Area enclosed by a circle
From Latin: area - "level ground, an open space,"
The number of square units it takes to exactly fill the interior of a circle.
Try this Drag the orange dots to move and resize the circle. As the size of the circle changes, the area is recalculated.

A circle is actually a line, one that connects back to itself making a loop. Imagine the circle to be a loop of string. The string itself has no area, but the space inside the loop does. So strictly speaking a circle has no area.

However, when we say "the area of a circle" we really mean the area of the space inside the circle. If you were to cut a circular disk from a sheet of paper, the disk would have an area, and that is what we mean here.

## If you know the radius

Given the radius of a circle, the area inside it can be calculated using the formula where:
R  is the radius of the circle
π  is Pi, approximately 3.142

## If you know the diameter

If you know the diameter of a circle, the area inside it can be found using the formula
where:
D  is the diameter of the circle
π  is Pi, approximately 3.142

## If you know the circumference

If you know the circumference of a circle, the area inside it can be found using the formula
where:
C  is the circumference of the circle
π  is Pi, approximately 3.142

## Calculator

 ENTER ANY ONE VALUE Radius clear Diameter clear Area clear Circumference clear

Use the calculator on the right to calculate the properties of a circle.

Enter any single value and the other three will be calculated. For example: enter the radius and press 'Calculate'. The area, diameter and circumference will be calculated.

Similarly, if you enter the area, the radius needed to get that area will be calculated, along with the diameter and circumference.

## Try this

1. In the figure above, click on "hide details"
2. Drag the orange dot on the edge of the circle to make a random-size circle.
3. Now try to estimate the area enclosed by the circle just looking at the squares inside it
When you done click "show details" to see how close you got. While you are here..

... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone. However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site? When we reach the goal I will remove all advertising from the site.

It only takes a minute and any amount would be greatly appreciated. Thank you for considering it!   – John Page

Become a patron of the site at   patreon.com/mathopenref