The Lesson
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:
How to Find the Area of a Circle Using the Diameter
Finding the area of a circle using the diameter is easy.
What is the area of a circle with a diameter of 10 cm, as shown below?
Step-by-Step:
1
Start with the formula:
Area = πd2⁄4
Don't forget: π is
pi (≈ 3.14)
and d
2 = d × d (d
squared)
and / means ÷.
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
Answer:
The area of the circle with a diameter of 10 cm is 78.5 cm
2.
Lesson Slides
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
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
d⁄2 for
r:

The
d⁄2 in the brackets 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 length
2. (All areas are lengths squared).
This affects the units used. If the diameter is in cm, the area is in cm
2. If it is in inches, the area is in inches
2.