Spread Ratio Diameter-to-Carat

Compare measured face-up diameter/area to caller independently calibrated mass-scaling reference; no universal ideal diameter, commercial cut grade or assumed same-density mineral.

Description

Face-up spread compares measured diameter with an independently calibrated mass-scaling reference.

Face-up spread compares measured diameter with an independently calibrated mass-scaling reference. Squaring the diameter ratio gives an area ratio for circular outlines.^[1]

Compare measured face-up diameter/area to caller independently calibrated mass-scaling reference; no universal ideal diameter, commercial cut grade or assumed same-density mineral.

When to use Spread Ratio Diameter-to-Carat

Use this tool to compare measured face-up diameter/area to caller independently calibrated mass-scaling reference; no universal ideal diameter, commercial cut grade or assumed same-density mineral.

Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.

How to use Spread Ratio Diameter-to-Carat 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 observedDiameterMm, observedCaratMass, callerReferenceDiameterMmAtOneCarat, callerMassScalingExponent using the field table and calculation rules, then run the tool.
Read referenceModelDiameterMm, diameterSpreadRelativeToMassModel, faceUpAreaSpreadRelativeToModel. 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
observedDiameterMm	Observed diameter mm	number	Required
observedCaratMass	Observed carat mass	number	Required
callerReferenceDiameterMmAtOneCarat	Caller reference diameter mm at one carat	number	Required
callerMassScalingExponent	Caller mass scaling exponent	number	Required

Use positive observed diameter, carat mass, one-carat reference diameter and scaling exponent. Return reference diameter and diameter/area spread ratios.

reference diameter=one-carat reference × carat mass^exponent; area ratio=(observed/reference diameter)²

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
referenceModelDiameterMm	Reference model diameter mm	number
diameterSpreadRelativeToMassModel	Diameter spread relative to mass model	number
faceUpAreaSpreadRelativeToModel	Face up area spread relative to model	number

json

{
  "input": {
    "observedDiameterMm": 6,
    "observedCaratMass": 1,
    "callerReferenceDiameterMmAtOneCarat": 6,
    "callerMassScalingExponent": 0.3333333333333333
  },
  "output": {
    "referenceModelDiameterMm": 6,
    "diameterSpreadRelativeToMassModel": 1,
    "faceUpAreaSpreadRelativeToModel": 1
  }
}

Limitations and assumptions

No universal ideal diameter, same-material density or commercial cut grade is assumed.

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 Total Depth Percentage: Audit measured total depth against independently measured crown/girdle/pavilion depth ledger and girdle diameter; closure error remains signed, not another solitary component-percentage alias. 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

Spread Ratio Diameter-to-Carat — tool.io

Similar or alternative tools

Total Depth Percentage
Audit measured total depth against independently measured crown/girdle/pavilion depth ledger and girdle diameter; closure error remains signed, not another solitary component-percentage alias.
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.