A mathematical scheme was developed to calculate particle diameter as well as particle lumped density and shape factor using the information obtained from particle trajectory calculations using a 3-beam aerosizer (a time-of-flight particle size determination instrument). A suitable drag coefficient for the flow regime present in the aerosizer was selected by comparison of the calculated trajectories with experimental data (Numerical study on the simultaneous determination of particle physical diameter, lumped density and shape factor using time-of-flight sizers, Illinois Institute of Technology, Chicago, 1996, Aerosol Sci. Technol 29 (1998) 433). A model for particle trajectory in a one-dimensional supersonic compressible flow (Oskouie et al., 1998) was extended to provide the density and shape factor for the particles. The velocity of a particle was calculated along the centerline of three equidistant laser beams downstream of a sonic nozzle, and the physical diameter of this particle, and its lumped density and shape factor were theoretically calculated and compared to experimental results. (C) 2002 Elsevier Science Ltd. All rights reserved.