How the area of a circle is calculated
Area is π times the radius squared. Everything else converts to the radius first.
A = π × r²
- From the diameter: radius = diameter ÷ 2.
- From the circumference: radius = circumference ÷ (2 × π).
- Square the radius and multiply by π (about 3.14159).
- The answer is in square units of your measurement, such as cm².
Worked example — A circle with a 10 cm radius: π × 10² = 314.16 cm². Its diameter is 20 cm and circumference 62.83 cm.
Common circle sizes
| Diameter | Measured in | Area | Circumference |
|---|---|---|---|
| 20 cm | Centimetres | 314.16 cm² | 62.8319 cm |
| 30 cm | Centimetres | 706.86 cm² | 94.2478 cm |
| 1.2 m | Metres | 1.13 m² | 3.7699 m |
| 12 in | Inches | 113.1 in² | 37.6991 in |
| 16 in | Inches | 201.06 in² | 50.2655 in |
Swipe the table sideways to see the rest.
Diameters of everyday round things.
Things to consider
- Can't find the centre? Measure around the outside with a tape and use the circumference.
- Doubling the radius makes the area four times bigger.
- For a round table or garden bed, use the diameter straight across.
- 1 m² is 10,000 cm².
Frequently asked questions
What is the formula for the area of a circle?
A = π r². Square the radius and multiply by π.
How do I find the area from the diameter?
Halve the diameter for the radius, then use π r². Or use A = π d² ÷ 4.
How do I find the area from the circumference?
Divide the circumference by 2π for the radius, then square it and multiply by π. Or use A = C² ÷ 4π.
What value of π is used?
The full precision value JavaScript provides, about 3.141592653589793, rounded only for display.
Results are estimates for general information only, not financial, medical or professional advice.