Diamond weight is expressed in metric carats. One metric carat equals 0.200 grams or 1/5 gram. There are 100 points to a 1.00 carat diamond.
Accordingly a 50-point diamond is ½ carat and a 75-point diamond is a ¾ carat. Due to the uniformity of proportions for round diamonds, the carat weight and the diameter are usually predictable.
Because of the complexity of fancy shaped diamond, (any diamond shapes other than round) carat weight and millimeter dimensions are not as predictable. The majority of fancy colour diamonds will be cut into a fancy shaped diamond.
The following relationships are for fancy shapes with aesthetically pleasing length to width ratio for that particular shape.
Emeralds, Radiants & Ovals