A grinding circuit simulation combined with ball weal law was used to determine the optimum composition of the make-up ball sizes in tumbling ball mills. It was found that the optimum composition depends on various factors, including the feed size, the product size, the mill diameter and the breakage parameters. In all cases, binary mixtures of two ball sizes (50.8mm and 25.4mm) performed better than a mixture of the three ball sizes. An equation therefore could be developed for calculating the optimum composition of the make-up balls as a function of various parameters. Display omitted •The optimum composition of the make-up ball sizes in ball mills is presented.•The effect of various factors was investigated via a grinding circuit simulation.•Binary mixtures of two ball sizes always perform better than other mixtures.•An equation is proposed for calculating the optimum composition of the make-up balls.