Square Calculator
Calculate the area, perimeter, and diagonal of a square from its side length. Enter one value to get all three measurements instantly.
How It's Calculated
Formula
\text{Area} = s^2
\text{Perimeter} = 4s
\text{Diagonal} = s \times \sqrt{2}A square is a special rectangle where all four sides are equal — so every rectangle formula still applies, just with length and width being the same value. This calculator is built as its own single-input tool rather than a rectangle wrapper: enter one side length, and it returns the area, perimeter, and diagonal directly. Area measures the space enclosed (side squared), perimeter measures the total distance around the four sides (four times the side), and diagonal measures the straight-line distance corner to corner (side times the square root of 2).
Worked Examples
Standard case: side = 5
- Area = s² = 5² = 25.0000
- Perimeter = 4s = 4 × 5 = 20.0000
- Diagonal = s × sqrt(2) = 5 × 1.41421356... = 7.0711
Decimal side: side = 2.5
- Area = s² = 2.5² = 6.2500
- Perimeter = 4s = 4 × 2.5 = 10.0000
- Diagonal = s × sqrt(2) = 2.5 × 1.41421356... = 3.5355
Frequently Asked Questions
Why does this calculator only ask for one value?
A square's defining property is that all four sides are equal, so a single side length is all the information needed to determine its area, perimeter, and diagonal. Requiring two inputs (like a rectangle's length and width) would just mean typing the same number twice.
How is a square's diagonal calculated?
The diagonal splits a square into two right triangles, so it follows the Pythagorean theorem: diagonal = sqrt(side² + side²) = sqrt(2 × side²) = side × sqrt(2). That's why the diagonal is always about 1.41421 times the side length.
What happens if I enter a side length of 0 or a negative number?
The calculator treats that as invalid input. A square must have a strictly positive side length — zero or negative values don't describe a real square, so no area, perimeter, or diagonal can be computed.
Is a square just a special rectangle?
Yes — geometrically, a square is a rectangle with equal length and width, so every rectangle formula (area = length × width, perimeter = 2 × (length + width), diagonal = sqrt(length² + width²)) reduces to this calculator's formulas when length equals width. This tool is kept separate from the Rectangle Calculator purely for a simpler, single-input experience.
Can I use this for squares measured in any unit?
Yes. Enter the side length in whichever unit you're working with (inches, feet, meters, etc.) — the area will be in that unit squared, and the perimeter and diagonal will be in that same linear unit.