How to Find the Area of a Circle
(KS3, Year 7)
The area of a circle is found using the formula:

area circle formula In this formula, r is the radius of the circle. The image below shows what we mean by radius:

circle radius1

How to Find the Area of a Circle

Finding the area of a circle is easy.

Question

What is the area of a circle with a radius of 5 cm, as shown below? circle radius

Step-by-Step:

1

Start with the formula:
Area = πr2
Don't forget: π is pi (≈ 3.14) and r2 = r × r (r squared).

2

Substitute the radius into the formula. In our example, r = 5.
Area = π × 52 = π × 5 × 5 = 78.5 cm2

Answer:

The area of the circle with a radius of 5 cm is 78.5 cm2.

"Find the Area" Widget

Here is a widget to help you learn the formulas to find the areas of different shapes.
  • Click on the shape you're learning about.
  • Click on the pad to start.
  • Follow the instructions in the bottom-left corner.
  • On the last click, the formula, workings, and answer will appear in the yellow box.
  • Enjoy!
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Lesson Slides

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: area_circle_diameter_formula In the formula, d is the diameter of the circle. The image below shows what we mean by diameter:

circle diameter1 how to find the area of a circle using the diameter

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:

pi2 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 length2. (All areas are lengths squared). This affects the units used. If the radius is in cm, the area is in cm2. If it is in inches, the area is in inches2.
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This page was written by Stephen Clarke.