Square Area Calculator
The area of a square from one side — side times side, with the perimeter and diagonal alongside.
A square is the simplest case: all four sides equal, so the area is a × a.
How the square area calculator works
A square is the simplest case: all four sides equal, so the area is a × a. Doubling the side quadruples the area, which is why a 6 m room has four times the floor of a 3 m one rather than twice. The perimeter is 4a and the diagonal is a√2.
Formula: square a²; rectangle ab; triangle ½bh; circle πr²; parallelogram bh; trapezoid ½(a+b)h; ellipse πab
Worked examples
| Inputs | Area | Note |
|---|---|---|
| Side 6 | 36 | area 36, perimeter 24 |
| Side 2.5 | 6.25 | 6.25 |
| Side 12 | 144 | 144 |
FAQFrequently asked questions
How do I find the area of a square?
Multiply the side by itself: a 6 m square is 36 m².
What is the perimeter?
Four times the side — 24 for a side of 6.
What is the diagonal?
The side times √2, about 1.414 times — so a 6 m square has an 8.49 m diagonal.
If I know the area, what is the side?
The square root: 144 m² means 12 m sides.
Why does doubling the side quadruple the area?
Because area grows with the square of the length — the same reason a pizza twice the diameter feeds four people, not two.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.