Brittle particles fragment when compressed or under impact. The particle fragmentation leads to a power-law relation of the number or mass of particles as a function of the particle size. The resulting power-law relation is accurately characterised by a fractal dimension of the particle fragmentation. The fractal dimension of particle fragmentation depends on the probability of particle failure, which correlates with the applied stress and fracture energy according to Weibull's statistics. Thus, the fractal dimension of particle fragmentation is related to the applied stress and fracture energy, and the relation of the fragmentation fractal dimension to the applied stress and fracture energy is proposed in this paper. It can be validated by the experimental data of marble particle fragmentation and brittle fracture data for rock particles published previously. (C) 2017 Elsevier B.V. All rights reserved.