How many Squares are in a 7 by 7 grid?

Answer 1

There are 49 of the smallest squares.

However, any grid forms "squares" that consist of more than one of the smallest squares.

For example, there are four different 6x6 squares that each include 36 of the small squares, nine different 5x5 squares, sixteen 4x4 squares, twenty-five 3 x 3 squares, and thirty-six different squares that contain 4 of the small squares. One could therefore discern 140 distinct "squares."

The number can be calculated from the formula

[(n)(n+1)(2n+1)] / 6

where n is the grid size.