I am not a fan of buying ring online unless I have seen or tried the same thing on in real life. For several reasons – sizing is often difficult because different countries use different systems and don’t always convert sizes properly between systems. Fingers are really individual and the wider the band, the tighter they fit. Some people have big knuckles. Big stones can slide around on your finger, or look ridiculous.
I find this site to be quite helpful. It is not always completely accurate, but it is rather fun to play around on, and has been a useful aid for me when buying online.