Two and a quarter inches is typical of the balls at the American "pool" halls where I go to play eight ball or nine ball. However, interestingly enough, there are quite a few ball size standards for the various billiard games around the world. Read the Wikipedia entry on the Billiard ball to learn more:
http://en.wikipedia.org/wiki/Billiard_ball
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Very big. Billiards and the pocket billiards games have many millions of players worldwide and in many countries. In the US alone, there are over 32 million pool and billiards players. With tournaments, leagues, pool halls and the equipment it is a many billion dollar industry.
On average, the balls are 2.25 inches in diameter and all balls weigh 5.5 oz except for the cue, which weighs 6 oz.
Viper1
This depends upon what game and where you are playing.
In the US, the maximum diameter allowed for a pocket billiards ball is 2.255 inches.
For pocket billiards under BCA and APA rules, each must be 5 1/2 to 6 ounces and 2 1/4 inches in diameter.