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How are Gold and Gemstones Weighed?

Troy Weight
Used in weighing the precious metals.
24 grains = 1 pennyweight (dwt.)
20 dwt = 1 ounce Troy
12 ounces = 1 pound Troy
5760 grains = 1 pound Troy
480 grains = 1 Troy oz.

1 kilogram = 2.68 pounds
1 kilogram = 32.15 Troy oz.
1 kilogram = 2.2046 lbs. Avoir
1 kilogram = 35.2740 oz. Avoir
1 kilogram = 15,432 grains

Troy oz. - 1.0972 Avoir oz.

Carat Weight
Used in weighing precious and semi-precious stones. (The term "Karat" refers to the quality of purity in gold.)

1 carat = 31/16 grains Troy
1 carat = .007 ounce Acoir
1 carat = 1/5 gram

The carat is further divided into points for simple measurement:
1 carat = 100 points
1/2 carat = 50 points
1/4 carat = 25 points
1/8 carat = 12 1/2 points 

Avoirdupois Weight
Used in weighing base metals.

16 drams (or drachms) = 1 oz. Avoir
16 ounces = 1 pound Avoir
16 ounces = 7,000 grains
28 pounds = 1 quarter English
4 quarters = 1 hundredweight (cwt.)
20 hundredweight = 1 ton Avoir

1 pound Avoir = 14.5833 Troy oz.
1 ounce Avoir = 0.914 Troy oz.
1 pound Avoir = 7,000 grains
1 ounce Avoir = 437.5 grains
1 pound Avoir = .4359 kilo.
Gram Weight

1 gram = 15.43 grains Troy
1.555 grams = 1 pennyweight (dwt.)
31.104 grams = 1 ounce Troy
28.35 grams = 1 ounce Avoir

1 grain = 0.0648 grams
1 grain = 64.80 milligrams
1 milligram = .015432 grams
1 gram = .035274 Avoir oz.
1 gram = .032151 Troy oz.