This paper provides a method to scale-up horizontal tumbling ball mills, i.e. to determine the dimensions of the rotating drum and the drum rotational speed. In order to develop the scale-up methodology, the motion of grinding balls in tumbling ball mills with different drum diameters was calculated using the discrete element method (DEM). The impact energy of grinding balls was numerically analyzed, and the influence of drum dimensions and drum rotational speed on the impact energy was investigated. It was found that scale-up of the rotating drum should be carried out based on the mechanical energy instantaneously applied to the powder and its cumulative amount. The former was evaluated in terms of the frequency distribution of the impact energy and the latter its cumulative amount over the elapsed milling time, which could be controlled by the drum rotational speed and the milling time, respectively. Validity of the proposed scale-up methodology was evaluated through dry grinding experiments of aluminum hydroxide powder, and the experimental results supported its usefulness in practical applications. (C) 2010 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.