Continuous analytical solutions for the particle size distributions of char in steady and unsteady states in fluidized beds, when the inlet fuel feed is presented by monosize, lognormal, Rosin-Rammler or gamma distributions, are derived from a population balance model. The stationary size distribution is directly related to the rate of reduction of the particle size. Combustion and attrition reduce the particle size. Thus, it is possible to extract the dependence of the rate of reduction of radius (affected by a fuel's reactivity and attrition) on radius from a measured steady-state particle size distribution. Unsteady particle size distributions are derived for impulse, step and square pulse changes in the fuel feed, when the oxygen level in the reactor is maintained constant. (C) 2003 The Combustion Institute. All rights reserved.