The rule of thumb for square size is 4/3rds the king diameter. Since your rook is bigger and is 3 inches, then look for a 4 inch square, for example
https://www.megachess.com/collections/giant-chess-boards-with-4-inch-squares
Or you could commission someone like Brad Borkowski, https://www.etsy.com/shop/ColoradoWoodWorker https://shoutoutcolorado.com/meet-brad-borkowski-construction-teacher-chessboard-maker/
Brad Borkowski is ColoradoWoodWorker (ETSY.com).....custom solid wood boards...
https://www.etsy.com/shop/ColoradoWoodWorker
You can check out the board that CWW made for me (my posts here on 7 & 10 March 2017)...
https://www.chess.com/forum/view/chess-equipment/cb-gm-blitz-set?page=4
Chess Set Sizing - Pieces vs Board.....any deviation from this rule of thumb becomes a matter of personal preference...
http://blog.chesshouse.com/how-to-select-the-right-size-chessboard-for-pieces/
Background/setup:
In the 1970's, the Sear catalogue sold a chess set where the pieces were ceramic, and pretty large.
The bishops (the tallest pieces) are almost 7 inches tall. The rooks (the widest pieces) are about 3 inches wide.
Originally, they were sold with a "board" that was actually a rug.
Recently, I inherited a set of the pieces, and they are exquisite.
However, I didn't get a board that I can use these pieces on.
I have contacted thechessstore.com, and they do not sell a board that has spaces large enough to accommodate those chess pieces.
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My question to you all:
Can you help me find a board that will properly accommodate those pieces?
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Any help you can give is much appreciated.
Sarge