Gold Purity Calculation Formula and Karat Conversion

Gold purity as a percentage is calculated by dividing the mass of pure gold in an item by its total mass, then multiplying by 100. Enter the gold’s karat rating to calculate its nominal purity percentage and parts per thousand; for example, 18-karat gold is 75% gold by mass.

Formula

The basic mass-based formula is:

Gold purity (%) = (mass of pure gold ÷ total mass of the alloy) × 100

When a karat rating is known, the equivalent formula is:

Gold purity (%) = (karat rating ÷ 24) × 100

Here, karat is the gold rating on the 24-part scale, and purity is the proportion of the item’s total alloy mass that is gold, expressed as a percentage. Fineness expresses that same proportion in parts per thousand: fineness = (karat ÷ 24) × 1,000. For instance, 18-karat gold has a nominal fineness of 750.

Worked Example

Using the calculator’s default karat rating of 18:

1. Divide the karat rating by 24: 18 ÷ 24 = 0.75.
2. Convert the fraction to a percentage: 0.75 × 100 = 75.00% gold purity.
3. Convert the fraction to parts per thousand: 0.75 × 1,000 = 750 parts per thousand.

The calculation describes the nominal gold content by mass; it does not determine the item’s actual composition or account for its stones, solder, or other non-alloy components.

How Karats and Fineness Work

Karat, abbreviated kt or K, divides an alloy into 24 parts by mass. Pure gold is designated 24 karat on this scale; lower ratings indicate that some of the alloy’s mass consists of other metals. The arithmetic conversion is direct: divide the rating by 24 to get the gold fraction, then multiply by 100 for a percentage.

Fineness uses a 1,000-part scale instead. A fineness number of 750 means that, nominally, 750 of every 1,000 mass units are gold. The two systems describe the same proportion in different formats:

• 24 kt = 1,000 fineness = 100% nominal gold content.
• 18 kt = 750 fineness = 75% nominal gold content.
• 14 kt = about 583.3 fineness = about 58.33% nominal gold content.
• 10 kt = about 416.7 fineness = about 41.67% nominal gold content.

These are mathematical conversions, not a promise that a particular object has been independently verified. A marking such as “750” commonly communicates a fineness claim, while “18K” communicates a karat claim. The stamp alone is not a laboratory result.

Calculating Gold Content by Mass

If you know an item’s total alloy mass and its purity, estimate its pure-gold mass by multiplying the total mass by the purity as a decimal:

Pure-gold mass = total alloy mass × (purity percentage ÷ 100)

For example, an 18-karat alloy weighing 10 grams contains a nominal 10 × 0.75 = 7.5 grams of gold. The remaining 2.5 grams are other alloy metals, assuming the stated rating applies to that entire mass. The same calculation works in ounces or another mass unit, provided both quantities use the same unit.

Be careful about what is being weighed. A finished piece may contain gemstones, a clasp made from another material, solder, or hollow spaces. Its gross weight is not necessarily the mass of the gold alloy. To estimate gold content, use the mass of the alloy itself—not the combined weight of unrelated materials.

When to Use the Formula—and Its Limits

The karat formula is useful for converting a stated rating to a percentage or fineness, and for estimating gold mass when the alloy’s weight is known. It does not test an object. If the karat rating is unknown or a stamp may be inaccurate, entering a guessed rating only calculates the result for that assumption.

Actual composition is established through appropriate testing. Different testing approaches have different capabilities and limitations; a surface measurement may not reveal whether the inside has a different composition. When a reliable result matters, seek a qualified professional or testing service that can explain the method and what it measures.

Also distinguish purity from value. Purity tells you the proportion of gold by mass. It does not, by itself, establish an item’s market value, because weight, condition, workmanship, non-gold components, and other factors can matter. This formula intentionally calculates composition only.

Common Mistakes and Misconceptions

• Dividing by 100 instead of 24: Karat is a 24-part scale, so convert karat to a fraction by dividing by 24.
• Confusing karat with carat: Karat measures gold purity. Carat is a unit used for the mass of gemstones.
• Reading 18 kt as 18%: It means 18 parts gold out of 24, or 75%, not 18%.
• Mixing percentage and fineness: 75% and 750 parts per thousand represent the same proportion. They are not separate measures of quality.
• Rounding too early: Keep the fraction through the calculation and round only the displayed result. For 14 kt, 58.33% is more informative than rounding immediately to 58%.
• Assuming 24 kt means mathematically perfect purity: The conversion treats 24 kt as the reference point of the scale. A calculation cannot establish the precise composition of a real item.

Frequently Asked Questions

What is the formula for gold purity?
Divide the mass of pure gold by the total mass of the alloy and multiply by 100. If you know the karat rating, divide it by 24 and multiply by 100.

How pure is 18-karat gold?
18 ÷ 24 × 100 = 75%, equivalent to 750 parts per thousand. This is the nominal gold proportion by mass.

What does 750 mean on gold?
It indicates a fineness of 750 parts per thousand, corresponding to 75% gold by mass, or 18 karat by the standard arithmetic conversion.

How do I calculate the gold in a 10-gram 18-karat item?
Multiply 10 grams by 18 ÷ 24. The result is 7.5 grams of nominal gold, provided the full 10 grams is the relevant alloy mass.

Can I calculate purity from an item’s weight alone?
No. Weight gives the amount of material, not the fraction that is gold. You also need a reliable purity rating or a composition test.

Is 24-karat gold 100% pure?
In the karat conversion, 24 kt is the 100% reference point. The formula cannot verify a particular item’s actual composition; that requires testing.

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in karat | Karat rating | kt | 18 | 0
out purity | Gold purity | % | karat / 24 * 100 | 2
out fineness | Fineness | parts per thousand | karat / 24 * 1000 | 0