Crown Angle from Height Ratio
Infer coaxial truncated-cone crown slope from measured table/girdle diameters and crown height; not individual faceted crown angles or an ideal-cut recommendation.
Description
A crown envelope slope depends on height and the radial distance from girdle to table.
A crown envelope slope depends on height and the radial distance from girdle to table. This differs from measuring individual faceted crown angles.1
Infer coaxial truncated-cone crown slope from measured table/girdle diameters and crown height; not individual faceted crown angles or an ideal-cut recommendation.
When to use Crown Angle from Height Ratio
Use this tool to infer coaxial truncated-cone crown slope from measured table/girdle diameters and crown height; not individual faceted crown angles or an ideal-cut recommendation.
Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.
How to use Crown Angle from Height Ratio and understand its results
- Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.
- Enter girdleDiameterMm, tableDiameterMm, crownHeightMm using the field table and calculation rules, then run the tool.
- Read axisymmetricCrownSlopeDegrees. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| girdleDiameterMm | Girdle diameter mm | number | Required |
| tableDiameterMm | Table diameter mm | number | Required |
| crownHeightMm | Crown height mm | number | Required |
Use positive girdle diameter, nonnegative table diameter/height in mm and table strictly smaller than girdle. Return the coaxial crown slope in degrees.
slope=atan2(crown height,(girdle diameter−table diameter)/2) × 180/π Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| axisymmetricCrownSlopeDegrees | Axisymmetric crown slope degrees | number |
{
"input": {
"girdleDiameterMm": 10,
"tableDiameterMm": 6,
"crownHeightMm": 2
},
"output": {
"axisymmetricCrownSlopeDegrees": 45
}
}Limitations and assumptions
No ideal-cut recommendation or optical-performance model is embedded.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Pavilion Angle from Depth: Infer coaxial truncated-cone pavilion slope from measured girdle/culet diameters and depth, preserving nonzero culet geometry; no crown-table measurement or ideal-cut/light-return certification. For a complementary task, use Total Surface Area Round Brilliant: Evaluate closed coaxial crown-frustum/girdle-cylinder/pavilion-frustum external envelope area including table/culet under supplied geometry; approximation is not true individual faceted round-brilliant geometry or carat weight.
References
-
Crown Angle from Height Ratio — tool.io
Similar or alternative tools
- Pavilion Angle from Depth
Infer coaxial truncated-cone pavilion slope from measured girdle/culet diameters and depth, preserving nonzero culet geometry; no crown-table measurement or ideal-cut/light-return certification.
- Total Surface Area Round Brilliant
Evaluate closed coaxial crown-frustum/girdle-cylinder/pavilion-frustum external envelope area including table/culet under supplied geometry; approximation is not true individual faceted round-brilliant geometry or carat weight.