Princess Carat Size vs. Surface Area
The below diamond size chart shows the changing dynamic between an increase in carat size and the respective increase in an princess cut diamond's visual appearance. While carat weight is typically thought of as an indication of a diamond's size (meaning visual appareance), carat is actually a measure of weight. Diamonds of the same carat size can vary slightly in their visual appearance depending on how they are cut. For instance, a diamond with a deeper cut will appear smaller than a diamond of the same carat weight with a shallower cut.
For our princess cut diamond analysis we averaged the diameters of hundreds of thousands of diamonds from Blue Nile, Enchanted, Whiteflash, and Brian Gavin Diamonds to come up with a simple exponential function (shown on the chart below). Using this formula we can study the corresponding changes in diameter and surface area for a given change in carat weight. Interestingly, as the carat size increases we notice a significant slowing of the surface area. This is because carat weight scales as a measure of volume (mm cube) while surface area scales at a slower rate (mm squared).
Princess Carat, Diameter and Surface Area
| Carat | Diameter (mm) | Surface Area (sq. mm) |
|---|---|---|
| 0.3 ct. | 3.63 | 13.15 |
| 0.4 ct. | 4.00 | 15.99 |
| 0.5 ct. | 4.31 | 18.61 |
| 0.6 ct. | 4.59 | 21.06 |
| 0.7 ct. | 4.84 | 23.39 |
| 0.8 ct. | 5.06 | 25.61 |
| 0.9 ct. | 5.27 | 27.74 |
| 1 ct. | 5.46 | 29.80 |
| 1.1 ct. | 5.64 | 31.80 |
| 1.2 ct. | 5.81 | 33.73 |
| 1.3 ct. | 5.97 | 35.62 |
| 1.4 ct. | 6.12 | 37.46 |
| 1.5 ct. | 6.27 | 39.26 |
| 1.6 ct. | 6.40 | 41.02 |
| 1.7 ct. | 6.54 | 42.74 |
| 1.8 ct. | 6.67 | 44.44 |
| 1.9 ct. | 6.79 | 46.10 |
| 2 ct. | 6.91 | 47.73 |
| 2.1 ct. | 7.02 | 49.34 |
| 2.2 ct. | 7.14 | 50.93 |
| 2.3 ct. | 7.24 | 52.49 |
| 2.4 ct. | 7.35 | 54.03 |
| 2.5 ct. | 7.45 | 55.55 |
| 2.6 ct. | 7.55 | 57.05 |
| 2.7 ct. | 7.65 | 58.53 |
| 2.8 ct. | 7.75 | 60.00 |
| 2.9 ct. | 7.84 | 61.45 |
| 3 ct. | 7.93 | 62.88 |
| 3.1 ct. | 8.02 | 64.29 |
| 3.2 ct. | 8.11 | 65.70 |
| 3.3 ct. | 8.19 | 67.09 |
| 3.4 ct. | 8.27 | 68.46 |
| 3.5 ct. | 8.36 | 69.82 |
| 3.6 ct. | 8.44 | 71.17 |
| 3.7 ct. | 8.52 | 72.51 |
| 3.8 ct. | 8.59 | 73.84 |
| 3.9 ct. | 8.67 | 75.15 |
| 4 ct. | 8.74 | 76.45 |
| 4.1 ct. | 8.82 | 77.75 |
| 4.2 ct. | 8.89 | 79.03 |
| 4.3 ct. | 8.96 | 80.31 |
| 4.4 ct. | 9.03 | 81.57 |
| 4.5 ct. | 9.10 | 82.83 |
| 4.6 ct. | 9.17 | 84.07 |
| 4.7 ct. | 9.24 | 85.31 |
| 4.8 ct. | 9.30 | 86.54 |
| 4.9 ct. | 9.37 | 87.76 |
| 5 ct. | 9.43 | 88.97 |
