Diamonds are weighed on a carat scale (not to be confused with Karat- a unit of gold purity). The weight unit's name "carat" is derived from the carob seed - a measuring unit used in the Middle Ages. There are 100 points in one carat. Therefore, weight can also be understood as a ratio (i.e. points/ 100). A fifty point diamond or half a carat is 50/100's of a carat.
The size of a diamond measured in millimeters can also assist in approximately determining the diamond's carat weight. This can be done by using the following formula: [Average Diameter in mm] x [Depth in mm] x 0.0061 (where "x" stands for "multiply" and 0.0061 is the Size/Weight conversion factor).
It is important to understand that there is no direct relationship between size and weight (i.e. fifty point diamond is not twice as large (or wide) as a twenty five point diamond, only twice as heavy).
The size alone is not enough to determine a diamond's value. We have to consider the cut and proportions of a diamond as well as the quality of its polish. Even a large diamond holds little value when cut poorly or shaped in a vulgar manner.
The chart above illustrates the relationship between a stone's weight and its diameter. When we measure small stones (melee, or stones less than 0.05 carats in weight), we stop speaking of diamond weight and speak in terms of the diameter of a stone when referring to its size. A very small stone (under 1.2 mm in diameter) is very difficult to accurately weigh individually. We use "parcel weight" or in different terms the weight of a bunch of stones to accurately gauge the weight used to be set in pave.
Center stones are usually weighed up to 100th of a carat. Recently, gem labs started issuing certificates that state a diamond weight up to one-thousandth of a carat.