This paper investigates the time-dependence of the median particle size during comminution processes in horizontal and vertical stirred media mills. The shape of the time-dependent function describing the particle size is proposed, and it is shown that this function precisely traces the temporal variation of the particle size in comminution processes. The grinding rate constant is defined as the coefficient of time in the function. The effect of stirrer tip speed and mill size on the grinding rate constant is examined, and it is found that the grinding rate constant can be correlated proportionally with the quantity which is related to specific energy. This correlation provides the basis for scale-up of stirred media mills. (C) 2010 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.