... without him/her realizing it?
I'm going to tell you the story of a friend who wanted to propose to his girlfriend, and do it as a surprise. She was to be completely unsuspecting and it was to be perfect.
The hardest part was knowing her finger size... how could I do that when she wasn't wearing any jewelry?
So it's quite possible, thanks to photography, geometry and a few rules of three.
First of all, you need to decide which finger the engagement ring should be worn on. In general, it's worn on the ring finger of the right hand, the same finger as the wedding band. However, there are no rules, and depending on the type of engagement and wedding ring, the 2 cannot be worn on the same side.
So the choice is yours, bearing in mind that the right and left hands are not identical, so there may be slight differences in size. However, a jeweller will always be able to adapt the size if the engagement ring suddenly needs to be moved to another side.
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So you chose which finger you wanted to put the ring on!
Get out your best camera and take lots of photos of those hands, but it's best to take photos where she's holding something whose exact size you know. For example, a cup, the telephone, the steering wheel of the car etc...
Then calculate....
A word of advice: be very precise and take lots of photos.
Classic size: 52mm to 57mm circumference