Charging and coagulation influence one another and impact the particle charge and size distributions in the atmosphere. However, few investigations to date have focused on the coagulation kinetics of atmospheric particles accumulating charge. This study presents three approaches to include mutual effects of charging and coagulation on the microphysical evolution of atmospheric particles such as radioactive particles. The first approach employs ion balance, charge balance, and a bivariate population balance model (PBM) to comprehensively calculate both charge accumulation and coagulation rates of particles. The second approach involves a much simpler description of charging, and uses a monovariate PBM and subsequent effects of charge on particle coagulation. The third approach is further simplified assuming that particles instantaneously reach their steady-state charge distributions. It is found that compared to the other two approaches, the first approach can accurately predict time-dependent changes in the size and charge distributions of particles over a wide size range covering from the free molecule to continuum regimes. The other two approaches can reliably predict both charge accumulation and coagulation rates for particles larger than about 0.04 micrometers and atmospherically relevant conditions. These approaches are applied to investigate coagulation kinetics of particles accumulating charge in a radioactive neutralizer, the urban atmosphere, and an atmospheric system containing radioactive particles. Limitations of the approaches are discussed. © 2016 Author(s).