 # How many squares on a chess board – Step by step guide

A chessboard is a game board that is used to play chess, on which chess pieces and pawns are placed. The shape of a chessboard is usually square which has an alternating pattern of squares in two different colors (black and white). In western chess, the shape of the board is square, with its side being divided into eight parts. It ultimately results in sixty-four squares.

This question- “how many squares on a chess board?” may quite seem simple to you now. However, it is not that simple to answer this question. We have some answers that will surely blow your mind up (don’t worry! just on a knowledge basis).

To attain the correct answer, you need to approach this question methodically or simply putting, in the permutation and combination method.

While looking at a chessboard you can say that there are 64 squares, which is partially correct. But, there is more to it.

Hint

Can you guess any other way around to say how many squares are on a chess board ?

Let’s give you a hint:

Step 1- Find out the number of squares from (1 X 1) squares up to (8 X 8) squares.

Step 2- Add the numbers and (Ta-Da) you will get the results. ## How many squares on a chess board

Number of Squares in a Chessboard (step by step)

There are more squares in a chessboard than the 64 (1 × 1) squares.

The square count starts from (1 x 1) all the way up to (8 × 8).

Let us count them and find a way to know actually how many squares are there on a chessboard by adding up the numbers. After all, it’s all just a number’s game, right?

Come let’s find out-

1. The number of squares after multiplying (1 × 1) squares with 8 squares across the width and 8 squares along the length = (8 × 8) = 64 squares.
2. The number of squares after multiplying (2 × 2) squares with the size of the square increasing by 1 square as the number of squares across the width will be down to 7 squares and the ones along the length will also decrease to 7 squares. So, there are (7 × 7 )= 49 (2 x 2) squares.
3. The number of squares after multiplying (3 × 3) squares with 6 squares across the width and 6 along the length, the number of squares are (6 × 6) = 36 (3 x3) squares.
4. The number of squares after multiplying (4 × 4) squares with 5 squares across the width and 5 along the length = (5 × 5) = 25 (4 × 4) squares.
5. The number of squares after multiplying (5 × 5) squares with 4 squares across the width and 4 along the length is = (4 × 4) = 16 (5 × 5) squares.
6. The number of squares after multiplying (6 × 6 squares) with 3 squares across the width and 3 along the length = (3 × 3)= 9 (6 × 6) squares.
7. The number of squares after multiplying (7 × 7) squares with 2 squares across the width and 2 along the length = (2 × 2) = 4 (7 × 7) squares.
8. The number of squares after multiplying (8 × 8) squares with 1 square across the width and 1 along the length = (1 × 1) = 1 (8 × 8) squares. Therefore, the total number of squares on the chessboard will be by adding all the numbers above:-

[ 64 + 49 + 36 + 35 + 16 + 9 + 4 + 1 ]

By adding the numbers we get, 204 which is the number of squares on a chessboard.

There is also a formula for quickly calculating the number of squares on a chessboard.

If you figured that the number of squares is the summation of squares of natural numbers up to the number 8, you could have also used the formula given below. The total number of squares is thus:

Here,

[n(n+1)(2n+1)/6, where n is 8, Answer= 204]