Batch grinding kinetics with assumptions is applied to continuous tube milling to describe the grinding performance, relating the degree of size reduction to the milling conditions including the scale -up variables. As to the scale -up effect on the degree of size reduction, the trend predicted is confirmed with that observed in industrial cement mills in reasonable agreement. The equation of the grinding performance alone, however, does not evaluate the mill diameter and the length individually nor guarantee the powder filling to be a desired level. Then, it is proposed to use one more equation representing the material hold-up (or the powder filling) in relation to the milling conditions. That is, the solution of the two simultaneous equations enables the two variables (the mill diameter and the length) to be evaluated, satisfying the powder filling to be a desired value. C 2020 Elsevier B.V. All rights reserved.