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Gemstone -> Carat
Weight in gems is calculated in metric carats, where five carats equal one gram. Generally, as a gem’s weight increases, so does the per-carat price. Such a relationship has long been known, and was first quantified by Villafane in 1572, for diamonds. Today it is most commonly referred to as the ‘Indian Law’ or ‘Tavernier’s Law’, and works as follows:
 

Wt2 x C = price per stone
Weight of gem = 5 ct (Wt)
Cost of a 1-ct gem of equal quality = $1000 (C)
5 x 5 x 1000 = $25,000 total stone price
 
The following shows how the price of a gem might increase with this formula applied using a $1000/ct base price.

Weight
Total stone price
1 ct
$1000
2 ct
$4000
3 ct
$9000
4 ct
$16,000
5 ct.
$25,000
10 ct.
$100,000

Unfortunately, things were not so simple, even for diamonds in the time of Tavernier. The law could not accurately predict the price of diamond below 1 ct, and there were also problems with exceptionally large stones. But it does give a general idea of how prices increase with size.
 
 
Carat psychology :
In the case of many gems, including ruby and sapphire, psychological (but all too real) price jumps occur at certain weights. For example, a 0.99-ct ruby might be worth significantly less than one which weighs 1.05 ct. The 1.05 ruby would be worth more than one which weighed exactly 1.00 ct, as repolishing a 1.00-ct stone (or weighing it on someone else’s scale) might send it below the important 1-ct barrier. Similar psychological weight hurdles are found at the 2, 5, 10, 20, 50 and 100-ct levels.
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Above. Graph representing the relationship between price and quality/weight/rarity. Note that this is not a linear relationship. Price increases more quickly as quality/weight/rarity increases.
 
@copyright 2008