One metric carat is exactly 0.2 grams, or 200 milligrams. The number is deliberately round: the carat was standardised on that value in the early twentieth century precisely so that the gemstone trade could stop arguing about it.
About the units
The carat descends from the carob seed, which was traditionally used as a counterweight for small masses because the seeds were believed to be unusually uniform. They are not, in fact, particularly uniform, and the actual values in use varied from about 0.19 to 0.21 g across different European markets. The metric carat of exactly 200 mg was adopted internationally between 1907 and the 1920s and is now universal. It should not be confused with the karat used for gold purity, which is not a mass at all but a fraction: 24 karat is pure gold, 18 karat is 18/24 or 75 per cent gold. English distinguishes them by spelling in American usage and by context in British usage, where both are spelled carat.
The exact factor
The factor is exactly 0.2, so grams to carats multiplies by five and carats to grams divides by five. Both directions are exact and easy to do mentally. Within the carat, the trade subdivides into points: one point is one hundredth of a carat, 2 mg, so a stone described as 75 points is 0.75 carat or 150 mg. Because price rises sharply at round carat weights, stones are commonly cut to land just above a threshold — a 1.01 carat diamond can be worth substantially more than a 0.99 carat one of identical quality.
Where you meet this conversion
Gemstone and diamond trading exclusively, along with pearls, which are sometimes measured in a related unit called the momme. Jewellery appraisals, insurance valuations and certification reports from laboratories all state weight in carats to two decimal places. The conversion to grams matters mainly for shipping and customs, where declared mass must be in metric units, and for anyone comparing the mass of a stone to the mass of the metal it is set in, which is quoted in grams.