With this simple square calculator, you can find all the parameters in the blink of an eye. Fill in one box, and the calculator will display all the remaining parameters: side, area, perimeter, and diagonal. Scroll down if you want to remind yourself about the basic formulas in square calculations.
What is a square?
A square is a quadrilateral with four equal sides and four equal angles (right angles = 90°). It's one of the most basic shapes.
It's a special case of a rhombus, a kite, a trapezoid, a parallelogram, and a rectangle, so it has all the properties of these shapes:
- All four sides are of equal length (a).
- All four interior angles are right angles (90°).
- The two diagonals are equal, bisect each other at right angles, and each divides the square into two congruent right isosceles triangles.
- Opposite sides are parallel.
Square calc: find P (perimeter)
The perimeter of a square is equal to the sum of all sides. Because the square has all four sides equal, the perimeter is then:
where a is a square side.
Square calc: find A (area)
The area of a square is the product of the length of its sides:
where a is a square side.
Square calc: find d (diagonal)
The diagonal of a square connects two opposite corners. Using the Pythagorean theorem on the right isosceles triangle formed by two sides and the diagonal, we get:
where a is a square side.
Square properties
Knowing any single one of the parameters lets you reconstruct all the others. Starting from the side a:
- Area: A = a²
- Perimeter: P = 4 × a
- Diagonal: d = a × √2
- Inscribed circle radius (inradius): r = a / 2
- Circumscribed circle radius (circumradius): R = d / 2 = a × √2 / 2
And if you only know one of the other quantities, you can always recover the side first:
- From the area: a = √A
- From the perimeter: a = P / 4
- From the diagonal: a = d / √2
Unit Systems
Metric System
Enter the side, perimeter, or diagonal in centimeters (cm) and the area in square centimeters (cm²). Lengths are also shown in millimeters (mm), meters (m), and inches (in); areas in mm², m², and in².
US / Imperial System
Enter the side, perimeter, or diagonal in inches (in) and the area in square inches (in²). Lengths are also shown in feet (ft), yards (yd), and centimeters (cm); areas in ft², yd², and cm².
How to use square calc: find perimeter example
- Choose what you know — the side, the area, the perimeter, or the diagonal.
- Pick your unit system — metric (cm) or US/Imperial (in).
- Enter that single value into the highlighted box.
The calculator instantly returns the side together with the area, perimeter, diagonal, inradius, and circumradius of the square.
Example. Suppose you know the side of a square is a = 5 cm and you want its perimeter:
P = 4 × 5 = 20 cm
At the same time the calculator reports A = 5² = 25 cm² and d = 5 × √2 ≈ 7.07 cm.
FAQs
How do I find the area of a square?
Multiply the side length by itself: A = a². For example, a square with a 5 cm side has an area of 5² = 25 cm².
How do I find the perimeter of a square?
Add up all four equal sides, i.e. multiply the side by four: P = 4 × a. A square with a 5 cm side has a perimeter of 4 × 5 = 20 cm.
How do I find the diagonal of a square?
Multiply the side by the square root of two: d = a × √2 ≈ 1.41421 × a. A 5 cm side gives a diagonal of about 7.07 cm.
Can I find the side if I only know the area?
Yes. Take the square root of the area: a = √A. A square of 25 cm² has a side of √25 = 5 cm.
Is a square a rectangle?
Yes — a square is a special rectangle in which all four sides are equal. It is also a special rhombus (a rhombus with right angles), so it inherits the properties of both shapes.