Gold alloy purity conversion — the math explained
How much 24K gold do you need to add to convert 9K gold to 18K? Here's the complete formula with worked examples for any karat combination.
Why goldsmiths need to convert alloys
Melting and re-mixing gold is daily work in a workshop. You might be upgrading a pile of 9K scrap to 18K for casting, or matching a client's existing piece to mount a new stone, or simply standardising your stock to one karat for production.
Understanding the equation
Let x = grams of 24K to add to your starting alloy. After mixing, the total pure gold (existing + added) divided by total weight (existing + added) must equal the target purity. From this we solve for x.
The master formula
x = (target_purity × start_weight − pure_gold_now) ÷ (1 − target_purity) where: target_purity = target_karat / 24 pure_gold_now = start_weight × (start_karat / 24)
Worked example 1: 9K to 18K
target_purity = 18 / 24 = 0.75
pure_gold_now = 100 × (9 / 24) = 37.5 g
x = (0.75 × 100 − 37.5) ÷ (1 − 0.75) = 37.5 ÷ 0.25 = 150 g of 24K
Total weight after = 100 + 150 = 250 g of 18K.
Sanity check: total pure gold = 37.5 + 150 = 187.5 g. 187.5 / 250 = 0.75 ✓
Worked example 2: 14K to 22K
target_purity = 22 / 24 ≈ 0.9167
pure_gold_now = 50 × (14 / 24) ≈ 29.17 g
x = (0.9167 × 50 − 29.17) ÷ (1 − 0.9167) ≈ 16.67 ÷ 0.0833 ≈ 200 g of 24K
Total weight = 250 g of 22K. Verification: (29.17 + 200) / 250 ≈ 0.9167 ✓
Worked example 3: Mixing two alloys
When mixing two alloys (no pure gold added), the resulting purity is the weighted average:
result_purity = (w1 × p1 + w2 × p2) ÷ (w1 + w2)
(30 × 0.375 + 20 × 0.75) ÷ 50 = (11.25 + 15) ÷ 50 = 0.525
0.525 × 24 ≈ 12.6K result.
Important notes
- The master formula assumes you add pure 24K only. Adding a different karat alloy requires the mixing formula above.
- Metal loss during melting (oxidation, splatter) is not included. Real workshops typically lose 1–3%.
- Always weigh and verify the final alloy with a touchstone after melting.
Try this in the Purity Converter
Enter starting karat, weight, and target karat — Goldify tells you exactly how much 24K to add.