Round Brilliant Diamond Weight Estimation
Estimates the carat weight of a mounted round brilliant cut diamond without unsetting it, using caliper measurements of average diameter and total depth.
\[ W_{ct} = d_{avg}^2 \cdot h \cdot 0.0061 \cdot C_{girdle} \]
Plain Text Formula:
Weight_ct = (d_avg^2) * depth * 0.0061 * Girdle_Factor
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ W_{ct} \] | Estimated Weight | carats (ct) | Computed carat weight of the cut stone |
| \[ d_{avg} \] | Average Diameter | mm | Mean of minimum and maximum girdle diameters: (d_min + d_max)/2 |
| \[ h \] | Total Depth | mm | Table-to-culet vertical height |
| \[ 0.0061 \] | Specific Gravity Optical Factor | dimensionless | Empirical optical constant for diamond (SG 3.52) |
| \[ C_{girdle} \] | Girdle Thickness Correction | factor | Adjustment factor ranging from 0.98 (thin) to 1.05 (thick) |
💡 Worked Engineering Example
Problem Statement:
Estimate the carat weight of a round brilliant with 6.5 mm diameter, 3.96 mm depth, and medium girdle (factor 1.00).
Step-by-Step Solution:
- Calculate d^2 = 6.5 * 6.5 = 42.25
- Multiply by depth: 42.25 * 3.96 = 167.31
- Apply constant: 167.31 * 0.0061 = 1.02 ct
🎯 Result: The estimated weight is 1.02 carats (classic 1-carat round brilliant standard dimensions).