European ring sizes
European countries now use the ISO 8653 Ring Size Standard for jewellery rings. This standard uses the inner circumference of the ring in mm (i.e. the measurement around the inside of the ring) as its basis. Some places will use inner diameter (i.e. the distance from inside of one side of the ring to the inside of the other side of the ring across its widest point.) rather than inner circumference, but these are directly related.
Inner Circumference = π * Inner Diameter. (3.14 * Inner Diameter)
Some european countries, for instance Switzerland, used to use an arbitary numeric system similar to the US or Asian systems, but these are rarely used nowadays.
ISO 8653 was issued in 1986 and has been taken up by the European Committee for Standardisation (CEN) as EN 28653. The standard is known as BS EN 28653 in the UK, DS EN 28653 in Germany and prefixed by the local standards organisation codes in other European countries (e.g. BAS EN 28653 - Bosnia, CSN EN 28653 Czech Republic, LST EN 82653 - Lithuania)