How Many Squares On A Chess Board?

Home Play Puzzles Learn Watch News Social More Sign Up Log In English Light UI Dark UI Support

• Forums
• Fun With Chess

Sort: rterhart Jun 15, 2019 0 #1

How many squares can you form on a chess board?

Obviously, there's the 64 squares. Together they form another square. Then there are 2x2 squares (a1-a2-b1-b2, for example), 3x3 squares (a1-c3), 4x4, 5x5, 6x6 and 7x7 squares. (There are 4 of those.)

If you add all that up, how many do you get?

And this is not a quiz question. I would like to know the answer.

scrabblechecs Jun 15, 2019 0 #2

64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 (8x8) = 168 squares !

rterhart Jun 15, 2019 0 #3

So that is 8^2 + 7^2 + 6^2 + 5^2 + 4^2 +3^2 + 2^2 + 1^2 squares.

That's beautiful.

Thanks!

Yeloby Feb 16, 2020 0 #4 62 squares. The kings take up two squares. DiogenesDue Feb 16, 2020 0 #5 scrabblechecs wrote:

64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 (8x8) = 168 squares !

Ummm...try again...

64+49+36+25+16+9+4+1=204

tyrannosaurical Feb 16, 2020 0 #6

Lol

Virmus Feb 16, 2020 0 #7 This isn’t easy to calculate. I’m guessing 8! (8x7x6x5x4x3x2) Sred Feb 18, 2020 0 #8

There is even an animated answer: http://datagenetics.com/blog/february12019/index.html.

BirdWing435 Mar 7, 2020 0 #9 We did that once in maths. The textbook said 204. BirdWing435 Mar 7, 2020 0 #10 Not kidding. btickler was right TPonder Mar 7, 2020 0 #11

64, not Nintendo. -Swaggeneral T Ponder

snoozyman Jun 29, 2021 0 #12 1 CM EvinSung Jun 29, 2021 0 #13

204

CastawayWill Jun 30, 2021 0 #14

1 1x1

5 2x2

14 3x3

30 4x4

55 5x5

91 6x6

140 7x7

204 8x8

285 9x9

385 10x10

506 11x11

650 12x12

819 13x13

1015 14x14

1240 15x15

Doniedarkojg Nov 22, 2021 0 #15

For n*n grid, no. Of squares=n*(n+1)*(2n+1)/6

Hence 8*9**17/6=204

Or sum of n^2 from 1 to 8

 

andrew47221 Nov 24, 2021 0 #16

Try the same thing, but for the XXL chess board

CM EvinSung Nov 24, 2021 0 #17

1496 then

tygxc Nov 25, 2021 0 #18

Now try the same for an 18 x 18 go board.

rudscoe Nov 25, 2021 0 #19

64 playable squares plus the board itself equals 65 squares

maricrisespaldon Mar 8, 2022 0 #20

 

1.  

Log In or Join Forums Hot Topics Unanswered -- Category -- Most Recent King's Gambit - post your favourite games as White! RalphHayward 4 min ago 📢ADVERTISE YOUR CLUB 📢 Dedo1362 5 min ago 12/23/2008 - Preparing a Surprise DefineBrilliant 10 min ago 5/12/2012 - Mate in 5 DefineBrilliant 11 min ago 12/25/2025 - Run, Run, Rudolph! 🦌 DefineBrilliant 11 min ago 9/24/2025 - Botez Gambit? 🎁 DefineBrilliant 12 min ago 9/13/2025 - Passing with Flying Colors DefineBrilliant 12 min ago 4/10/2011 - Down a Queen, Up a Mate DefineBrilliant 12 min ago 10/9/2025 - Made You Blink! DefineBrilliant 13 min ago 12/21/2025 - Round of Applause DefineBrilliant 13 min ago Forum Legend Following New Comments Locked Topic Pinned Topic