In the United States and Canada, ring sizes are specified using a numerical scale, with quarter and half sizes. An increase of a full size is an increase of 0.032 inch (0.8128 mm) in diameter, or roughly 1/10 inch (more precisely, 0.1005 in or 2.55 mm) in inside circumference.
Generally, sizes in quarters and halves will not relate conventionally to anything on any known ruler. Also, on one finger alone a person may vary more than a whole ring size- depending on time of day, work performed, and other swelling-inducing activities/conditions. Therefore, in most cases quarter-sizes are meaningless unless one needs precise accuracy with a particular ring.
In Europe (excluding Ireland and the United Kingdom), ring sizes are specified using a numerical scale, with half sizes.
In Ireland, the United Kingdom and Australia, ring sizes are specified using an alphabetical scale, with half sizes.
In Japan, ring sizes are specified using a numerical scale, that only has whole sizes.
In Switzerland, ring sizes are specified using a numerical scale, with quarter and half sizes.
In Germany, ring sizes are specified using actual internal circumference in mm. (the same as ISO)
The ISO standard for ring sizes is ISO 8653:1986, which defines standard ring sizes in terms of the inner circumference of the ring measured in millimetres.