Maths
How do you find the area of a circle?
Quick answer
The area of a circle is pi times the radius squared: A = πr². A circle with radius 5 cm has an area of about 78.5 square centimetres.
In one sentence
The area of a circle is found by multiplying pi by the radius, and then by the radius again.
Explained
The area of a circle is the amount of flat space inside it. The formula is
A = π × r × r, usually written A = πr².
Here r is the radius, the distance from the centre to the edge, and π is about 3.14. The little 2 means "squared": multiply the radius by itself. See pi and square numbers.
Why does it work? Imagine cutting a circle into thin slices like a pizza, then laying them side by side, point up and point down. The shape looks almost like a rectangle. Its height is the radius, r. Its width is half the circumference, which is half of 2πr, so πr. Multiply them and you get πr × r = πr².
pie
pizza
pencil
Example: a circle has radius 5 cm.
Step by step
- Square the radius.5 × 5 = 25.
- Multiply by pi.3.14 × 25 = 78.5.
- Add units.The area is about 78.5 cm².
If you are given the diameter, halve it first to get the radius. A circle with a diameter of 8 cm has a radius of 4 cm, so the area is 3.14 × 4 × 4 = 50.24 cm². If you use the π button on a calculator, you get slightly more accurate answers. For the parts of a circle, see parts of a circle. Compare it with the general idea of area.
Examples
| Radius | r² | Area (π ≈ 3.14) |
|---|---|---|
| 2 cm | 4 | 12.56 cm² |
| 3 cm | 9 | 28.26 cm² |
| 5 cm | 25 | 78.5 cm² |
| 10 cm | 100 | 314 cm² |
Common mistakes
- Using the diameter in place of the radius. Halve it first.
- Doing 2 × r instead of r × r. r² means r times r.
- Mixing up area and circumference. Circumference is a length (2πr); area is a space (πr²) and uses square units.
Quick quiz
Area of a circle
Check what you know with 4 quick questions.
Question 1 of 4
What is the formula for the area of a circle?
Practise it
Try it
Geometry practice
Practise it step by step in a full course: Grade 8 Maths
For grown-ups
Related topics
Pi (π)
Pi (π) is the number you get when you divide any circle's circumference by its diameter. It is about 3.14, and its digits go on forever without repeating.
Parts of a circle
A circle has a centre, a radius, a diameter and a circumference. The radius runs from the centre to the edge, and the diameter is twice the radius.
Area
Area is the amount of flat space inside a shape, measured in square units like cm² or m². A rectangle 4 cm by 3 cm has an area of 4 × 3 = 12 cm².
Area of a triangle
The area of a triangle is half of its base times its perpendicular height: A = ½ × b × h. A triangle with base 8 cm and height 5 cm has an area of 20 square centimetres.
Pythagoras' theorem
Pythagoras' theorem says that in a right-angled triangle, a² + b² = c², where c is the longest side (the hypotenuse). For sides 3 and 4, the hypotenuse is 5.
Surface area
Surface area is the total area of all the outside faces of a 3D shape. For a cube with side a, it is 6a², because a cube has six equal square faces.