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As of 2008 the circumference of a regulation size baseball is between nine and nine and a quarter inches which converts to between about 7.3 cm and 7.5 cm in diameter according to the official rules of Major League Baseball (MLB).
Bat barrel diameters are usually 2-1/4 inch, 2-5/8 inch, or 2-3/4 inch. The smallest size is required by Little. League (up to age 12) as well as some lower divisions of other organizations. Be clear on what limits.