# 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

Area = πd

^{2}/4**Don't forget:**π is pi (≈ 3.14)

**and**d

^{2}= d × d (d squared)

**and**/ means ÷

Step 2

Area = π × 10

Area = π × 10 × 10 ÷ 4

Area = π × 100 ÷ 4

Area = π × 25

Area = 3.14 × 25

Area = 78.5 cm

The area of the circle with a diameter of 10 cm is 78.5 cm^{2}/4Area = π × 10 × 10 ÷ 4

Area = π × 100 ÷ 4

Area = π × 25

Area = 3.14 × 25

Area = 78.5 cm

^{2}^{2}.

# 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

##### Interactive Test

**show**

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

**for**

^{d}⁄_{2}**r**:

The

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

^{d}⁄_{2}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 radius or diameter are in cm, the area is in cm

^{2}. If they are in inches, the area is in inches

^{2}.