:K = 24 &times; (M / M)
where
: K is the karat rating of the material,
: M is the mass of pure gold in the alloy, and
: M is the total mass of the material.
24-karat gold is pure (while 100% purity is very difficult to attain, 24-karat as a designation is permitted in commerce for a minimum of 99.95% purity), 18-karat gold is 18 parts gold, 6 parts another metal (forming an alloy with 75% gold), 12-karat gold is 12 parts gold (12 parts another metal), and so forth.
In England, the carat was divisible into four grains, and the grain was divisible into four quarts. For example, a gold alloy of  fineness (that is, 99.2% purity) could have been described as being 23-karat, 3-grain, 1-quart gold.
The karat fractional system is increasingly being complemented or superseded by the millesimal system, described above for bullion, though jewelry generally tends to still use the karat system.
Conversion between percentage of pure gold and karats:
* 58.33–62.50% = 14 k (acclaimed 58.33%)
* 75.00–79.16% = 18 k (acclaimed 75.00%)
* 91.66–95.83% = 22 k (acclaimed 91.66%)
* 95.83–99.95% = 23 k (acclaimed 95.83%)
* 99.95–100% = 24 k (acclaimed 99.95%)