# 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 = πr

^{2}**Don't forget:**π is pi (≈ 3.14)

**and**r

^{2}= r × r (r squared)

Step 2

Substitute the radius into the formula. In our example, r = 5.
Area = π × 5

The area of the circle with a radius of 5 cm is 78.5 cm^{2}= π × 5 × 5 = 78.5 cm^{2}^{2}.

# 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

##### Interactive Test

**show**

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 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}.