A square is just a special case of a regular polygon, having equal four sides. In a square all the angles are right angle and its diagonals are equal. Opposite sides of the square are equal and parallel. All the square has four vertex and these are the corners of the square.

The above figure is a Square with sides $s$. The diagonals of the given square are AC and BD.  Square calculator is an online tool to calculate the area, perimeter and diagonal of a square.

Formula for Square

Area of a Square : The space covered by the boundary of the square is called the area of a square, which is measured in square units. The formula for area of a square is given below

$Area\ (A)$ = $Side \times Side$

= $s \times s$

$Area$ = $s^{2}$

Perimeter of a Square: The sum of all sides of square is called perimeter of the square. Since all the sides of the square are equal the perimeter can be written as,

$Perimeter$ = $Sum\ of\ all\ the\ sides$

=$AB+BC+CD+AD$

=$s+s+s+s$

$Perimeter$ = $4s$

Diagonal of a Square: Diagonal is the largest side in a square. Each square has two diagonals which is a line drawn between the opposite vertices of square. The two diagonals of the same square are equal. One can calculate the length of diagonal with help of Pythagorean Theorem.

Consider a square $ABCD$. Here the Diagonal drawn between $A$ and $C$ divides the square into Two equal triangle. By applying Pythagorean Theorem in $\Delta ADC$ one can calculate the diagonal length $AC$

$AC$ = $\sqrt{AD^{2}+DC^{2}}$

=$\sqrt{s^{2}+s^{2}}$

= $\sqrt{2s^{2}}$

= $s \sqrt{2}$

$Diagonal$ =  $s \sqrt{2}$

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