Key takeaways
- The area of a circle is A = π × r², where r is the radius.
- Always halve the diameter first. Using it by mistake makes the answer 4× too big.
- Area is measured in square units, such as cm² or m².
- Doubling the radius makes the area four times bigger.
In this guide
What is the area of a circle?
Area is the amount of flat space inside a shape. For a circle, it tells you how much paint covers a round table top, how much grass fits in a round lawn, or how much pizza you actually get.
We measure area in square units. Imagine covering the circle with tiny 1 cm × 1 cm tiles. The number of tiles you need is the area in cm².
Why does the area of a circle matter?
Circles are everywhere: plates, wheels, pipes, clocks, ponds and pizzas. Whenever you need to buy material to cover a round surface, the area tells you how much to buy.
It also stops you being fooled. Area grows with the square of the radius, so a circle that looks a little wider is actually a lot bigger.
A 16-inch pizza has about 201 in² of pizza. Two 12-inch pizzas have about 226 in² together, only about 12.5% more, even though it feels like far more food.
The formula
| Symbol | What it means | Example |
|---|---|---|
| A | The area you want to find | 28.27 m² |
| π (pi) | A fixed number, about 3.14159 | 3.14159 |
| r | The radius: centre to edge | 3 m |
The little ² means squared: multiply the radius by itself. So r² = r × r, not r × 2.
How to find the area step by step
- 1Find the radius. If you only know the diameter, divide it by 2.
- 2Square the radius. Multiply it by itself, for example
3 × 3 = 9. - 3Multiply by π. Use the π button, or 3.14159:
9 × 3.14159 ≈ 28.27. - 4Add square units. If the radius was in metres, the answer is in m².
Now try it yourself. Change the radius in the calculator below and watch the area update, with every step shown.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Doubling instead of squaring.
5²is 25, not 10. - Mixing up area and circumference. Circumference (
2πr) is the distance around the circle. Use the circumference calculator for that. - Forgetting square units. Area is always in units², such as m² or in².
- Rounding π too early. Keep 3.14159 (or the π button) until the last step.
Tips and tricks
- To estimate quickly, use 3 for π. It gets you within about 5% of the real answer.
- Working backwards from area to radius? Divide by π, then take the square root:
r = √(A ÷ π). - For half a circle or a quarter circle, find the full area and divide by 2 or 4. For any other slice, use the sector area calculator.
Where you'll use it in real life
- Home and garden: seed or turf for a round lawn, paint for a round table.
- Cooking: comparing pizza and cake sizes, or scaling a recipe to a bigger tin.
- Engineering: the cross-section of a pipe, which controls how much water flows through it.
- 3D shapes: the area of the circular base is the first step for the cylinder volume calculator and the cone volume calculator.
Quick summary
To find the area of a circle, square the radius and multiply by π. Halve the diameter first if that's what you measured, and always give the answer in square units. Use the calculator above whenever you want the answer with every step shown.
Worked example
You want to sow grass seed on a round lawn that is 12 meters across. Seed is sold by the square meter, so you need the area. The diameter is 12 m, so the radius is 12 ÷ 2 = 6 m.
- 01A = π × r²
- 02A = π × 6²
- 03A = π × 36
- 04A = 113.0973 m²
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I find the area of a circle from the diameter?
Halve the diameter to get the radius, then use A = πr². Or use A = π × d² ÷ 4, which gives the same answer.
Why is a 16-inch pizza more than a 12-inch pizza by so much?
Area grows with the square of the radius. A 12-inch pizza is about 113 in² and a 16-inch pizza is about 201 in², roughly 1.8 times as much food.
What units is the area of a circle in?
Square units of whatever you measured the radius in: a radius in cm gives an area in cm², a radius in feet gives ft².
How do I find the radius if I know the area?
Divide the area by π, then take the square root. For an area of 50 m², r = √(50 ÷ π) ≈ 3.99 m.
