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.

Description

A round-brilliant outline can be approximated by coaxial crown and pavilion frustums joined by a girdle cylinder.

A round-brilliant outline can be approximated by coaxial crown and pavilion frustums joined by a girdle cylinder. This envelope differs from the actual individually faceted surface.^[1]

When to use Volume of Round Brilliant

Use this tool to 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.

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

How to use Volume of Round Brilliant 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, culetDiameterMm, crownHeightMm, girdleHeightMm, pavilionDepthMm using the field table and calculation rules, then run the tool.
Read axisymmetricEnvelopeVolumeMm3. 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
culetDiameterMm	Culet diameter mm	number	Required
crownHeightMm	Crown height mm	number	Required
girdleHeightMm	Girdle height mm	number	Required
pavilionDepthMm	Pavilion depth mm	number	Required

Use positive girdle diameter and nonnegative table/culet diameters and component heights in mm; table and culet cannot exceed girdle. Halve diameters to radii r,t,c and return envelope mm³.

volume=π[crown(r²+rt+t²)/3+r²girdle+pavilion(r²+rc+c²)/3]

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

Output field	Meaning	Value type
axisymmetricEnvelopeVolumeMm3	Axisymmetric envelope volume mm3	number

json

{
  "input": {
    "girdleDiameterMm": 10,
    "tableDiameterMm": 6,
    "culetDiameterMm": 2,
    "crownHeightMm": 2,
    "girdleHeightMm": 1,
    "pavilionDepthMm": 4
  },
  "output": {
    "axisymmetricEnvelopeVolumeMm3": 311.01767270538954
  }
}

Limitations and assumptions

Facet cuts, cavities and density are not included. Envelope volume is not carat mass.

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 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. For a complementary task, 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.

References

Volume of Round Brilliant — tool.io

Similar or alternative tools

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.
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.