# How many squares on a Chess Board?

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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?

Read On!!!

## 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)

### Your Turn

Chess is full of tricks & amazing questions like this… I hope you liked it.

How many squares are on a chess board?

Share your answer with me in the comments? Did you get it right the first time?

Ask the same question to your chess friends, shock them with your knowledge!

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