Quick and Easy Buying Guide
Carat weight: 1 carat = 200 milligrams = 6.5 mm diameter. Doubling weight doesn't double diameter.
Diamond clarity: FL/IF/VVS/VS = super expensive, near perfect. SI = best value if you can check a photo for obvious inclusions (defects).
Color: D-G = colorless, expensive, only if you have money to burn. H-J = best value. Can go lower in gold metal settings than white metal.
Cut: Better cut ratings let more light into a diamond, making it sparkle more. Very important property, don't skimp here.
Set a budget and minimum cut (Premium). Go J color for gold and I/H for white metals. Go searching for SI1/SI2 clarity diamonds at James Allen. Pick a diamond with small/no inclusions. Choose a ring setting and buy it risk-free (60-day returns).
Actual 1.66 Carat Princess Shape Diamond Size on Hand
This article includes a handy picture showing you the apparent size of a 1.66 carat size princess shape diamond, when viewed in place on the hand of a woman. If you search around on the web to find the actual size of a 1.66 carat weight princess shape diamond, you may pick up that the numbers will vary slightly - this is due to the fact that the size (7.2 mm for this particular diamond) depends on things like cut as well.
The photo in this page shows an L 1/2 ring size, which is typical or perhaps on the small side of typical for a female ring.
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Photos can sometimes be notoriously deceptive - I've tried to make this one as clear as possible, but don't forget seeing the diamond in person may give you a very different impression of size to viewing it on the internet.
Don't stress if diamonds and the costs are getting you down - because the diamond will appear larger on her hand, you may not need to spend as much to get your desired effect.