Square Calculator
Enter a side length below to instantly get area, perimeter, and diagonal.
Square Formulas
Area = side². Perimeter = 4 × side. Diagonal = side × √2.
A common mistake is assuming perimeter and area scale the same way when a side length changes. They don't: perimeter grows in direct proportion to the side, but area grows with the side squared. Double the side length and the perimeter only doubles, while the area quadruples — a side of 6 has an area of 36, but a side of 12 has an area of 144, four times as much.
Worked example
A square with side 6.
Area: 6² = 36. Perimeter: 4 × 6 = 24.
Diagonal: 6 × √2 ≈ 8.49
A second example, with side 10.
Area: 10² = 100. Perimeter: 4 × 10 = 40.
Diagonal: 10 × √2 ≈ 14.14
Keep going
- A square is the simplest shape this calculator's perimeter formula covers; the perimeter calculator adds triangles, circles, and general rectangles alongside it. Perimeter Calculator
- A square's area is a special case of general square footage; the square footage calculator handles rectangles where the two sides differ. Square Footage Calculator
Frequently Asked Questions
How do you find the area of a square?
Area = side × side (side²). A square with side 6 has an area of 36.
How do you find the perimeter of a square?
Perimeter = 4 × side, since all four sides are equal.
How do you find the diagonal of a square?
Diagonal = side × √2, from the Pythagorean theorem applied to the two equal sides.
Is a square always a rectangle?
Yes. A square is a special case of a rectangle where all four sides happen to be equal length, so it satisfies a rectangle's definition: four right angles and opposite sides equal. A rectangle isn't always a square, though — that only happens when all four of its sides match.
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