Jade Bangle ID-to-Weight Estimator
Estimate measured smooth bangle as elliptical-section torus under supplied density; no jade identity, rectangular section substitution or assumption of hidden cracks/voids.
Description
A smooth bangle can be approximated as a torus with an elliptical cross-section.
A smooth bangle can be approximated as a torus with an elliptical cross-section. Density converts the geometric volume to mass.1
Estimate measured smooth bangle as elliptical-section torus under supplied density; no jade identity, rectangular section substitution or assumption of hidden cracks/voids.
When to use Jade Bangle ID-to-Weight Estimator
Use this tool to estimate measured smooth bangle as elliptical-section torus under supplied density; no jade identity, rectangular section substitution or assumption of hidden cracks/voids.
Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.
How to use Jade Bangle ID-to-Weight Estimator 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 innerBangleDiameterMm, radialBandThicknessMm, axialBandHeightMm, materialDensityGramsPerCm3 using the field table and calculation rules, then run the tool.
- Read ellipticalTorusVolumeMm3, modeledBangleMassGrams. 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 |
|---|---|---|---|
| innerBangleDiameterMm | Inner bangle diameter mm | number | Required |
| radialBandThicknessMm | Radial band thickness mm | number | Required |
| axialBandHeightMm | Axial band height mm | number | Required |
| materialDensityGramsPerCm3 | Material density grams per cm3 | number | Required |
Use positive inner diameter, radial band thickness, axial height in mm and material density in g/cm³. Set major radius=(inner diameter+radial thickness)/2, use half thickness/height as semiaxes and convert mm³ to cm³ by dividing by 1000.
volume=2π² × major radius × radial semiaxis × axial semiaxis Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| ellipticalTorusVolumeMm3 | Elliptical torus volume mm3 | number |
| modeledBangleMassGrams | Modeled bangle mass grams | number |
{
"input": {
"innerBangleDiameterMm": 50,
"radialBandThicknessMm": 10,
"axialBandHeightMm": 8,
"materialDensityGramsPerCm3": 3
},
"output": {
"ellipticalTorusVolumeMm3": 11843.52528130723,
"modeledBangleMassGrams": 35.53057584392169
}
}Limitations and assumptions
Rectangular sections, voids and cracks violate the envelope assumptions. The model does not identify jade.
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 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. For a complementary task, use Graduated Strand Weight: Account heterogeneous graduated spherical bead density/count inventory using exact centered-bore napkin-ring volume, not subtracting a full-length cylinder through curved sphere; excludes cord/clasp and non-spherical pearls.
References
-
Jade Bangle ID-to-Weight Estimator — tool.io
Similar or alternative tools
- 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.
- Graduated Strand Weight
Account heterogeneous graduated spherical bead density/count inventory using exact centered-bore napkin-ring volume, not subtracting a full-length cylinder through curved sphere; excludes cord/clasp and non-spherical pearls.