The word "carat" is taken from the carob seeds that people once used in ancient times to balance scales. So uniform in shape and weight are these little seeds that even today's sophisticated instruments cannot detect more than three one-thousandths of a difference between them.
[NOTE: Don't confuse "carat weight" with "karat," the method of determining the purity of gold.]
The process that forms a diamond happens only in very rare circumstances, and typically the natural materials required are found only in small amounts. That means that larger diamonds are uncovered less often than smaller ones. Thus, large diamonds are rare and have a greater value per carat. For that reason, the price of a diamond rises exponentionaly to its size.