A model for unipolar charging of nanoparticles based on the Fuchs birth-and-death theory is developed. It includes both diffusional and electrical losses for particles and ions. Electrical losses are modeled by inclusion of a radial electric field which is caused by space charge. The model can be used to obtain the initial ion concentration and mean radial electric field from data of charge distribution fractions, without additional measurements. It was successfully applied to results from three different unipolar chargers. In all cases, good agreement between experimental and modeling results has been obtained. The model can be used to assist the operation of unipolar chargers, e.g. by predicting charging efficiencies for particle sizes which are not experimentally accessible. (C) 2014 Elsevier Ltd. All rights reserved.