The larger a diamond, the rarer
Carat weight is the measure of a diamonds weight on a scale, not its dimensions. 100 points make up one carat, therefore a 50 point diamond is the same as a 1/2 carat and a 0.50 ct. diamond.
It is important to note that size alone is meaningless unless you consider cut, clarity, and color of a good quality diamond. However, size does increase the value of a good quality diamond for the simple reason that large diamonds are rarer than small diamonds.
Only one polished diamond in a thousand weighs more than a carat. Larger diamonds are found relatively infrequently in nature. While large diamonds are highly prized, diamonds of equal value can vary widely in price, based on it's color, clarity and cut.

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