Calculate the Area of a Circle

A circle is one of the most interesting geometric shapes but is one of the more difficult ones to understand. Follow these steps to find the area of a circle. You will also learn how to find the area of a sector, which is a slice of a circle, similar to the shape of a slice of pie or pizza.

[edit] Steps for Calculating Area of a Circle

Figure out the length of the radius. This may be as simple as dividing the diameter by 2.
Note the formula. The formula for finding the area of a circle is:
Multiply the radius by itself to square it.
Multiply by pi.
- If the instructions say "leave in terms of pi", then just stick the pi onto your number.
- If the instructions say anything about rounding, replace pi with 3.14 or use your calculator's pi button.

Here is an example:

Occasionally you will see a circle inside of a square. The side length of the square matches the diameter of the circle.
Occasionally you may see a square inside of a circle. The diagonal of the square is also the diameter of the circle.

[edit] Steps for Finding the Area of a Partial Circle

Find out how big the partial circle is in terms of degrees. Unfortunately, there is no set way to do this. It will vary considerably, depending on what informationcient for pi. You will have to decide whether to: a) keep the fraction as a fraction and pi as pi, and cross-cancel as much as possible; or b) substitute 3.14 and finish the division completely.

[edit] Steps for Measuring the Diameter of Round Objects

Use a set of calipers, if possible, to measure across the object. This will give you the diameter.
Use a flexible tape measure, like the ones used in sewing, to measure around the outside of the object. Be sure to measure it in centimeters. This will give you the circumference. Divide by 3.14 to find the diameter.
With a cylindrical object, like a soup can, you can rest a ruler across the top of the can. Keep one end stationary while you rotate the other end. Keep rotating until you find the spot where the distance is the longest. This is the diameter.

[edit] Tips

It is handy to have a calculator with you. A simple 4-function will do fine, but more complex calculators can store your measurements to use later. Or you might be able to use one on your computer.

[edit] Warnings

On a large scale, it is difficult to be precise with these measurements. Take that into consideration when calculating and measuring.
While forming a triangle to eliminate the curved edge is a quick way to generalize the area of a sector, it is not at all precise, especially on large circles.