Carat Weight vs. Face-Up Size

Analysis of a relationship between carat weight and face-up size

This page outlines the findings of an analysis of a relationship between carat weight and face-up size. I've analyzed data from a database of 698552 diamonds. The database was checked and cleaned, meaning that the obvious incorrect entries were preliminarly deleted.

I've split this report into two parts: Round cut analysis and Fancy shapes analysis. Since Round cut is by far the most popular shape and makes about 61% of the diamonds in my database (that's 424849 diamonds), it deserves a separate section.


Round Cut Analysis

The following graph illustrates the relationship between carat weight and average face-up diameter:


Carat weight vs. diameter graph
Average diameter was calculated for 23 different carat weights. Click here for detailed info on each plotted point: number of diamonds used, mean, median, standard deviation, and range.

As one would expect, the relationship is not linear; diameter increases slower than carat weight. Reference diamond line (dashed red line) is expectedly showing that the average diameter of diamonds on the market lags a bit behind the ideal, indicating the overall tendency of cutters to maximize weight rather than cut quality.


Carat Weight Distribution

The following graph was plotted with 575 data points (distinct carat weights) and shows the quantity of diamonds available for carat weights ranging from 0.1 to 6.1 carats.


Carat weight availability graph

As diamond prices jump at certain carat weights (especially at half and full carats), so does the availability of diamonds. It's pretty clear from the graph that diamond cutters aim to achieve these economically sound carat weights, even if it means sacrificing the beauty (cut quality) of the stones. These "magic" carat weights have the highest standard deviation in terms of size, which means that the spread of diamonds at these weights varies the most. For example, a diameter of 1 carat Round can range from 5.59 to 6.8 mm. The ideal would be around 6.5 mm.

0.5 carat diamonds are available in the highest numbers, closely followed by 0.7 and 1.01 carat stones. The latter is quite interesting as it shows how cutters like to play it safe to make sure they don't miss the magic 1 carat mark. Better safe than sorry. For comparison: there are 19268 1ct and 24317 1.01ct stones in my database, but only 236 0.99ct stones. The same trend can be observed at all weights where prices jump.



Fancy Shapes Analysis

The only way to compare face-up sizes of fancy shapes is to compare surface areas at the girdle plane. This can be tricky because each stone is unique in terms of outline. To overcome this problem I had to resort to estimations (more detailed explanation of how I do that can be found here). Although we're dealing with estimations, we can still see the overall trends.

The following graph shows the average relationship between carat weight and face-up size for all 11 main diamond shapes:


Carat weight vs. face-up size graph

Which shape faces up the largest? Look at the graph's legend, it's ordered from the largest to the smallest. The first place goes to marquise, followed by trillion, and then pear and oval, which basically overlap. Round is doing very well in the upper half of the bunch, at 5th place. The last place goes to asscher, mainly because of its large corners. If we compare asscher to second to last, princess, which is typically deeper and has in fact smaller length and width, it would still have larger surface area on account of asscher's deeply trimmed corners.


Carat Weight Distribution (Fancy Shapes)

Carat weight distribution of fancy shapes is very similar to that of round diamonds. The spikes indicate price jumps, where the availability is the highest:


Fancy shapes weight distribution graph


Conclusion

This analysis confirmed the overall tendency of the diamond cutting industry to maximize carat weight instead of focusing on the quality of the cut and producing more beautiful, but less heavy stones. It makes sense, since the general public mostly (and wrongly) equates carats with size. In the end, it's all about the money.

As we could see, the difference in face-up size at the same carat weight (for the same shape) can be quite considerable. When buying a diamond it pays to take this into account. It also pays to avoid weights where prices take big jumps. But then we come to the problem of availability.

Average diameter and reference diameter are plotted on the graph against carat weight.

Carat weight Nr. of diamonds Reference diameter Average diameter Median Standard deviation Range (min-max)
1 0.1 133 3.02 3.03 3.04 0.04 2.94-3.11
2 0.25 1060 4.09 4.06 4.07 0.041 3.88-4.26
3 0.5 25454 5.16 5.05 5.06 0.086 4.65-5.77
4 0.7 25055 5.77 5.64 5.65 0.088 5.25-6.11
5 0.75 2574 5.91 5.81 5.81 0.076 5.56-6.20
6 0.9 16874 6.28 6.13 6.14 0.1 5.50-6.72
7 1 19258 6.5 6.32 6.35 0.136 5.59-6.8
8 1.2 5568 6.91 6.79 6.8 0.08 6.39-7.12
9 1.25 1915 7 6.9 6.9 0.075 6.53-7.27
10 1.5 8346 7.44 7.29 7.3 0.104 6.7-7.78
11 1.75 463 7.83 7.72 7.71 0.088 7.4-8.16
12 2 2794 8.19 8.01 8.02 0.125 7.47-8.5
13 2.25 274 8.52 8.39 8.39 0.085 8.09-8.71
14 2.5 762 8.82 8.66 8.66 0.095 8.28-8.98
15 3 621 9.37 9.19 9.19 0.137 8.75-9.64
16 3.5 218 9.87 9.7 9.7 0.116 9.27-10.19
17 4 131 10.32 10.12 10.14 0.151 9.71-10.45
18 5 49 11.11 11 11 0.219 10.41-11.34
19 6 32 11.81 11.66 11.67 0.155 11.43-12.11
20 7 9 12.43 12.27 12.21 0.169 12.03-12.55
21 8 4 13 12.93 12.91 0.163 12.76-13.14
22 9.03 3 13.54 13.38 13.41 0.053 13.22-13.42
23 10.01 5 14 13.93 13.86 0.146 13.77-14.09




Round reference diamond has the following "ideal" proportions:
Proportions:
Table: 57%
Crown angle: 34°
Pavilion angle: 40.7°
Girdle: 2.8%
Star length: 50%
Lower half-length: 80%
Culet: None
Calculated values:
Depth: 60.3%
Crown height: 14.5%
Pavilion height: 43%