In order to convert centimeters or milimeters to a ring size you need to know what you have measured. A ring is a circle and a circle can be described by the diameter (or radius) and by the circumference. It is important to know what you have measured. If you measured the Diameter you can covert that to circuference as follows: Circumference = π x Diameter (Where π is pi which is 3.141).
The measured size can be converted to an USA ring size or to UK, Japan or Euro ring size. Select what you have measured if it is in millimeters , centimeters or inches. Now select if it was the diameter or the circumference, finally select to which ring size you want it converted.