Square Side from Area
A square's area is its side squared, so the square root of the area gives the side. The diagonal is √2 — about 1.414 — times the side.
Your numbers
Side length
20cm
Perimeter
80cm
Diagonal
28.284cm
Formula
Side length = √Area
The area has to quadruple for the side to double. Doubling the area lengthens the side by only 1.414 times.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Area (cm²)The space a shape covers — length squared. | 400 | 0 and up |
Step by step
Quick reference table
Results when only Area (cm²) changes and everything else stays put.
| Area (cm²) | Side length (cm) | Perimeter (cm) | Diagonal (cm) |
|---|---|---|---|
| 200 | 14.142 | 56.569 | 20 |
| 300 | 17.321 | 69.282 | 24.495 |
| 400 | 20 | 80 | 28.284 |
| 600 | 24.495 | 97.98 | 34.641 |
| 800 | 28.284 | 113.137 | 40 |
What each result means
| Result | At default values |
|---|---|
| Side length (cm)One side of a regular polygon — they are all the same. | 20 |
| Perimeter (cm)The total length around the outside of a shape. | 80 |
| Diagonal (cm)Corner to opposite corner. | 28.284 |
Common mistakes
The area has to quadruple for the side to double. Doubling the area lengthens the side by only 1.414 times.
Glossary
- Area
- The space a shape covers — length squared.
- Side length
- One side of a regular polygon — they are all the same.
- Perimeter
- The total length around the outside of a shape.
- Diagonal
- Corner to opposite corner.
Frequently asked questions
Q. How is Square Side from Area calculated?
Side length = √Area — A square's area is its side squared, so the square root of the area gives the side. The diagonal is √2 — about 1.414 — times the side.
Q. Can you walk through an example?
With Area 400cm², the answer is Side length 20cm.
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) 200 → Side length (cm) 14.142 and Area (cm²) 800 → Side length (cm) 28.284. 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?
The area has to quadruple for the side to double. Doubling the area lengthens the side by only 1.414 times.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.