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Short answer
The area of a circle is A = πr². With a radius of 5 the area is 78.54. From the diameter use A = πd² ÷ 4, and from the circumference use A = C² ÷ 4π.
1. The formulas
- From the radius: A = πr²
- From the diameter: A = πd² ÷ 4
- From the circumference: A = C² ÷ 4π
2. Worked examples
| Known value | Working | Area |
|---|---|---|
| Radius 5 | π × 5² | 78.54 |
| Diameter 20 | π × 20² ÷ 4 | 314.16 |
| Circumference 44 | 44² ÷ 4π | 154.06 |
| Radius 12 | π × 12² | 452.39 |
3. Radius 1 to 10
| Radius | Area |
|---|---|
| 1 | 3.14 |
| 2 | 12.57 |
| 3 | 28.27 |
| 4 | 50.27 |
| 5 | 78.54 |
| 6 | 113.10 |
| 7 | 153.94 |
| 8 | 201.06 |
| 9 | 254.47 |
| 10 | 314.16 |
4. Common mistakes
- Using the diameter in place of the radius. Halve it first.
- Forgetting to square the radius.
- Reporting area in length units. Area is in square units.
Doubling the radius makes the area four times as large.
5. Frequently asked questions
What is the formula for the area of a circle?expand_more
A = πr², where r is the radius.
How do I find the area from the diameter?expand_more
Use A = πd² ÷ 4, or halve the diameter and use A = πr².
How do I find the area from the circumference?expand_more
Use A = C² ÷ 4π.
Why is the area in square units?expand_more
Because it measures a surface, which is two-dimensional.