i made a set of chess piece, with its king base diameter of 5cm what would be the proportional chess board size for that? a perfect square for that size would be?... i need help thanks....

10 cm ...

To determine the optimal square size, divide the diameter of the base of the king by .75, and then add between 1/8" and 1/4" (.3 to .6 cm).  So, a king with a base of 5cm would require playing squares between 7.0 and 7.3 cm.

These links may help. Whitehorsechess and FIDE.

The squares are too small, too big and just right.

Squares of about 6.5 cm should fit nicely.

- Michael