Chess Board Piece Sizing Help

I have a Chess Board which has squares which are 3.5cm x 3.5cm (4.95cm diagonal) or  1.375in x 1.375in (1.95in diagonal).

What piece size should I be looking for? I cant find anything on the Chesscom Shop smaller than King base diameter of 1in/2.54cm. I've been told that the King's base diameter should be 75% of the square's size, but does the square size mean its diagonal distance or by length?

This is my board:

Square size is measured by the length of the sides of the square. 

A 1" king base would be 73% of the 1.375" size you quoted.

Staunton 0 (not 00) which is king heigth 60mm would fit.

Is it possible to find 1in King base size pieces in wood? I've only been able to find it in plastic. Honestly crazy to me that this big board is considered very small.

https://www.chesshouse.com/collections/wooden-chess-pieces/products/english-staunton-chessmen-weighted-handpolished-wood-2-1-2

https://www.chessbazaar.com/tournament-series-staunton-chess-pieces-with-german-knight-in-ebonized-boxwood-box-wood-3-king.html

You can probably find more, but here's a couple examples that might work for you.

Thanks, for the help, I'll probably buy the 2nd set at some point. 

Chess Set Sizing - Pieces vs Board...
The primary sizing criteria for the set and board is that of square size vs King base diameter...

A good rule of thumb is...
King base diameter = 0.75 * square size
or equivalently....
Square size = 1.33 * King base diameter

Any variation from these ratios, or the size of individual pieces and pawns becomes a matter of personal preference...
http://blog.chesshouse.com/how-to-select-the-right-size-chessboard-for-pieces/

You might also want to consult the FIDE Manual, Sections 2 and 3 on equipment regulations for FIDE events...
https://www.fide.com/FIDE/handbook/Standards_of_Chess_Equipment_and_tournament_venue.pdf