Surface area of a cylinder
The number of square units it takes to exactly cover the surface of a cylinder. Given by the formula:
, approximately 3.142
is the radius
of the cylinder
height of the cylinder
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:
Combining these parts we get the formula:
- The two circles that make up the ends of the cylinder.
- The side of the cylinder, which when "unrolled" is a rectangle
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.
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.
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?
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