Radius from Area
Divide the area by π and take the square root. This is how you size a circle when the required area is fixed.
Your numbers
Radius
10cm
Diameter
20cm
Circumference
62.832cm
Formula
Radius = √(Area ÷ π)
An area of 314.16 cm² means a 10 cm radius. To double the area you only enlarge the radius by √2 (about 1.41×).
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Area (cm²)The space a shape covers — length squared. | 314.16 | 0 and up |
Step by step
Quick reference table
Results when only Area (cm²) changes and everything else stays put.
| Area (cm²) | Radius (cm) | Diameter (cm) | Circumference (cm) |
|---|---|---|---|
| 157 | 7.0693 | 14.1386 | 44.418 |
| 236 | 8.6672 | 17.3345 | 54.458 |
| 314 | 9.9975 | 19.9949 | 62.816 |
| 471 | 12.2443 | 24.4887 | 76.933 |
| 628 | 14.1386 | 28.2771 | 88.835 |
What each result means
| Result | At default values |
|---|---|
| Radius (cm)Centre to edge — half the diameter. | 10 |
| Diameter (cm)The longest line across a circle — twice the radius. | 20 |
| Circumference (cm)The distance once around a circle. | 62.832 |
Common mistakes
An area of 314.16 cm² means a 10 cm radius. To double the area you only enlarge the radius by √2 (about 1.41×).
Glossary
- Area
- The space a shape covers — length squared.
- Radius
- Centre to edge — half the diameter.
- Diameter
- The longest line across a circle — twice the radius.
- Circumference
- The distance once around a circle.
Frequently asked questions
Q. How is Radius from Area calculated?
Radius = √(Area ÷ π) — Divide the area by π and take the square root. This is how you size a circle when the required area is fixed.
Q. Can you walk through an example?
With Area 314.16cm², the answer is Radius 10cm.
Q. What do I need to enter?
Enter Area. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Area (cm²) moves the answer to Area (cm²) 157 → Radius (cm) 7.0693 and Area (cm²) 628 → Radius (cm) 14.1386. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
An area of 314.16 cm² means a 10 cm radius. To double the area you only enlarge the radius by √2 (about 1.41×).
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.