Perimeter of a Chess Board

Hey there, chess enthusiasts and geometry nerds!

Are you ready for some mind-bending calculations?

Buckle up, because we’re about to answer the ultimate question: how many squares on the perimeter of a chess board?

Why on earth would I want to know how many squares are on the perimeter of a chessboard? Well, my friend, maybe you’re trying to impress your friends with your knowledge of useless information.Or maybe you’re just really into geometry. Whatever the reason, I’m here to help.

When looking at the search results, things can get a bit tricky as there are multiple factors to consider and different explanations for what may seem like the same thing.

What is the Perimeter of a Chess board?

You see, the perimeter is the distance around the outside of the board.

It’s like the fence around your house, except instead of keeping your annoying neighbors out, it keeps your chess pieces in (or, in my case, it keeps them from falling off the table).

The perimeter is the outer edge of the chess board – the part that goes all the way around.

In other words, the perimeter of a chess board is simply the sum of the lengths of all four sides of the board.

How many Squares are there on the Perimeter of a Chess Board?

There are 28 Squares on the Perimeter of a Chess Board. 

Perimeter of Chess board

A standard chess board has eight rows and eight columns, so the perimeter of chess board would be 4 x a or a + a + a +a , so assuming each column and row is 8 then 8+8+8+8 = 32.

But guess what? That’s not quite the case when it comes to the number of squares! You see, each of the 4 corner squares is shared by two edges, which means they get counted twice.

All we have to do is subtract the number of shared corners. So instead of counting the corners twice, we count them once. That means the total number of squares on the chess board is 64, and the perimeter is actually 32 – 4 (one corner shared by two edges) = 28.

 

What is the area perimeter of a chess board? 

The area perimeter of a chess board is a whole other ballgame. It’s like the size of your yard, but instead of measuring in square feet, we measure in squares.

the calculation for this is quite simple – just multiply 2 sides, each side has got 8 squares so

a x a = 64

 

 

Now going to another question which is often given as an answer to how many squares are on the perimeter of a chess board – How many squares are on the actual chess board? It may seem simple however, as with everything in chess, there are some BUTs.

Number of Squares in a Chess Board

Believe it or not, the chess board has more squares than you’d expect.

Are you ready to learn?

well, the simplest and most common answer will be 64 squares. If we take into account 1×1 squares.

But how about the total amount of squares you can fit into a chess board?

 

So, the answer is 204 squares. How did we get that? Well, we calculated how many squares of different sizes there are on the board.

You’ve got your 1×1 squares, 2×2 squares, 3×3 squares, and so on. We call these square numbers, and they go like this:

64 squares that are 1×1

49 squares that are 2×2

36 squares that are 3×3

25 squares that are 4×4

16 squares that are 5×5

9 squares that are 6×6

4 squares that are 7×7

1 square that is 8×8

All of these squares on the chess board (64+49+36+25+16+9+4+1) add up to 204 total. And if you want to get super technical, you can count the squares in the chairs on either end of the board, bringing the grand total to 206.

But for now, let’s stick with the 204 as a number of squares in a chess board.

Table of how many Squares fit on a Chess Board

Square Size	Number of Squares
1×1	64
2×2	49
3×3	36
4×4	25
5×5	16
6×6	9
7×7	4
8×8	1
Total	204

 

below is an awesome gif from datagenetics who go into much more detailed calculations

 

 

 

How many Rectangles are on a chess board?

Well, the thing Is – you ask about squares but you get an answer about how many rectangles are on the chessboard. So let us tackle this one too:

 

First things first, let’s establish what a rectangle is.

It’s a shape with four sides, and each angle is a right angle. It will be a shape with any 2 vertical and 2 horizontal lines.

Got it? Good.

Now, let’s get to the fun part. To figure out how many rectangles can fit on an 8×8 chess board, we need to do some hardcore counting.

 

First, let’s count how many 1×1 rectangles we can fit on the board. It’s quite simple really, we just count all the squares! 8×8 equals 64, so there are 64 1×1 rectangles.

Next up, we count how many 2×1 rectangles we can fit on the board. To do this, we take the number of columns (8) minus the length of the rectangle (2) and add one. So, 8-2+1 equals 7. We can fit 7 2×1 rectangles in each row, and there are 8 rows, so 7×8 equals 56.

Moving on to 3×1 rectangles, we do the same calculation. 8-3+1 equals 6, and we can fit 6 3×1 rectangles in each row. There are 8 rows, so 6×8 equals 48.

We can continue this pattern for all the other possible rectangle sizes, including 1×2, 1×3, 2×2, 2×3, 3×2, 3×3, and so on. Each time, we just use the formula of columns minus length plus one to find out how many rectangles we can fit in each row, and then multiply that by the number of rows.

 

To make it even more clear here is the table with all possible Rectangle combinations

Table of how many Rectangles fit on a Chess Board

Rectangle Size	Number Of Rectangles
1 x 1	64
1 x 2	56
1 x 3	48
1 x 4	40
1 x 5	32
1 x 6	24
1 x 7	16
1 x 8	8
2 x 1	56
2 x 2	49
2 x 3	42
2 x 4	35
2 x 5	28
2 x 6	21
2 x 7	14
2 x 8	7
3 x 1	48
3 x 2	42
3 x 3	36
3 x 4	30
3 x 5	24
3 x 6	18
3 x 7	12
3 x 8	6
4 x 1	40
4 x 2	35
4 x 3	30
4 x 4	25
4 x 5	20
4 x 6	15
4 x 7	10
4 x 8	5
5 x 1	32
5 x 2	28
5 x 3	24
5 x 4	20
5 x 5	16
5 x 6	12
5 x 7	8
5 x 8	4
6 x 1	24
6 x 2	21
6 x 3	18
6 x 4	15
6 x 5	12
6 x 6	9
6 x 7	6
6 x 8	3
7 x 1	16
7 x 2	14
7 x 3	12
7 x 4	10
7 x 5	8
7 x 6	6
7 x 7	4
7 x 8	2
8 x 1	8
8 x 2	7
8 x 3	6
8 x 4	5
8 x 5	4
8 x 6	3
8 x 7	2
8 x 8	1

After all the counting and calculating, we end up with a grand total of 1296 rectangles!

That’s a lot of rectangles!

But, if we want to get technical, we should subtract the 64 squares we counted earlier because they are technically rectangles as well.

So, 1296 minus 64 equals 1232.

to be even geekier or weirder – the square root of 1296 is 36, and a square root of that is 6. No idea whatsoever why would you need to know that , but you do now.

 

Sooo, now you know that 1296 rectangles can fit on an 8×8 chess board.

 

So, there you have it, guys. The answer to the age-old question: how many squares are on the perimeter of a chess board?

And if you’re still not sure, just remember this: it’s a lot.

Like, seriously, way too many.

Maybe we should just stick to checkers.

 

 

FAQ – for those who just want a quick answers