# How many squares on a Chess Board?

0 Shares

How many squares on a chess board?

The answer may surprise you as it’s not 64 squares which is the first response I hear almost every time I ask this question to someone.

Total Squares on a chessboard includes all the possible positions for 1×1 squares (64) up to 8×8 size squares (1) which makes different squares in total.

Let’s count all the squares one-by-one to find out how many squares are there on a chess board?

## How many squares on a Chess Board?

There are a total of 204 squares (not 64 squares) on a chessboard.

No. There are not 64 squares on a chessboard because you forgot to count squares with dimensions of 2*2, 3*3, 4*4 squares, and more…)

There are a total of 204 squares in a chessboard (8*8)

This is because chessboards are usually drawn with a grid of alternating black and white squares forming the checkered pattern as below:

• 1×1 = 64 squares
• 2×2 = 49 squares
• 3×3 = 36 squares
• 4×4 = 25 squares
• 5×5 = 16 squares
• 6×6 = 9 squares
• 7×7 = 4 squares
• 8×8 = 1 square

Total Squares On a Chess Board = 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1

= 204 Squares

### Another Formula to Find How many Squares are on a Chess Board

Total Squares = n(n+1)(2n+1)/6

In our case, n = 8

So, Total Squares = 8 (8+1)(2×8+1)/6 = 8x9x17/6 = 1224/6

= 204 Squares

Interestingly, as n gets larger, this formula tends to n3/3 (for some other time)