Gemstone Carat Weight Formula
The universal standard metric carat unit used to quantify the mass of diamonds and gemstones, where 1 carat equals exactly one-fifth of a gram (200 mg).
\[ 1 \text{ ct} = 200 \text{ mg} = 0.200 \text{ g} = 100 \text{ points} \]
Plain Text Formula:
1 Carat (ct) = 200 mg = 0.200 g = 100 points
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ ext{ct} \] | Metric Carat | ct | Standard unit of gemstone mass |
| \[ ext{mg} \] | Milligram | mg | One thousandth of a gram |
| \[ ext{points} \] | Diamond Points | pts | Subdivision where 1 point equals 0.01 carat (2 mg) |
💡 Worked Engineering Example
Problem Statement:
A diamond is graded at 75 points. Express its weight in carats and grams.
Step-by-Step Solution:
- Carat weight = 75 / 100 = 0.75 ct
- Gram weight = 0.75 * 0.200 g = 0.150 g (150 mg)
🎯 Result: The diamond weighs 0.75 carats or 150 milligrams.