Free Square Calculator (Side, Area, Perimeter, Diagonal)

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Key Features

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A square's side length, area, perimeter, and diagonal are all related by simple formulas — knowing any single one of them lets you solve for all the others. This all-in-one solver is useful whenever a real-world problem hands you just one of these measurements (a floor tile's known area, a picture frame's known diagonal, fencing material measured as a perimeter) and you need the rest to finish a calculation for construction, crafting, or homework.

How it works

Choose which value you know and enter it. The calculator first solves for the side length: if you gave the area A, side = √A; if you gave the perimeter P, side = P/4; if you gave the diagonal d, side = d/√2. Once the side length is known, the other three values follow directly: Area = side², Perimeter = 4×side, and Diagonal = side×√2 (from the Pythagorean theorem applied to two adjacent sides).

Enter what do you know?.
Enter value.
Click Calculate to see your results.

Examples

Area = 25

Side = √25 = 5. Perimeter = 4(5) = 20. Diagonal = 5√2 ≈ 7.07.

Diagonal = 10

Side = 10/√2 ≈ 7.07. Area ≈ 7.07² ≈ 50. Perimeter ≈ 4(7.07) ≈ 28.28.

Common mistakes to avoid

Selecting the wrong "known field" from the dropdown, which changes which formula is applied first and produces an incorrect side length.
Forgetting to take the square root when going from area back to side length (using the area value directly as the side).
Dividing the diagonal by 2 instead of √2 when recovering the side length.
Using the perimeter value directly as the side length instead of dividing it by 4 first.

Frequently asked questions

By the Pythagorean theorem, since the diagonal splits a square into two right triangles with both legs equal to the side length, diagonal = side×√2.

The area quadruples — since area = side², doubling the side length means squaring a doubled number, which multiplies the result by 4, not 2.

No — perimeter is directly proportional to the side length (doubling the side doubles the perimeter), while area grows with the square of the side length, so area and perimeter scale very differently as a square gets bigger.

Yes — a square is a rectangle where all four sides happen to be equal, which is why it also qualifies as a rhombus (all sides equal) with right angles.

Since a square has four equal sides, divide the perimeter by 4 to recover the side length — for example, a perimeter of 20 means each side is 20/4=5.

The diagonal splits the square into two right triangles with both legs equal to the side length s; by the Pythagorean theorem, the diagonal is √(s²+s²)=√(2s²)=s√2, which is where that specific constant comes from.

Only if the perimeter and area are consistent with equal sides — specifically, if side=√area also satisfies perimeter=4×side; otherwise the shape described is a non-square rectangle instead.