How Many Squares Are on a Chessboard? (64 or 204?)

A chessboard has 64 squares (8×8), but 204 if you count every square of every size. See the math, the 1,296 rectangles and an interactive board.

A chessboard has 64 squares, arranged in 8 rows and 8 columns (8 × 8 = 64): 32 light and 32 dark. But if you count every square you can draw on the board, including the 2×2, 3×3 and bigger squares made of smaller ones, the answer is 204. That second number is a classic math puzzle, and this guide shows exactly where it comes from, along with a few more board facts that players, kids and teachers like to know.

The short answer: 64 playing squares

When chess players talk about squares, they mean the 64 small squares that pieces stand on. At the start, the 32 pieces fill half of them (rows 1, 2, 7 and 8). To get the board ready to play, see our guide on how to set up a chessboard.

Why the answer can also be 204

The puzzle version of the question asks: how many squares of any size can you find on a chessboard? Look at the board and you will see bigger squares hiding inside it. Four small squares form a 2×2 square, nine form a 3×3 square, and so on, up to the whole board, which is one big 8×8 square.

Here is how to count them, one size at a time:

• 1×1 squares: 8 across × 8 down = 64
• 2×2 squares: a 2×2 frame fits in 7 positions across and 7 down = 49
• 3×3 squares: 6 × 6 = 36
• 4×4 squares: 5 × 5 = 25
• 5×5 squares: 4 × 4 = 16
• 6×6 squares: 3 × 3 = 9
• 7×7 squares: 2 × 2 = 4
• 8×8 squares: the whole board = 1

Add them up: 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204.

Why does each size give a square number?

Take the 2×2 frame. Its left edge can start on file a, b, c, d, e, f or g, but not on h, because there would be no room for the second column. That is 7 starting columns. The same reasoning gives 7 starting rows, so there are 7 × 7 = 49 positions. In general, a square that is k squares wide fits in (9 − k) positions each way, so there are (9 − k)² squares of that size.

That makes the total the sum of the first eight square numbers: 1² + 2² + 3² + … + 8² = 204. Math fans can check it with the formula n(n + 1)(2n + 1) ÷ 6, which for n = 8 gives 8 × 9 × 17 ÷ 6 = 204.

A tip for teachers

This puzzle works well in class because students can discover the pattern themselves. Start with a 2×2 grid (5 squares), then a 3×3 grid (14 squares), and ask them to predict the 4×4 grid (30) before counting. Once they spot that each new size adds the next square number, the full chessboard is easy. Free printable activities are on our worksheets page, and it makes a good Week 1 warm-up in our 8-week chess lesson plans.

How many rectangles are on a chessboard?

The answer is 1,296, and the counting trick is neat. A chessboard has 9 horizontal lines and 9 vertical lines (the edges plus the 7 lines between rows or columns). Every rectangle is fixed by choosing 2 of the horizontal lines and 2 of the vertical lines.

There are 36 ways to choose 2 lines out of 9 (9 × 8 ÷ 2 = 36). So the number of rectangles is 36 × 36 = 1,296. That count includes the 204 squares, because a square is a special kind of rectangle, which leaves 1,092 rectangles that are not squares.

Light and dark squares

The board has 32 light squares and 32 dark squares, alternating like a checkerboard, so no two squares that share a side have the same color. In chess books the light squares are called "white" and the dark ones "black", whatever their real colors (green and cream boards are common).

The board must be turned so that each player has a light square in the bottom-right corner. The rhyme "light on the right" helps you remember. This is why the white queen starts on a light square (d1) and the black queen on a dark one (d8).

Files, ranks and coordinates (a1 to h8)

Every square has a name made of a letter and a number:

• Files are the 8 columns, labeled a to h from White's left to right.
• Ranks are the 8 rows, numbered 1 to 8 starting from White's side.
• A square's name is its file plus its rank: a1 is White's bottom-left corner, h8 is the opposite corner, and e4 is a central square.

These coordinates are the backbone of chess notation, the way players write down moves. A quick color trick: a1 is dark. If you number the files a = 1 to h = 8 and add the rank, an even total means a dark square and an odd total means a light one (h1: 8 + 1 = 9, light).

Try it yourself: find the square d5 on this board.

How many diagonals does a chessboard have?

Diagonals are lines of squares of the same color, running corner to corner at a slant. Each direction has 15 diagonals, from single corner squares up to the two longest ones, so there are 30 in total (26 if you leave out the four one-square corners).

The two long diagonals have 8 squares each: a1 to h8 (all dark) and h1 to a8 (all light). A bishop stays on its starting color for the whole game because it only moves diagonally, which is why each side has one light-squared and one dark-squared bishop.

How many squares can a knight reach?

From the middle of the board, a knight can jump to 8 squares. From a corner it has only 2. The 16 central squares (c3 to f6) all give a knight 8 moves, while edge squares give it 3 or 4. This is why coaches say "a knight on the rim is dim."

Given enough moves, a knight can reach every square; no square is more than 6 knight moves from any other (a1 to h8 takes exactly 6). To learn how all the pieces move, see how chess pieces move.

How big is a tournament chessboard?

Board size is a matter of equipment standards rather than the rules of play. The US Chess rulebook recommends squares of about 2 to 2.5 inches (roughly 5 to 6.35 cm) on a side, which makes the playing area about 16 to 20 inches across. FIDE's equipment standards ask for squares of 5 to 6 cm. Both also want the pieces to fit the board, with the king's base filling most of a square. Wording changes between editions, so for an official event check the current rules. Smaller travel sets are fine for casual play.

The wheat and chessboard story

In a famous legend, a wise man asks a king for one grain of wheat on the first square, two on the second, four on the third, doubling across all 64 squares. The total is 2⁶⁴ − 1, about 18.4 quintillion grains, far more wheat than the world has ever grown.

Start playing on those 64 squares

Now that you know the board, the best next step is to use it. Our free chess lessons teach the pieces and the rules one step at a time, and Chess for Kids has games and puzzles made for young players.