I was trying to calculate the exact dimensions including crown and pavilion depths from the standard dimensions as given on a GIA cert, namely spread (diameter), table, total depth and carat weight. So I approximated the total volume of a round brilliant as the composition of a cone (for the pavilion), a truncated cone (crown) and a flat cylinder (girdle). Using some highschool math as well as the density of a diamond (3.51 g/cubic cm), one should indeed be able to calculate crown and pavilion depths from the standard measurements. However, I found the formula not very useful, apparently for two reasons:
(1) it seems I have to assume a much larger girdle than given on the cert, e.g. if the girdle is "medium", say 1.3%, I have to use 2.6% to arrive at the correct values. To put it another way, pavil depth, crown depth and girdle don't add up to total depth.
(2) the calculation is extremely sensitive to changes in girdle width, e.g. a 0.1% variation in the girdle can gives many times that variation in crown depth.
Does anybody know how to do this correctly?
(1) it seems I have to assume a much larger girdle than given on the cert, e.g. if the girdle is "medium", say 1.3%, I have to use 2.6% to arrive at the correct values. To put it another way, pavil depth, crown depth and girdle don't add up to total depth.
(2) the calculation is extremely sensitive to changes in girdle width, e.g. a 0.1% variation in the girdle can gives many times that variation in crown depth.
Does anybody know how to do this correctly?