same side area.

The skin and the space

This is the cylinder's outer skin. For the space it holds, see the volume of a cylinder calculator. And for the other round surfaces, see the cone and the sphere, or the all-in-one surface area calculator. There is a nice link to the sphere worth knowing: a sphere's surface area is exactly equal to the curved side of the cylinder that just contains it.

Questions people ask

What is the surface area of a cylinder with radius 10 and height 20?

About 1,884.96 square units: two ends of roughly 628.32 together and a side of roughly 1,256.64.

Why is the side 2 × π × radius × height?

Because unrolling the side gives a rectangle whose height is the cylinder's height and whose width is the circumference, 2 × π × radius. Width times height gives the side area.

Can I get just the side?

Yes. The tool reports the side on its own, 2 × π × radius × height, which is what you want for a label or wrap that does not cover the ends.

Why two circles?

A closed cylinder has a top and a bottom, each a circle of area π × radius², so the two together are 2 × π × radius².

What unit is the answer in?

Whatever unit you used, squared. The tool shows plain numbers, so a cylinder in centimetres gives cm².

References

A note on where this comes from. The curved side of a cylinder unrolls into a rectangle whose width is the base circumference, 2 × π × radius, and whose height is the cylinder's height, giving a side area of 2 × π × radius × height. Adding the two circular ends, 2 × π × radius², gives the total. The value of π used is the one tabulated by the US National Institute of Standards and Technology. For further reading, see Cylinder.

1. The unrolled side of a cylinder, a rectangle of width 2 × π × radius and height equal to the cylinder's height.
2. National Institute of Standards and Technology (NIST), Digital Library of Mathematical Functions, value of π. https://dlmf.nist.gov/