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.

Description

A coaxial envelope estimates a round-brilliant surface using two frustums and a cylinder.

A coaxial envelope estimates a round-brilliant surface using two frustums and a cylinder. Including the table and culet disks closes the model's external area.^[1]

When to use Total Surface Area Round Brilliant

Use this tool to 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.

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

How to use Total Surface Area 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 axisymmetricExternalAreaMm2. 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 heights in mm, with smaller diameters no greater than girdle. Convert to radii and sum sloped lateral areas, cylinder area and end disks for mm².

area=π[(r+t)hypot(r−t,crown)+2r girdle+(r+c)hypot(r−c,pavilion)+t²+c²]

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

Output field	Meaning	Value type
axisymmetricExternalAreaMm2	Axisymmetric external area mm2	number

json

{
  "input": {
    "girdleDiameterMm": 10,
    "tableDiameterMm": 6,
    "culetDiameterMm": 2,
    "crownHeightMm": 2,
    "girdleHeightMm": 1,
    "pavilionDepthMm": 4
  },
  "output": {
    "axisymmetricExternalAreaMm2": 240.54717059813052
  }
}

Limitations and assumptions

This envelope area does not represent individual facets, optical performance or 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 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 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.

References

Total Surface Area Round Brilliant — 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.
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.