Ring sizing systems throughout the world vary. It would be great if everyone used the same system, it would certainly make things easier for me, but we don't. Below I will list what I know of these systems and include a reference chart at the bottom.
I make rings in both the UK and US systems.
United Kingdom and Commonwealth.
In the UK we use a system referred to as the Wheatsheaf system (although few call it wheatsheaf). The scale goes from A to Z with half sizes in between . Beyond Z is often expressed as Z+ 1, 2, 3, 4 etc. where each number represents a half size. This system is also used by many Commonwealth countries including Australia, New Zealand and South Africa to name a few. The only obvious exception is Canada, which uses the US scale. Virtually everything I make is in the UK sizing scale.
This system was revised in 1987, but is virtually identical to the previous system. As the UK was entirely imperial measurements, it shouldn't come as a surprise that this scale was based on a imperial measurement. Each difference in size was based on an increase of 1/64th of an inch in diameter. Although the UK is now decimal/metric, this system is still used.
United States and Canada.
The US and Canada use a system of numbers from 0 to 13 ordinarily, but can be extended beyond this as the difference between full sizes is 4/125" (0.032 inches (0.81 mm) of internal diameter, a wider difference between sizes than the UK system, but then there are 1/4 sizes in between.
Europe.
Europe uses 3 different systems which are all based on a metric measurement.
The European system, also known as the ISO standard, uses the internal circumference in mm. Straightforward and simple in theory and it's a scale that technically has no end as you could use this scale to make a hula hoop. This method is used in Austria, Belgium, Finland, France, Norway and Sweden. Germany, Russia and The Middle Eastern countries also use this system, but may use another Both Germany and Russia have their own systems and The Middle East often uses the Asian system.
The Swiss system uses the same measurement as above (internal circumference), but subtracts 40. For example a size M (UK scale) is a popular finger size which would be a European 53 or a Swiss 13. I'm not entirely sure of the reason for this adjustment, but would guess at the lower numbers being more flattering (thinking of dress and shoe sizes etc.). Countries that use this system include Italy, The Netherlands, Spain and Switzerland of course.
The German system uses the internal diameter, not circumference. This is typically measured to 0.1mm. To me this makes more sense as when you measure a ring on a ring stick (see image below), effectively this is what you are doing, measuring the diameter. If the ring has a gap at the back of the head, such as on a hollow signet ring, which bit do you measure? The diameter often gives a better fit. Germany uses this system alongside the European Standard as does Russia.
Japan and Asia.
The Japanese system is another numerical system starting at size 1, and again, technically stopping when you run out of numbers. It's similar to the German system where it's based on differences in measurement of diameter, but it is not the same. Each full size increases in 0.3mm increments with the starting size being 1. It's important to remember that a 1 isn't an actual, physical, measurement, it's the starting point. A Japanese size 1 has an internal diameter of approximately 13mm, a 2 would be 13.3mm and so on. Japan and China use this system almost exclusively, but many other countries use it occasionally. If you're in South America there is a good chance this is the system being used, but many others are also.
Russia.
Russia has it's own system that is not dissimilar to the German system where the internal diameter is used, but there is one very important difference, rounding. As an example a German size 15.6 (UK J) would be rounded to 15.5 (I 3/4 ish UK), 15.8 would be 16 and so on.
General Notes.
My preferred system to use is the UK system, no surprise there. It's simply because I was brought up with it and have always used it. I also use the US system. I don't like using the European system as it's too precise, which may seem a daft statement when it comes to measuring, but anyone who has worn a ring will know it feels different depending on the time of day, temperature etc. As I'm typing this post my wedding ring is happily spinning around on my finger, but first thing in the morning it's a little more firm, during the summer (interesting concept in the UK) it's bordering on too tight. It's roughly a variable of one UK size, in European sizes this could be 3 sizes.
Below there is a table of ring size comparisons which I have compiled and calculated this should give you an idea of the size you need, but please bear in mind that I work in the UK and US systems, so you need to find the nearest comparable size and go from there.
Please note that this is a chart I have researched and calculated to the best of my abilities, but I cannot be held liable for errors as they may exist. I have done my best to make sure the information is correct, but there is always the possibility of an issue.
Hopefully this will give you a bit of an overview on the ring sizing systems and how they are calculated. Working out the differences and producing this chart was a bit of a headache, but it got there.
Best wishes,
Damian