RAPAPORT... Diamonds are sold by weight and not by visible size or measured diameter. Given two diamonds of the same average diameter, quality factors and visual appearance — but different weights — the heavier diamond will sell for more. This design aspect, called Weight Ratio, is used in the Gemological Institute of America (GIA) Diamond Cut Grading System to assess hidden weight. If a round brilliant possesses more than a specified tolerance of hidden weight that does not contribute to a larger appearance or better performance, the diamond will receive a lower cut grade.
The GIA Diamond Cut Grading System calculates a Weight Ratio value for each round brilliant diamond graded by the laboratory. The volume of the diamond to be graded, calculated from the rounded, reported proportions of the stone, is compared to the volume of a specific theoretical reference diamond using the same average diameter as the submitted stone. Because both volumes are for diamond, and have the same specific gravity, the value for this volume ratio is identical to a weight ratio.
This reference diamond (Figures 1 and 2) has the following proportions:
• Table: 57%
• Crown angle: 34.0°
• Pavilion angle: 40.7°
• Girdle thickness: 2.5%
• Star length: 50%
• Lower half-length: 80%
• Additional features: excellent symmetry and no culet, painting or digging out.
Calculated values derived from these proportions are total depth, 60.0 percent; crown height, 14.5 percent and pavilion depth, 43.0 percent.
These reference proportions define a Weight Ratio of 1.00, the lowest value for which this parameter is evaluated. Round brilliants receiving Excellent proportion grades most commonly have Weight Ratio values between 1.02 and 1.05. Diamonds with higher Weight Ratio values have extra thickness in the crown, the pavilion or, most typically, the girdle region. In some cases, extra thickness in all three regions results in a higher Weight Ratio value and therefore a lower cut grade.
Example Calculations
1. A diamond with an average diameter of 10.00 mm (Figures 3 and 4) is submitted to the GIA Laboratory for grading services. The following rounded proportions are obtained for this diamond:
• Table: 53%
• Crown angle: 35.0°
• Pavilion angle: 41.2°
• Girdle thickness: 4%
• Star length: 50%
• Lower half-length: 80%
• Additional feature: no culet
Calculated values derived from these proportions are total depth, 64.2 percent; crown height, 16.5 percent; pavilion depth, 43.8 percent and weight, 3.943 carats.
The weight for the theoretical reference diamond is calculated using the same diameter as the diamond to be graded — 10.00 mm. The resulting weight is 3.592 carats. To determine the Weight Ratio, the derived weight of the submitted diamond is divided by the calculated weight of the reference diamond:
Weight Ratio = 3.943 carats divided by 3.592 carats = 1.098
This Weight Ratio value of 1.098 falls into the Very Good grade range. In this case, the total depth value, calculated from the rounded proportions, is also large enough to limit the grade. This combination — round brilliants too heavy and too deep for an Excellent cut grade — is fairly common (Figure 5).
2. A round brilliant with an average diameter of 4.70 mm is submitted for grading (Figures 6 and 7). The following rounded proportions are obtained for this diamond:
• Table: 55%
• Crown angle: 34.0°
• Pavilion angle: 40.8°
• Girdle thickness: 4.5%
• Star length: 55%
• Lower half-length: 80%
• Additional feature: no culet
Calculated values derived from these proportions are total depth, 62.8 percent; crown height, 15.2 percent; pavilion depth, 43.2 percent and weight, 0.405 carat.
The weight for the theoretical reference diamond is calculated using the same diameter as the diamond to be graded — 4.70 mm. The resulting weight is 0.373 carat. To determine the Weight Ratio, the derived weight of the submitted diamond is divided by the calculated weight of the reference diamond:
Weight Ratio = 0.405 carat divided by 0.373 carat = 1.086
Unlike the first example, this diamond carries almost all of its extra weight in the girdle region (Figure 8). The total depth for this proportion combination is within the Excellent grade range, but the Weight Ratio exceeds the threshold for the highest grade and limits this proportion combination to a grade of Very Good.
Using Weight Ratio
Weight Ratio values are not provided on GIA Diamond Grading and Diamond Dossier reports because they are not used as a separate parameter for determining the overall cut grade. As the GIA Diamond Cut Grading System evolved, the benefit of linking all the grading aspects related to proportions to each combination of rounded proportions in the system became apparent. Associations between the appearance and design aspects of the system and the six proportion parameters not only simplified the system, but allowed for the development of a predictive tool, the GIA Facetware® program. Rather than determine each diamond’s individual scores for brightness, fire, various scintillation components, weight ratio, total depth, durability, etc., and the resulting cut grade, the Facetware program contains the results of precomputed scores for each rounded proportion combination in the system. This means that the estimated grade given by the Facetware program, whether online or imbedded in a measuring system, already includes the cumulative effect of all the grading system components related to the reported proportions. The same six proportion parameters that determine the estimated cut grade — in the Facetware program or in GIA reports — also determine whether Weight Ratio limits the grade, as in the example calculations above, and the five examples in the chart below.
Chart 1 shows five sets of proportions, one set for each grade range — Excellent, Very Good, Good, Fair and Poor — along with the corresponding calculated total depth percentages and Weight Ratio values. These examples are provided to illustrate common proportions for which Weight Ratio is a significant component of the cut grade. Overlapping profile views of these five examples (Figure 9) show how the volume of the diamond increases across each grade boundary.
An estimated Weight Ratio value can be useful for manufacturers to consider as they pursue maximum yield and a particular cut grade. A simple formula can be used to calculate a reference weight:
Reference weight = Average diameter multiplied by Average diameter multiplied by Average diameter multiplied by 0.003592
To finish estimating the Weight Ratio, divide the actual weight of the diamond by this reference weight. The graded diamond’s actual weight may differ slightly from the derived weight because of rounded proportions, symmetry factors and painting or digging out. However, an estimated Weight Ratio is easy to calculate and can provide a helpful warning of diamonds that are pushing grade boundaries, especially those weighing 0.50 carat or more.
When the estimated Weight Ratio is between 1.08 and 1.09, the diamond’s rounded proportions are quite close to the border between Excellent and Very Good cut grades. For such cases, it would be prudent to use the Facetware program to check both the specific proportions of the diamond and the surrounding proportions. If a change of one unit to table percentage, crown angle, pavilion angle or average girdle thickness changes the grade, the diamond may be too close to that grade border for comfort. For most cases in which the Weight Ratio is 1.09, the diamond is likely to receive a Very Good cut grade. Similarly, Weight Ratios between 1.16 and 1.17 occur for proportions close to the border between cut grades of Very Good and Good.
Note that the relationship between diameter and weight varies with the proportion combination. Although diameter is an important component of the overall volume, a round brilliant is not a sphere; other proportions also make important contributions. The conversion factor above works for these reference proportions, but not for other proportion combinations, even similar ones, as shown in Chart 2.
Some diamonds with a high Weight Ratio also exceed the total depth limits of the grading system. For more information on total depth and other parameters, see “Estimating a Cut Grade Using the GIA Diamond Cut Grading System,” available for download at www.gia.edu/diamondcut/08_tools_for_the_trade.html.
As shown in the examples, a total depth percentage is calculated from the rounded proportions that are used to determine the estimated cut grade. This rounded total depth percentage may be slightly larger or smaller than the actual measured and reported total depth percentage. An upgrade to the online Facetware program in the autumn of 2009 eliminated total depth percentage as an input parameter in order to encourage the use of the same proportion parameters used for GIA reports. Eliminating this parameter increased the accuracy of the online estimated cut grades. The program displays total depth calculated from the rounded proportions as output, for comparison to the reported total depth percentage.
Chart 1
Grade Excellent Very Good Good Fair Poor
Table% 57 56 56 53 52
Crown° 35 36 37 38 39
Pavilion° 41.0 41.4 41.6 42.0 42.6
Girdle % 3.0 4.5 5.5 7.0 9.0
Star % 50 50 50 50 50
Lower half % 80 80 80 80 80
Total depth % 61.3 64.3 66.2 70.2 74.2 Weight Ratio 1.04 1.12 1.18 1.27 1.42
Five examples, one from each grade in the GIA Diamond Cut Grading System, show how the Weight Ratio increases as the cut grade decreases.
Chart 2
reference example example example example
set 1 2 3 4
Table% 57 57 55 53 53
Crown° 34.0 35.0 35.0 36.0 36.0
Pavilion° 40.7 41.2 41.2 41.2 41.2
Girdle % 2.5 4.0 4.0 5.0 5.5
Star % 50 50 50 50 50
Lower Half % 80 80 80 80 80
Weight Ratio 1.00 1.08 1.09 1.15 1.17
Cut GradeEX EX VG VG GD
diameter weightweightweightweightweight
mm ct ct ct ct ct
3.5 0.154 0.166 0.168 0.177 0.180
4.0 0.230 0.248 0.250 0.264 0.269
4.5 0.327 0.354 0.357 0.377 0.383
5.0 0.449 0.485 0.489 0.517 0.525
5.5 0.598 0.646 0.651 0.688 0.699
6.0 0.776 0.839 0.845 0.893 0.908
6.5 0.986 1.066 1.075 1.135 1.154
7.0 1.232 1.332 1.342 1.417 1.441
7.5 1.515 1.638 1.651 1.743 1.772
8.0 1.839 1.988 2.004 2.116 2.151
8.5 2.206 2.384 2.403 2.538 2.580
9.0 2.618 2.830 2.853 3.013 3.063
9.5 3.079 3.329 3.355 3.543 3.602
10.0 3.592 3.882 3.913 4.132 4.201
15.0 12.12213.10313.20713.94714.180
20.0 28.73331.06031.30733.06033.612
The reference proportions are compared to four examples with successively larger Weight Ratio values. These examples lie near grade boundaries within the GIA Diamond Cut Grading System, and show just a few of the ways that a round brilliant can be overweight.
Ilene Reinitz, project manager, Gemological Institute of America, New York; Ron Geurts, research and development manager, Gemological Institute of America, Belgium, and Al Gilbertson, research associate, Gemological Institute of America, Carlsbad
Article from the Rapaport Magazine - February 2010. To subscribe click here.