Cabochon Carat Weight Estimator
Cabochon explicitly ideal elliptical HALF ellipsoid volume (no pavilion), measured dome height and density. Geometric envelope proxy under caller independently matching density/cut fill, no universal carat-by-shape empirical factor. Caller independently establishes geometry, assay, calibration and protocol; not material identity, laboratory grade, treatment or care safety.
Description
A cabochon can be approximated by a half ellipsoid with an elliptical base and dome height.
A cabochon can be approximated by a half ellipsoid with an elliptical base and dome height.1
This volume model does not include a flat backing layer, irregular profile or faceted underside unless independently accounted for. Use this tool to calculate cabochon carat weight estimator from the supplied measurements and assumptions.
When to use Cabochon Carat Weight Estimator
Use this tool to calculate cabochon carat weight estimator from the supplied measurements and assumptions. Establish the specimen, measurement protocol, units, geometry and any caller calibration or review limits.
How to use Cabochon Carat Weight Estimator and understand its results
- Establish the specimen, measurement protocol, units, geometry and any caller calibration or review limits.
- Enter cabochonLengthMm, cabochonWidthMm, domeHeightMm, independentlyMeasuredDensityGCM3, using the field meanings and rules below, then run the tool.
- Read conditionalEnvelopeVolumeMM3, conditionalMassCarats. Interpret the fields using their units, signs and evidence conventions below.
- If input validation fails, correct the reported field and run again. Before applying the result, check reference scope, model assumptions and any missing evidence or placeholder values.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| cabochonLengthMm | Cabochon length mm | number | Required |
| cabochonWidthMm | Cabochon width mm | number | Required |
| domeHeightMm | Dome height mm | number | Required |
| independentlyMeasuredDensityGCM3 | Independently measured density g c m3; caller assertion or measurement requiring independent evidence | number | Required |
Enter positive length, width and dome height in millimeters and positive density in g/cm³. Apply a half-ellipsoid volume π×length×width×height/6, then convert with density/200 to carats. There is no additional fill-fraction input or backing-layer correction.
volumeMm³=π×length×width×domeHeight/6; carats=volumeMm³×density/200 Use the exact units, boundary rules, ordering and missing-evidence conventions above.
| Output field | Meaning | Value type |
|---|---|---|
| conditionalEnvelopeVolumeMM3 | Conditional Envelope Volume MM3; follow the units, sign, ordering and evidence convention stated above | number |
| conditionalMassCarats | Conditional mass from modeled volume and supplied density; 1 carat=0.2 g | number |
{
"input": {
"cabochonLengthMm": 10,
"cabochonWidthMm": 6,
"domeHeightMm": 4,
"independentlyMeasuredDensityGCM3": 4
},
"output": {
"conditionalEnvelopeVolumeMM3": 125.66370614359171,
"conditionalMassCarats": 2.513274122871834
}
}Limitations and assumptions
This volume model does not include a flat backing layer, irregular profile or faceted underside unless independently accounted for. Interpretation depends on the units, sampling scope and exact model described above.
All listed fields require explicit values. Unexpected fields, incorrect types, nonfinite numbers and sparse evidence arrays fail validation; the specific bounds and alignment requirements are stated above. Extremely large inputs or outputs can also be rejected. An input error is distinct from a successful result reporting false, no matches or missing evidence.
Alternative or Complementary methods
Use Trillion Cut Carat Weight Estimator for this related task: A trillion-cut weight model combines a triangular plan area, depth and an independently chosen fill factor.
Use Round Brilliant Carat Weight Estimator when its separate inputs and assumptions fit the question: A round-cut weight model starts with a circular diameter envelope and depth.
References
-
Cabochon Carat Weight Estimator — tool.io
Similar or alternative tools
- Trillion Cut Carat Weight Estimator
A trillion-cut weight model combines a triangular plan area, depth and an independently chosen fill factor.
- Round Brilliant Carat Weight Estimator
A round-cut weight model starts with a circular diameter envelope and depth.