In this paper, a multi-objective analytical method to evaluate the impacts of optimal location and sizing of distributed generation is presented. This method is based on an analysis of the exact loss formula and continuous power flow in a radial distribution system. Based on two methods of analysis, power loss and weakest voltage buses and lines are calculated and then the optimal size of distributed generation is determined. After that, by considering the minimum power losses and the maximisation of voltage stability, the proposed index determines and ranks positions to decide the optimal distributed generation location in the system. This method allows us to find the best places and size to connect a number of distributed generation units by optimising the objective functions. The simulation results were obtained using a 33-bus radial distribution system to determine the location and size of the distributed generation units. The results show the effectiveness of voltage profile improvement, loading factor improvement and power loss reduction. Further, the problems of a single objective function and the placement of the distributed generation unit using analytical methods are solved by the proposed approach.