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.
Description
A pavilion frustum slope depends on depth and the radial run between girdle and culet.
A pavilion frustum slope depends on depth and the radial run between girdle and culet. A nonzero culet changes that run.1
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.
When to use Pavilion Angle from Depth
Use this tool to 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.
Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.
How to use Pavilion Angle from Depth 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, culetDiameterMm, pavilionDepthMm using the field table and calculation rules, then run the tool.
- Read axisymmetricPavilionSlopeDegrees. 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 |
| culetDiameterMm | Culet diameter mm | number | Required |
| pavilionDepthMm | Pavilion depth mm | number | Required |
Use positive girdle diameter, nonnegative culet/depth and culet strictly smaller than girdle. Return the coaxial envelope slope; zero depth gives zero angle.
slope degrees=atan2(pavilion depth,(girdle diameter−culet diameter)/2) × 180/π Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| axisymmetricPavilionSlopeDegrees | Axisymmetric pavilion slope degrees | number |
{
"input": {
"girdleDiameterMm": 10,
"culetDiameterMm": 2,
"pavilionDepthMm": 4
},
"output": {
"axisymmetricPavilionSlopeDegrees": 45
}
}Limitations and assumptions
Individual facet angles and light return are not reconstructed.
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 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. For a complementary task, use Volume of Round Brilliant: Evaluate closed coaxial crown-frustum/girdle-cylinder/pavilion-frustum envelope volume including table/culet under supplied geometry; approximation is not true individual faceted round-brilliant geometry or carat weight.
References
-
Pavilion Angle from Depth — tool.io
Similar or alternative tools
- 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.
- Volume of Round Brilliant
Evaluate closed coaxial crown-frustum/girdle-cylinder/pavilion-frustum envelope volume including table/culet under supplied geometry; approximation is not true individual faceted round-brilliant geometry or carat weight.