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How to Find the Area of a Circle (Mathematics Lesson)

How to Find the Area of a Circle

The area of a circle is found using the formula:



In this formula, r is the radius of the circle. The image below shows what we mean by radius:

A Real Example of How to Find the Area of a Circle

An Example Question

What is the area of a circle with a radius of 5 cm, as shown below?

Step 1
Start with the formula:
Area = πr2
Don't forget: π is pi (≈ 3.14) and r2 = r × r (r squared)

Step 2
Substitute the radius into the formula. In our example, r = 5.
Area = π × 52 = π × 5 × 5 = 78.5 cm2
The area of the circle with a radius of 5 cm is 78.5 cm2.

Another Real Example of How to Find the Area of a Circle

The slider below shows another real example of how to find the area of a circle:

How to Find the Area of a Circle Using the Diameter

The area of a circle can be found using the diameter rather than the radius.

The area of a circle, using the diameter, is found using the formula:



In the formula, d is the diameter of the circle. The image below shows what we mean by diameter:



Read more about how to find the area of a circle using the diameter

Curriculum
Geometry Lessons
Interactive Widget
Here is an interactive widget to help you learn about finding the area of a circle.
Interactive Test
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Here's a second test on finding the area of a circle.
Here's a third test on finding the area of a circle.
Note

What Is a Circle?

A circle is a shape containing a set of points that are all the same distance from a given point, its center.

Radius and Diameter

The diameter of a circle is twice the length of its radius.

If you are given the diameter of a circle, halve it to find the radius and put this in the formula.

Alternatively, use the formula containing diameter.

What Is Pi?

π is the symbol for pi.

π is how many times longer a circle's circumference is than its diameter. It is the circumference divided by the diameter



π is the same for all circles, and is approximately equal to 3.14.

A Note on Units

The area of a circle is a length times a length, so we say its dimension is length2. (All areas are lengths squared.)

This affects the units used. If the radius or diameter are in cm, the area is in cm2. If they are in inches, the area is in inches2.