In the process of synthesizing nanoparticles within an aerosol, the initial size of the particles and their process characteristics have a crucial effect on extent of adhesion between them and the formation of final nanoparticles. In the present study, a mathematical model based on the general dynamic equation of aerosols was used to predict the initial size of tungsten carbide nanoparticles, which was synthesized using electrical discharge erosion. A method was developed to calculate all of the parameters required for the mathematical model, solely with the input and output values of the electrical discharge process without the need for any external data. This model was evaluated through the synthesis of nanoparticles under an atmosphere of argon and nitrogen. The parameters required for the analytical model were obtained from experimental data, and its results were verified by comparing them with the results of experiments conducted under specific case-study parameters, which predicted a smaller size (approximately 18%) of synthesized nanoparticles in argon gas compared with nitrogen gas. Based on the theoretical results' remarkable consistency with the experimental data, this model can be used to adjust the input parameters of the electrical discharge erosion process to obtain primary tungsten carbide nanoparticles of desired sizes. (C) 2019 Elsevier B.V. All rights reserved.