A System for Sizing Chess Pieces and Boards (long)

I remember watching that a few years back. The test is only a go-nogo test. In the video, the bishop easily slides between the king and queen on a 55mm board, but it will also pass the same test on any board larger than 55mm as well. So which board is the right one? And what about sizing the remaining pieces (knight, rook, and pawns)? Shouldn't they be considered as well?

There is no rigid rule. But there are general useful rules like this with royal pair and bishop "dance" . Indeed, for a harmonious proportion several rules must be implemented, not just one. Others very useful general rules that I realy like it for a long time ago, which have been already exposed here even by others, are:
-for those who like it more air space-four pawns must fit about on a square.
- or for those who like it more tighter space- two pawns must fit about on the diagonal of the square
-King base diameter must be about 75%-80% from the square.

-King hight must be slightly smaller than two squares
-There may be other useful rules that do not contradict the above rules
If all this general rules match simultaneously with chess pices and the board, it will be a good proportion chess set and a pleasant play game.

loubalch's sizing chart looks optimal to me.  Seems to track well with the USCF sizing guidelines, which I realize are not universal.  Just my $.02.

For those who are not so inclined to "plug and chug" through the numbers, I offer the following tables to summarize the recommended king and pawn dimensions for various size chess boards.

For those living in most of the world, here's the table in centimeters (cm).

NOTE: The deviation is a measurement of how close (or not so close) a chess set is from the ideal ratios as proposed in the formulas. The closer the number is to zero, the close the set is to the ideal. A number of 5 or less indicates a very well balanced chess set.

Thank you very much for sharing!

You may be over-thinking it.

Very detailed.

Thank you 👍

Dimensioning System:

A – King's height

B – Base of kings and queens

a – Pawn height

b – Pawn base

L – Side of the square

A = 2a King's height = twice the pawn's height

L = 2b Pawn base = half the side (FIDE: 4 pawns on the same square).

A/L = a/b By similarity of triangles, the king's height is to the side of the square as the pawn's height is to its base.

A = 1.75 L King's height (in accordance with FIDE average parameters)

For the king's height, we find the greatest variations, generally between 1.5L and 2.0L.

Rook height = L (FIDE for average side)

(B+b)/2 = Bishop, knight, and rook bases

L = (B+d)(sqrt 2)

Where d is the distance between two pieces with the largest bases, one positioned on a square and the other diagonally, with its center coinciding with one of the corners of that same square. This distance d is necessary for the pieces to slide diagonally across the board without colliding and without creating visual blockages that impact reasoning.

B = (5/8) L = 62.5% L (king's base = five-eighths of the square's side)

It provides better visualization for the movement of the pieces, with d=8.2%L.

By the golden ratio, B = 61.8% L, resulting in d=8.9%L.

For the classic rule of thirds, B = (2/3) L = 66.6% L, we have d=4%L.

In the limit, for d=0, resulting in B = 70.7% L. Above that, it is an overcrowded board.

In short, what really matters is YOUR personal preference.