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How many squares are on a chessboard?

Updated · Sergei Tovmasian

Short answer

Sixty-four: eight files by eight ranks, half of them light and half dark. If the question means every square of every size drawn on the grid, from the 64 single squares up to the whole board, the answer is 204. The board is always turned so that h1, the corner on White's right, is a light square.

The answer is 64, and then somebody tells you it is 204 and the two of you spend the next twenty minutes drawing boxes on the back of a scoresheet. Both numbers are right. They answer different questions, and the first one is the one you play on: eight files across, eight ranks up, 32 light squares and 32 dark, alternating in both directions so that no two squares sharing an edge ever match.

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a1 and h8 are dark, h1 and a8 are light. Each long diagonal runs corner to corner in a single colour, eight squares of it.

The colours are not decoration. A bishop that starts on c1 stands on a dark square and stays on dark squares until it is captured, so it can only ever reach half the board. That is the whole argument for holding on to both bishops, and it is why a bishop can never change colour no matter how long the game runs.

Which corner is light

h1, the corner nearest White’s right hand. Article 2.1 of the FIDE Laws says so, and every diagram ever printed assumes it. a1 is dark, a8 is light, h8 is dark. Sit down at a board with a dark square on your right and it is turned the wrong way; see setting up a chess board for the rest of that check.

Each square has a name made of its file letter and its rank number, from a1 in the bottom left to h8 in the top right. Sixty-four squares, sixty-four names, and learning them is twenty minutes of work that pays for itself the first time you read a game score.

The trick answer: 204

Ask a mathematician how many squares are on a chessboard and you get a different number, because they count squares of every size drawn on the grid, not just the little ones you put pieces on.

There are 64 squares of one by one. There are 49 of two by two, because a two-by-two block can sit in seven positions across and seven up. Then 36 of three by three, 25 of four by four, 16, 9, 4, and exactly one eight-by-eight, which is the board. Add them: 64 plus 49 plus 36 plus 25 plus 16 plus 9 plus 4 plus 1 is 204.

Ask for rectangles instead of squares and the count jumps to 1,296. Nine lines run each way across the board, you pick any two of the nine for the sides and any two of the nine for the top and bottom, and 36 times 36 is 1,296.

None of that helps you win a game. But it is the same kind of thinking that makes chess problems fun, and the counting habit is exactly what you want when you are working out how many squares an enemy king has left.

More questions

How many black and white squares are there on a chessboard?

Thirty-two of each. Players say light and dark rather than white and black, because sets come in cream and walnut as often as anything else and the board colours have nothing to do with which side you are playing. The two colours alternate in both directions, so no two squares sharing an edge ever match.

How many squares does a bishop control over a whole game?

Thirty-two at most, and usually far fewer. A bishop never leaves the colour it started on, so the c1 bishop spends the entire game on dark squares and can never attack anything standing on a light one. That is the argument for keeping both bishops: together they cover all 64.

Go deeper

Related questions

Ranks, files and diagonals explainedHow to set up a chess boardHow are the squares named on a chessboard?Can a bishop change colour?

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