Specific Gravity Composition Checker

Invert actual coin specific gravity under caller two-constituent additive-specific-volume model; not measuring density, linear density-by-mass mixing or proof of composition/authenticity, out-of-envelope fractions retained.

Description

Specific gravity is relative density.

Specific gravity is relative density. An ideal two-material mass mixture has additive specific volumes, which leads to a reciprocal-density relation.^[1]

Enter positive measured and constituent specific gravities with distinct finite reciprocals. Return both complementary fractions and whether each lies within 0–1; retain out-of-range results.

When to use Specific Gravity Composition Checker

Use Specific Gravity Composition Checker when you need to evaluate the supplied records under the calculation and evidence rules below. Voids, plating, nonideal mixing and measurement error are excluded. This does not authenticate composition.

Prepare the measured coin evidence or explicitly verified catalog and prices requested. Keep measurement conditions, units and currency consistent.

How to use Specific Gravity Composition Checker and understand its results

Prepare the measured coin evidence or explicitly verified catalog and prices requested. Keep measurement conditions, units and currency consistent.
Enter observedCoinSpecificGravity, callerFirstConstituentSpecificGravity, callerSecondConstituentSpecificGravity using the field table and calculation rules, then run the tool.
Read inferredFirstConstituentMassFraction, inferredSecondConstituentMassFraction, withinIdealBinaryMixtureDensityEnvelope. 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
observedCoinSpecificGravity	Observed coin specific gravity	number	Required
callerFirstConstituentSpecificGravity	Caller first constituent specific gravity	number	Required
callerSecondConstituentSpecificGravity	Caller second constituent specific gravity	number	Required

Enter positive measured and constituent specific gravities with distinct finite reciprocals. Return both complementary fractions and whether each lies within 0–1; retain out-of-range results.

firstMassFraction=(1/observed−1/second)/(1/first−1/second)

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

Output field	Meaning	Value type
inferredFirstConstituentMassFraction	Inferred first constituent mass fraction	number
inferredSecondConstituentMassFraction	Inferred second constituent mass fraction	number
withinIdealBinaryMixtureDensityEnvelope	Within ideal binary mixture density envelope	boolean

json

{
  "input": {
    "observedCoinSpecificGravity": 6.666666666666667,
    "callerFirstConstituentSpecificGravity": 10,
    "callerSecondConstituentSpecificGravity": 5
  },
  "output": {
    "inferredFirstConstituentMassFraction": 0.5000000000000001,
    "inferredSecondConstituentMassFraction": 0.4999999999999999,
    "withinIdealBinaryMixtureDensityEnvelope": true
  }
}

Limitations and assumptions

Voids, plating, nonideal mixing and measurement error are excluded. This does not authenticate composition.

Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.

Alternative or Complementary methods

Use Ring Test Frequency Silver Calculator: Resonance peaks depend on dimensions, support and material. Comparing a frequency band is meaningful only when the caller confirms matched geometry and support. For a complementary task, use Measurement Scale Calibration Checker: A calibration maps measured readings back to reference mass. Piecewise linear correction requires ordered calibration pairs and in-range queries.

References

Specific Gravity Composition Checker — tool.io

Similar or alternative tools

Ring Test Frequency Silver Calculator
Resonance peaks depend on dimensions, support and material. Comparing a frequency band is meaningful only when the caller confirms matched geometry and support.
Measurement Scale Calibration Checker
A calibration maps measured readings back to reference mass. Piecewise linear correction requires ordered calibration pairs and in-range queries.