Distributed generation is the power generation which is realized by being integrated into power systems from the consumption side. DG promises high potential in terms of reducing environmental and economic concerns by increasing power systems efficiency and enabling renewable energy sources to be used in power generation. On the other hand, DG is contrary to the centralized generation infrastructure of the conventional power systems, and excessive DG penetration in the systems may cause serious problems. Therefore, planning is an essential issue in DG integrations. Overvoltage problems are one of the most serious and the most frequently encountered problems in DG integration. The voltage increase caused by DG integration in the system is directly related to the DG capacity integrated in the system. In the literature, several studies have been conducted to relate the voltage increase with the capacity of DG. These studies are open to criticism in terms of their feasibility and accuracy because of the assumptions which adopted in the proposed methodology. In this study, a new mathematical model has been developed for the calculation of the maximum capacity for the DG planned to be integrated into a radial distribution networks from a certain point without conducing overvoltage problems. The developed mathematical model has been analyzed with different case studies performed on a test system. The results obtained has been compared with the other mathematical models in the literature and the proposed mathematical model has given better results.