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Many department stores have a jewelry section. In this section, there is often a display of many rings where you can try on the different rings. In most cases, the rings are arranged by size, and the ring size is clearly indicated. Casually trying on rings for fun is the perfect way to get her ring size on the sly. Take her to the mall for a casual shopping trip, and plan it so that you just happen to pass by the ring display. When you pass by, act like there is a ring that has caught your interest. Usually, there will be rings for men and women. If you are a man, start casually trying on the men's rings and invite her to join in the fun. If you live together or spend the night together often, you can try to measure her ring finger while she is sleeping. The easiest way to do this is to use a piece of string. When she is in her deepest sleep, gently wrap the string around her finger so that it is snug, but not tight. If you see her finger changing color, the string is too tight.  Mark the spot where the string comes together and then use a ring size chart to figure out her ring size. You can find one at this website: http://qalo.com/pages/ring-size-chart. By doing it this way, you can measure the length of the string in inches or millimeters. This will be the circumference of her finger. You can then easily convert this into the correct ring size. If she is not a deep sleeper then this is probably not the safest option. If she wakes up, you'll probably have a hard time explaining what you're doing without arousing suspicion. This method isn't the most exact method in the world, but it can help give you an idea. Keep this as casual as possible. For example, if you are hanging out watching TV, hold her hand for awhile. Try to wait until she's really into whatever is on TV and then compare her ring finger with your fingers. Is there one that is pretty similar in size?  Do this casually, don't just grab her hand out of nowhere and start comparing all of your fingers. If you do have one finger that is quite similar to her ring finger you can go to the jewelers and explain the situation to them. They'll help you size your own finger to figure out her ring size.
Take her to the mall. Measure her finger while she is sleeping. Compare her fingers with your fingers.