Surface area of a cylinder
Definition:
The number of square units it takes to exactly cover the surface of a cylinder. Given by the formula:
where:
π is Pi, approximately 3.142
r is the radius of the cylinder
h height of the cylinder
Try this
Drag the orange dot to resize the cylinder, note how the area is calculated.
The surface area of a cylinder can be found by breaking it down into three parts:
 The two circles that make up the ends of the cylinder.
 The side of the cylinder, which when "unrolled" is a rectangle
Combining these parts we get the formula:
where:
π is Pi, approximately 3.142
r is the radius of the cylinder
h height of the cylinder
For a detailed look at how this formula is derived, see
Derivation of the surface area of a cylinder.
Units
Remember that the radius and the height must be in the same units  convert them if necessary. The resulting area will be in those square units.
So, for example if the height and radius are both in centimeters, then the area will be in square centimeters.
Calculator
Use the calculator on the right to calculate height, radius or surface area of a cylinder.
Enter any two values and the missing one will be calculated.
For example: enter the radius and height, and press 'Calculate'. The surface area will be calculated.
Similarly, if you enter the height and area, the radius needed to get that area will be calculated.
Things to try

In the figure above, adjust the height and diameter of the cylinder and note how the surface area is calculated.

Click 'reset' and 'hide details'. Adjust the cylinder to a new size and calculate the surface area. Click 'show details' to verify your answer.

Click 'reset'. Calculate what happens if you double the height  does the surface area double also?

Click 'reset'. Calculate what happens if you double the diameter  does the surface area double also?
While you are here..
... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone.
However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site?
When we reach the goal I will remove all advertising from the site.
It only takes a minute and any amount would be greatly appreciated.
Thank you for considering it! – John Page
Become a patron of the site at patreon.com/mathopenref
Related topics
(C) 2011 Copyright Math Open Reference. All rights reserved
