The number of square units it takes to completely fill a square.
Formula: Width × Height

Try this Drag the orange dots to move and resize the square. As the size of the square
changes, the area is recalculated.

Area formula

The area of a square is given by the formula

area = width × height

But since the width and height are by definition the same,
the formula is usually written as

area = s^{2}

where s is the length of one side.

In strictly correct mathematical wording the formula above should be spoken as "s raised to the power of 2", meaning s is multiplied by itself.
But we usually say it as "s squared". This wording actually comes from the
square. The length of a line s multiplied by itself, creates the square of side s. Hence "s squared".

Use the calculator on the right to calculate the properties of a square.

Enter any one value and the other three will be calculated. For example, enter the side length and the area will be calculated.

Similarly, if you enter the area, the side length needed to get that area will be calculated.

The "diagonals" method

If you know the lengths of the diagonals, the area is half the product of the diagonals.
Since both diagonals are
congruent (same length), this simplifies to: