Cut Grading Tool | How we measure

The grade

The grade is read from GIA’s published Cut Grade Estimation Tables for Standard Round Brilliant Cut Diamonds (revision 12-09): 18 tables, one per table size from 50% to 67%, each a grid of 37 crown angles (22.0° to 40.0°, in 0.5° steps) by 22 pavilion angles (38.8° to 43.0°, in 0.2° steps). That makes 14,652 graded cells.

We read the tables from the published document’s vector data, not by eye. Each cell’s grade was taken twice, from its fill colour and from its printed label, and the two agree on every cell. A separate pass over a 300 dpi image of each page found no differing cell.

Your inputs are snapped to the reporting steps (table 1%, crown 0.5°, pavilion 0.2°, star and lower half 5%, girdle 0.5%), rounding half up. There is no interpolation. The grade is the worst of:

the grid cell for the table, crown and pavilion angle;
the limits on each proportion, crown height and total depth, girdle, star and lower half;
culet, polish, symmetry, painting and digging.

The breakdown lists every component at that worst grade. Outside the tables the grade is the worse of the nearest cell and the individual limits. The tables assume star 55%, lower half 80% and girdle 3.0%; other values can shift the grade in ways the limits do not capture, and the tool says so. Digital Gemology is not affiliated with GIA, and the tool’s result is not a GIA grade.

Derived proportions

With the diameter set to 100 and the table measured corner to corner:

\begin{array}{l} h_{c} = \frac{100 - t}{2} \tan c \\ d_{p} = 50 \tan p \\ D = h_{c} + g + d_{p} - 0.25 \end{array}

for table t, crown angle c, pavilion angle p and girdle g, all in per cent of the diameter. The −0.25 offset is calibrated. Of seven candidate formulas, it is the only one that reproduces both depths worked in the published document (62.8% at a 3.0% girdle and 63.3% at 3.5%) without contradicting the grids. Crown height is limited at its value rounded to 0.5, the only rounding with no conflicts. The T73 as cut (53 / 34.5° / 40.75° / 2.5%) gives 16.15 + 2.5 + 43.16 − 0.25 = 61.6%.

Light maps

There are 814 light maps, one for each crown and pavilion cell at 53% table, plus the T73 as cut. All are traced on the T73 (star 50%, lower half 77%, girdle 2.5%, no culet), with only the crown and pavilion angles changed. They use the zones in Light Return, face up and orthographic, at index 2.417, with no Fresnel, no dispersion and no head shadow. Each is traced at 1024 × 1024 and stored at 512 × 512 without loss. The shares are fractions of the face-up area, with rounding remainders assigned so the four sum to exactly 100.

Brilliance, fire and scintillation

Brilliance is traced. It is the ISO figure from the Brightness & Tilt Analysis, with a 23° head shadow, averaged over 13 tilts:

B = \frac{1}{13} \sum_{τ} {ISO}_{h = 23 °} (τ)

over the tilts τ = −30°, −25°, …, 30°, each on an 84 × 84 grid. The even dome and the 23° head shadow follow Hemphill et al. (1998) and Moses et al. (2004), in Gems & Gemology; 23° was not fitted to the grade tables. Values run from 41.7% to 65.1%, with a sampling noise of about ±0.2 points. Brilliance is traced on the T73 base for every cell of all 18 tables, so it does not follow the star, lower half, girdle or culet controls.

Fire and scintillation in this tool are modelled, not traced. They are smooth functions of the crown angle c and pavilion angle p, peaking at 100:

\begin{array}{l} fire = 100 e^{- {(\frac{c - 35.5}{2.2})}^{2}} e^{- {(\frac{p - 40.9}{0.95})}^{2}} \\ scintillation = 100 e^{- {(\frac{p - 40.8}{0.9})}^{2}} e^{- {(\frac{c - 34.5}{2.7})}^{2}} \end{array}

They show where each effect is strongest across the grid; the numbers are not measurements.

The Cut Grading Tool grades a round brilliant from its proportions. It is for education: not a grading standard, and not a substitute for a laboratory report.