Gold Karat Fineness Ratio
Calculates the millesimal fineness (parts per thousand) and pure gold mass fraction of an alloy based on traditional karat ratings (9K to 24K).
\[ \text{Millesimal Fineness } (‰) = \frac{K}{24} \cdot 1000 = \frac{m_{Au}}{m_{alloy}} \cdot 1000 \]
Plain Text Formula:
Fineness = (K / 24) * 1000 = (mass_Au / mass_alloy) * 1000
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ K \] | Karat Rating | karats (0–24) | Fractional parts of fine gold out of 24 total parts |
| \[ m_{Au} \] | Pure Gold Mass | grams (g) | Net mass of pure elemental gold (Au) |
| \[ m_{alloy} \] | Total Alloy Mass | grams (g) | Gross weight including base metal binders (Cu, Ag, Zn) |
💡 Worked Engineering Example
Problem Statement:
Calculate the pure gold content in 45.0 grams of 14K yellow gold jewelry.
Step-by-Step Solution:
- Fineness ratio = 14 / 24 = 0.5833 (583.3‰)
- Pure gold mass = 45.0 g * (14 / 24) = 26.25 g
🎯 Result: The piece contains exactly 26.25 grams of fine 24K gold.