Area of a Circle

UFO Over Water
Image Source:

UFOs are amazing circular shapes, but wouldn’t they have to fly spinning around very fast like a frisbee ? Aliens obviously don’t get dizzy like us humans do!

Let’s start with our favorite music video about circles.

The formula for the Area of a Circle is as follows:

Area of Circle Formula
Image Source:

The symbol that looks like an “11” with a hat on top is called Pi.

The Area of any circle is PI x Radius x Radius where Pi is usually set to be 3.14

If we have a Diameter on our circle, then we need to halve it to obtain the Radius.

A very common mistake is to use the Diameter of a Circle in the area formula, which will result in an answer that is way too big.

Here is a great video about how the Area of a Circle formula was figured out by mathematicians.


In the following short video, we are shown how to substitute values into our formula and calculate the Area of a Circle.


A really important part of working on Circles is the value of Pi.

Sorry Picture Not Found
Image Source:

Pi is a mathematical constant whose value is the ratio of any circle’s circumference to its diameter.

Eg. Pi = c divided by d.

As stated previously we usually substitute in 3.14 to replace Pi in all of our circle formulas.

Interactive Circle

Mathwarehouse Circle

Click the link below, and try out the re-sizable circle to calculate areas automatically.

Try a Radius of 2.5cm and get an Area of 19.63 sq cm.
Then double the Radius to 5cm and obtain Area = 78.53 sq cm.

Notice that doubling the Radius does not double the Area.

The Area is made much bigger than double, because of the r squared in the Area formula.

Circle Area Games

Try this fun basketball game. The Coach will give you a really good lesson all about Area, when you click the Coach button.

When you are ready to play, click the Play button. After the instructions are given, make sure you click Play again to start the game.

If you get a question correct, the guy automatically shoots a basket.

Area BBall Game

Here is a Millionaire Circles Game.

This game covers Area, Circumference, and Perimeter.

Circle Millionaire

If you want a very challenging Jeopardy Game that covers Circumference and Area then try this one out.

Circle Jeapardy

Note that to calculate Diameter given Circumference, we need to do Circumference divided by 3.14.

To calculate radius we need to work out the square root of (Area divided by 3.14)

Circle Area Tests

Math Goodies has a great lesson with examples on Area of a Circle, followed by an online test you can do at the bottom of the page.

Here is a more challenging Circles test you can do.

Note that to calculate Diameter given Circumference, we need to do Circumference divided by 3.14 .

To calculate radius we need to work out (Area divided by 3.14), and then take the square root of this answer.

Related Items

Area of Simple Shapes
Interesting Circles
Composite Areas
Measurement Formulas
Tall Buildings and Huge Water Dam
My Virtual Home

If you enjoyed this post, why not get a free subscription to our website.
You will then receive notifications of new pages directly to your email address.

Just find the subscribe area on the right hand sidebar, fill in your email address and click the “Subscribe” button.

To find out exactly how free subscription works, click the following link:

How Free Subscription Works


This entry was posted in Area, Area of Circle, Circles, Measurement, Online Math Lessons, Perimeter. Bookmark the permalink.