From the statistical point of view the individual errors of gears are considered to act according to a certain rule of distribution. The theoretical analysis of the rule, however, has not been made for a reason of complexity. This fact causes the difference among the standardized tolerances for individual errors adopted by some nations. The author investigated theoretically the rule of distribution of individual errors and studied the relationship between the accuracy of a gear and eligible probability under the given tolerance. According to the theory the rule of distribution is expressed as follows : [numerical formula] where f(x) stands for probability density function, x random variable, x0 integral variable and a stands for a constant which is determined theoretically by the number of teeth, the type of individual errors etc.