Gold Karat Conversion: The Formula, With Worked Examples

Gold karat conversion means expressing a weight of gold at one karat as the equivalent weight at another karat, so that both contain the same amount of pure gold. The whole job is one formula: target weight = source weight × source fineness ÷ target fineness. Everything else in this guide — the factor table, the alloying maths, the rounding rules — is that formula applied carefully.

TL;DR. Fineness is purity in parts per thousand. For any karat K, the arithmetic fineness is K ÷ 24 × 1000, so 21 karat is 875 and 18 karat is 750. To convert, multiply the weight by the source fineness and divide by the target fineness: 60 g of 21 karat equals 70 g of 18 karat. To physically raise a karat you add fine gold; to lower it you add alloy. Agree in writing whether 24 karat counts as 999 or 1000, and round only at the end.

Fineness first: the number every conversion uses

Karat is a fraction out of 24. Fineness is the same idea out of 1000. The World Gold Council describes fineness as purity "in parts per thousand" and lists, among others, 750 for 18 carat, 583 or 585 for 14 carat, and 999 for 24 carat pure gold.

For karats the Council does not list, the arithmetic is the same: divide by 24 and multiply by 1000. That gives the figures a gold counter in Egypt uses every day.

Karat	Arithmetic fineness (K ÷ 24 × 1000)	Pure gold in 1 g	Note
24	1000 (often stamped 999)	1.000 g or 0.999 g	Decide which basis you use
22	916.7	0.917 g	Commonly rounded to 916
21	875	0.875 g	Exact, no rounding
18	750	0.750 g	Matches the WGC figure
14	583.3	0.583 g	WGC lists 583 or 585

The karat you plug into the formula must be the karat the piece really is. In Egypt, testing and hallmarking jewellery falls to the hallmarking authority under the Ministry of Supply and Internal Trade, which is why the karat on your records should be read from the stamp, not guessed from colour or weight.

The one formula, and a factor table to pin by the scale

Pure gold = weight × fineness ÷ 1000. Target weight = weight × source fineness ÷ target fineness.

Because the second formula is just a ratio, you can precompute the factor once and multiply. Using 875 for 21, 750 for 18 and 1000 for 24:

From → To	Factor	10 g becomes
21 → 18	875 ÷ 750 = 1.1667	11.667 g
18 → 21	750 ÷ 875 = 0.8571	8.571 g
24 → 21	1000 ÷ 875 = 1.1429	11.429 g
21 → 24	875 ÷ 1000 = 0.875	8.750 g
24 → 18	1000 ÷ 750 = 1.3333	13.333 g
18 → 24	750 ÷ 1000 = 0.75	7.500 g

If your trader or workshop counts 24 karat as 999 instead of 1000, every factor involving 24 shifts slightly: 21 → 24 becomes 875 ÷ 999 = 0.8759, not 0.875. On one gram the gap is invisible. On a kilo moving through a trader account every month, it is a real balance difference that nobody can explain at settlement. Pick one basis, write it on the account, and use it every time.

Worked examples you can check by hand

Example 1 — a customer's 18 karat in 21 karat terms. A customer brings 42 g of 18 karat. Pure gold = 42 × 750 ÷ 1000 = 31.5 g. As 21 karat: 31.5 ÷ 0.875 = 36 g. So 42 g of 18 karat carries the same gold as 36 g of 21 karat.

Example 2 — a trader balance across karats. You owe a trader 200 g of 21 karat and want to settle partly in 18 karat stock. Each gram of 18 karat clears 750 ÷ 875 = 0.8571 g of 21 karat. Handing over 70 g of 18 karat clears 70 × 0.8571 = 60 g, leaving 140 g of 21 karat owed.

Example 3 — total stock in one figure. Shelves hold 300 g of 21, 120 g of 18 and 50 g of 24. Pure gold = 262.5 + 90 + 50 = 402.5 g. In 21 karat equivalent: 402.5 ÷ 0.875 = 460 g. That single figure is what lets you compare this month with last month, as long as the basis never changes. The broader logic of a gram ledger beside a cash ledger is in our gold shop accounting guide.

The numbers in these examples are chosen to make the arithmetic easy to follow. They are not prices, norms or market data.

Physically changing the karat: the alloying maths

Converting on paper is one thing. Sometimes a workshop actually melts metal to change its karat, and then you need to know how much fine gold or alloy should go in, so you can check the batch that comes back.

Raising the karat (add fine gold). To turn W grams at fineness a into fineness t by adding pure gold at fineness p:

Fine gold to add = W × (t − a) ÷ (p − t)

Turning 30 g of 18 karat into 21 karat with 1000-fine gold: 30 × (875 − 750) ÷ (1000 − 875) = 30 × 125 ÷ 125 = 30 g. You add 30 g of fine gold and expect 60 g of 21 karat back, before any workshop loss.

Lowering the karat (add alloy). Alloy has no gold in it, so the final weight is simply W × a ÷ t, and the alloy added is the difference. Taking 60 g of 21 karat down to 18 karat: 60 × 875 ÷ 750 = 70 g, so 10 g of alloy goes in.

Job	Formula	Example input	Expected output
Raise 18 → 21	W × (t − a) ÷ (p − t) of fine gold	30 g at 18 + 30 g fine	60 g at 21
Lower 21 → 18	Final = W × a ÷ t	60 g at 21	70 g at 18 (10 g alloy)
Check returned batch	Pure out vs pure in	Pure in = 52.5 g	Pure out should match, minus agreed loss

The check in the last row is the one that protects you. Whatever the karat on the way out and on the way back, the pure gold should balance, less the loss you agreed. How to agree and track that loss is covered in jewellery workshop and making charge accounts.

Converting prices uses the same ratio

The same fineness ratio links prices per gram across karats. If the price per gram of 24 karat is P, the metal value of a gram of 21 karat is P × 875 ÷ 1000, and of 18 karat P × 750 ÷ 1000, on the 1000 basis. This covers the metal only. Making charge is a separate line, set per piece or per gram, and should never be folded into a karat factor. Building a full selling price from the day's rate, making charge and stones is covered in how to price gold jewelry.

We deliberately give no prices here. Use the day's price your shop works with, apply the ratio, and keep the basis consistent with the one you use for weights.

Rounding and other traps at the counter

1. Round once, at the end. Rounding 0.8571 to 0.86 and then multiplying by a large weight inflates the result. Keep four decimals in the factor and round the final grams.
2. Use net weight for stone-set pieces. Converting a gross weight that includes stones converts stones into gold. Subtract the recorded stone weight first.
3. Never convert unknown scrap by eye. If a piece has no legible stamp, its karat is a guess until tested. Book it as untested, not as the karat it looks like.
4. Do not mix bases mid-month. Switching from 999 to 1000 halfway through makes this month incomparable with last month.
5. Write the basis on every trader and workshop account. A line such as "settled in 21 karat equivalent, 24 = 1000" ends most arguments before they start.
6. Count per karat in the stocktake, then convert. Weigh each karat separately and only add them up as pure gold or 21 equivalent afterwards, as the gold shop inventory count method describes.

How Tibr handles this

According to the Tibr product page, Tibr keeps inventory by karat for 18, 21 and 24, finished pieces and scrap, with total weights per karat. When you change the price of one karat, the others adjust by the international purity ratio, so the counter does not recompute factors by hand. Each piece carries a barcode with its weight and karat, and karat and making charge are calculated at the point of sale.

If you are still choosing a system, the gold shop management software guide lists what to ask a vendor. You can try Tibr on sample data from the signup page.

FAQ

What is the formula to convert gold from one karat to another?

Multiply the weight by the source fineness and divide by the target fineness. Fineness is the karat divided by 24, times 1000, so 21 karat is 875 and 18 karat is 750. For example, 60 g of 21 karat equals 60 × 875 ÷ 750 = 70 g of 18 karat.

How many grams of 21 karat is 10 grams of 18 karat?

Ten grams of 18 karat contain 7.5 g of pure gold. Dividing by 0.875 gives about 8.571 g of 21 karat. Keep the decimals until the end and round only the final figure.

Is 24 karat 999 or 1000 fine?

Arithmetically 24 out of 24 is 1000, while the World Gold Council lists 999 for 24 carat pure gold. Both bases are used in practice. What matters is that you and each trader or workshop agree one basis in writing and never switch mid-period.

How do I lower 21 karat gold to 18 karat?

Add alloy, which contains no gold. The final weight is the starting weight times 875 divided by 750, and the alloy added is the difference. Sixty grams of 21 karat becomes 70 g of 18 karat with 10 g of alloy, before any workshop loss.

Can I convert scrap gold that has no stamp?

Not reliably. Without a legible hallmark the karat is a guess, and converting a guess spreads the error into every balance. Record the piece as untested and have its karat verified before converting or pricing it.

Written by the Mindshift Team, Tibr product team.

Want karat totals and price ratios kept for you at every sale? See how Tibr works on its official page.