What karat, fineness and percent gold each measure
Karat measures gold content as a fraction of 24 parts by weight. 18K metal is 18 parts gold and 6 parts something else — copper, silver, zinc, nickel, palladium — in every 24 parts of mass. It says nothing about colour, hardness or quality; a rose 18K and a white 18K carry identical gold content and completely different working properties.
Fineness is the same ratio written in parts per thousand, and it is the mark most of the world stamps. 18K becomes 750, 14K becomes 583.33 (stamped 585), 9K becomes 375. Because fineness is a decimal fraction it multiplies cleanly, which is why refiners, assay offices and this calculator all work in fineness internally and convert back to karat at the end.
Percent gold is fineness divided by ten. It is the friendliest number for explaining a price to a customer and the least useful at the bench, because nothing on your scale or your alloy packet is labelled in percent.
All three are weight ratios, never volume ratios. A gram of 14K gold and a gram of 14K white gold contain the same 0.5833 g of gold even though they occupy noticeably different volumes. If you need the volume side of that relationship, the jewelry metal weight calculator converts between dimensions, density and mass.
The three equations that run the melt
Everything on this page comes out of one idea: gold atoms are conserved in a melt. Nothing you add to the crucible creates or destroys gold, so the fine gold content of the pour equals the fine gold content of everything you put in.
Write that down and the first equation follows immediately. If you melt m₁ grams at K₁ karat together with m₂ grams at K₂ karat, the gold in the ingot is (m₁K₁ + m₂K₂)/24 grams and the ingot weighs m₁ + m₂ grams, so its karat is the weight-weighted average of the two karats. Weight-weighted, not a plain average: 10 g of 18K melted with 30 g of 14K gives 15K, not 16K, because three quarters of the mass came from the lower lot.
The second equation answers the everyday task — you have metal at karat K and you want karat Kt, so how much gold-free master alloy do you add? Conservation says the gold mass stays at m·K/24 while the total grows to m + x. Setting (m·K/24)/(m + x) = Kt/24 and solving gives
x = m · (K − Kt) / Kt
and the finished ingot weighs m · K / Kt. That second form is the one to memorise: the finished weight is your starting weight scaled by the ratio of the karats. Going from 24K to 12K exactly doubles the metal; going from 24K to 18K multiplies it by 24/18 = 1.333.
The third equation runs the other way. To raise metal from K to Kt you add x grams of fine gold, and the same conservation argument gives x = m·(Kt − K)/(24 − Kt). The denominator is what makes high targets expensive: at Kt = 22 the denominator is 2, so every karat point of lift costs half the starting weight in fine gold. At Kt = 24 the denominator is zero and the equation has no solution, which is the algebraic way of saying you cannot dilute your way to purity — only refining removes base metal.
Worked example: 20 g of fine gold down to 14K
You have 20.000 g of clean 24K casting grain and you want to pour 14K yellow. Every step below can be done on paper.
- Find the gold content. The metal is 24 karat, so all of it is gold: mAu = 20.000 × 24/24 = 20.000 g.
- Check the karat of what you have. K = 24 × 20.000 ÷ 20.000 = 24.00, fineness 1000, 100.00% gold.
- Work out the finished weight. The gold content is fixed at 20.000 g and it has to be 14/24 of the finished ingot, so the ingot weighs 20.000 × 24 ÷ 14 = 34.286 g.
- Subtract to get the addition. 34.286 − 20.000 = 14.286 g of master alloy. The direct formula gives the same thing: 20.000 × (24 − 14) ÷ 14 = 200 ÷ 14 = 14.286 g.
- Verify. 20.000 ÷ 34.286 = 0.58333, and 0.58333 × 24 = 14.00 karat. Fineness 583.3.
Now change the problem. Suppose instead of grain you have 10.000 g of 18K bench scrap and 30.000 g of 14K sprue, and you want 18K. Gold content is (10 × 18 + 30 × 14) ÷ 24 = (180 + 420) ÷ 24 = 25.000 g in 40.000 g of metal, so the mix sits at 24 × 25 ÷ 40 = 15.00 karat — below your target. Adding fine gold: x = 40 × (18 − 15) ÷ (24 − 18) = 120 ÷ 6 = 20.000 g of 24K, giving 60.000 g of metal holding 45.000 g of gold. Check: 45 ÷ 60 = 0.750 = 18 karat exactly.
Notice how much fine gold that took — 20 g added to 40 g of scrap. Raising karat is always dearer than lowering it, and that asymmetry is the whole reason bench jewelers keep low-karat scrap segregated from high-karat scrap instead of throwing everything in one pot.
Choosing a target karat, and what you are allowed to stamp
In the United States the floor is 10 karat. The Federal Trade Commission's Guides for the Jewelry, Precious Metals, and Pewter Industries (16 CFR Part 23) treat any description of an article as "gold" as deceptive below 10 karat, and the National Gold and Silver Stamping Act (15 U.S.C. §§294–300) makes a quality mark actionable if the article does not meet it. The Act allows a tolerance of 3 parts per thousand below the marked fineness for an article assayed without its solder, and 7 parts per thousand for one assayed with solder — a working margin, not a licence to under-karat.
Other markets set their own floors. The United Kingdom hallmarks down to 375 (9K), and 9K is the everyday commercial karat there. Continental Europe and much of Asia favour 750 (18K), the Gulf and South Asia buy 916 (22K) and higher. If you are making for export, the target karat is a market decision before it is a metallurgical one.
Working properties push in the opposite direction from purity. More base metal means a harder, stronger, more castable alloy that holds a bright polish and takes stone setting without the prongs creeping; more gold means a softer, richer-coloured metal that resists tarnish. 14K is the American compromise for everyday jewelry, 18K the international compromise for fine work, and 22K a metal you set stones in only with care.
One number deserves a second look before you pour: the finished mass. Alloying 24K down to 10K nearly two and a half times your metal, and a crucible sized for 20 g will not hold 48 g. Read the finished-mass output before you light the torch, and check that your ingot mould, flask and scale range all cover it.
Karat, fineness and gold content
| Karat | Exact fineness | Usual stamp | Gold by weight | Gold per gram of alloy |
|---|---|---|---|---|
| 24K | 1000.00 | 999 / 9999 | 100.00% | 1.0000 g |
| 22K | 916.67 | 916 | 91.67% | 0.9167 g |
| 21K | 875.00 | 875 | 87.50% | 0.8750 g |
| 20K | 833.33 | 833 | 83.33% | 0.8333 g |
| 18K | 750.00 | 750 | 75.00% | 0.7500 g |
| 15K | 625.00 | 625 | 62.50% | 0.6250 g |
| 14K | 583.33 | 585 / 583 | 58.33% | 0.5833 g |
| 12K | 500.00 | 500 | 50.00% | 0.5000 g |
| 10K | 416.67 | 417 | 41.67% | 0.4167 g |
| 9K | 375.00 | 375 | 37.50% | 0.3750 g |
| 8K | 333.33 | 333 | 33.33% | 0.3333 g |
10K is the lowest that may be described as gold in the United States; the UK hallmarks to 375 and Germany historically marked 333.
Which fineness the stamp actually shows
14K is exactly 583.33 parts per thousand, yet nearly every modern 14K piece is stamped 585. That is not a rounding error in the wrong direction — it is deliberate. A mark must not overstate the metal, so manufacturers alloy slightly rich, to about 585, and stamp what the metal actually assays. The same logic gives 10K articles a 417 stamp against an exact 416.67. Set your target a fraction above the nominal karat if you intend to stamp a fineness mark, and assay the pour before you strike it.
Mistakes that spoil a pour
- Averaging karats instead of weighting them. Melting 10 g of 18K with 30 g of 14K gives 15K, not 16K. Always weight by mass.
- Trusting the stamp on unknown scrap. Plated, filled and under-karated goods all carry marks. Touchstone-test or assay anything you did not make yourself before it enters a calculation.
- Ignoring solder seams. Old repairs are often several karats below the body of the piece, and easy solder can carry cadmium or zinc that will fume and change your alloy. Cut seams out of anything destined for a clean melt.
- Forgetting melting loss. Flux, oxide skull and the crucible itself keep a little metal. Weigh the ingot after the pour and recompute rather than assuming the calculated finished mass appeared.
- Adding master alloy meant for a different colour. Yellow, white, red and green master alloys all bring the karat to the same place and the colour to very different ones. Match the alloy to the colour you want.
- Alloying white gold with a nickel master without checking the market. The EU restricts nickel release from items in prolonged skin contact; palladium-based white master alloys avoid the issue entirely.
- Sizing the crucible for the starting weight. Going from 24K to 10K multiplies your metal by 24/10. Read the finished-mass figure first.
What this calculator assumes, and what it cannot see
The arithmetic assumes your karat figures are true gold content by weight, that the master alloy contains no gold, and that nothing is lost or gained in the melt. Those three assumptions cover most bench work and none of them is automatically true.
It does not model karat solder, which does carry gold and must be entered as a lot of its own karat if it goes into the crucible in any quantity. It does not model melting loss, oxidation of zinc or the segregation you get when a heavy addition is stirred in badly. It says nothing about colour, melting range, casting temperature, grain size or work-hardening behaviour — for those you need the alloy manufacturer's data sheet, not a ratio.
It also assumes a single-phase homogeneous result. Adding a large mass of cold alloy to a small melt can freeze the pool and leave you with an ingot that assays differently at each end. When the addition is a multiple of the starting weight, melt the alloy first and add the gold to it.
Finally, karat is not value. To turn gold content into money at today's spot, use the scrap gold and silver value calculator, which handles troy weight, payout percentages and the difference between melt value and what a buyer will actually hand over.
Where this sits among the other bench calculations
Karat math is the first step in a chain. Once you know the karat and the finished mass you can size the stock: the ring blank length calculator turns a ring size and a stock thickness into the length of metal to cut, and the jewelry metal weight calculator converts sheet, wire, tube or a wax model into grams and pennyweight so you know how much to pour.
If you work in industrial rather than precious metals, the same conservation argument appears with different names — a metal weight calculator handles density-based weight for structural stock, and a scrap metal value calculator prices mixed loads by grade rather than by fineness.
Beyond arithmetic, three documents do the real work. ISO 9202 defines the recognised fineness grades for precious metal alloys internationally. The FTC Jewelry Guides govern how you may describe and mark gold in US commerce. And the assay report from an accredited laboratory is the only thing that settles a dispute about what a piece actually contains — a touchstone streak is a screening test, an X-ray fluorescence reading is a surface measurement, and neither is an assay.
Key terms
- Karat (K, kt)
- Parts of gold in 24 parts of alloy by weight. Distinct from carat (ct), which is a gemstone mass unit equal to 0.2 g.
- Fineness
- Gold content in parts per thousand by weight. 750 fineness is 18 karat. The standard mark in most of the world.
- Master alloy
- A pre-mixed, gold-free blend of copper, silver, zinc and other metals sold to bring fine gold to a target karat and colour.
- Fine gold
- Gold of 24 karat, commercially 999 or 9999 fineness. The reference point for every karat calculation.
- Assay
- A quantitative laboratory determination of precious metal content, classically by fire assay (cupellation). The legal benchmark for a fineness claim.
- Melting loss
- Metal not recovered from a melt — held in flux, oxide skull, crucible walls and spatter. Measured by weighing before and after.