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

How to Find the Area of a Circle Using the Diameter?

The area of a circle is found using the formula:



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

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

An Example Question

What is the area of a circle with a diameter of 10 cm, as shown below?

Step 1
Start with the formula:
Area = πd2/4
Don't forget: π is pi (≈ 3.14) and d2 = d × d (d squared) and / means ÷

Step 2
Substitute the diameter into the formula. In our example, d = 10.
Area = π × 102/4
Area = π × 10 × 10 ÷ 4
Area = π × 100 ÷ 4
Area = π × 25
Area = 3.14 × 25
Area = 78.5 cm2
The area of the circle with a diameter of 10 cm is 78.5 cm2.

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

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

How to Find the Area of a Circle Using the Radius

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

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



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



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

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

Why Does This Formula Work?

The formula for the area of a circle is better known in terms of the radius:



The radius can be found from the diameter. The radius is half the length of the diameter:



Substitute d2 for r:



The d2 in the bracket is being squared. When a fraction is squared, both the numerator and the denominator are squared:



This is is formula for the area of a circle using the diameter.

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.