2.3 The height of the pieces, in descending height order, is as follows: King – 9.5 cm, Queen – 8.5 cm, Bishop – 7 cm, Knight – 6 cm, Rook – 5.5 cm and Pawn – 5 cm. These dimensions may differ by up to 10%, but the pieces must remain in descending height order.
2.4 The diameter of a piece's base should measure 40-50% of its height.
https://handbook.fide.com/chapter/StandardsOfChessEquipment2022
This whole discussion is laughable. Dimensions, like beauty, are in the eye of the beholder.
Thank you all for this enlightening conversation. Lou, the charts are particularly helpful to me because I build chess sets. I've used a 74% ratio for my kings but was always a bit uncertain about pawn sizes. Including the weight size on the charts is very useful as well. I plan on consulting your charts, particularly for the Staunton sets I build. My sets and boards are sold through my Etsy website at FallingLeafChess.Etsy.com in case anyone is interested.
Practical sizing:
A – Height of the king
B – Base of kings and queens
a – pawn height
b – pawn base
S – Side of the square
A=2a (height of the king = twice the height of the pawn)
S=2b (base of the pawn = half the side of the square)
A/S = a/b
Tower height = side of the square.
Bishop, knight and rook bases = average between king and pawn bases.
S = (B+d) √2
Where d is the distance that makes it possible to slide a piece between two others with the same base arranged diagonally (a queen between the opponent's king and queen).
B = (2/3) S (king's base = two-thirds of the side of the square)
Classic, usual proportion, which preserves a minimum distance d.
In the limit, for d=0, B=70.7%S. For any proportion above this, visual blocks are created that can impact reasoning.
On a crowded board, pieces do not slide freely, they are easily knocked over and the visual paths of movement are not clearly visible.
A = (7/4) S (height of the king = seven quarters of the side of the square)
Also common proportion, with small variations, compatible with Fide specifications (H=95 and S=55 mm) and with sets used in championships.
The average referential inclination from the king to the pawn is around 10°.
In short, what really matters is YOUR personal preference.
I've had a chuckle reading this and the other thread on dimensions.
Some of you guys are really overthinking it. Just go and turn/carve/print the dang things.
Food for thought 1: Different people have different preference to how crowded they like their boards.
Food for thought 2: Base diameter is closely linked to the shape of the rest of the piece, so one base won't fit every design.
Food for thought 3: You need to try out different sizes to see which one works better. Prototyping the design, putting it on the board and empirically coming to final dimensions is the only way to go. If you just design the set on paper, you'll have no idea how it feels in your hand, and you might even be surprised by how it looks in 3d in real life.
So apart from king's base being around 77% of the square, calculating any other precise measurements is a bit of a waste of time imho. Just get the proportions from a small sample of tournament sets and use them as your rough guidelines.
Most importantly, have fun.