This letter presents the variation of localization error to network parameters, the number of range estimation results from anchor nodes (ANs) and average distance between ANs in centralized Wireless Sensor Network (WSN). In sensor network, ANs estimate the relative range to Target Node (TN) using Time-Of-Arrival (TOA) information of Ultra WideBand (UWB) radio and a fusion center determines the final localization of TN based on estimation results reported. From simulation results, the variation of localization error, which is defined as the difference between localization result of TN and its actual location, is represented as the function of number of estimation results to average distance between ANs. The distribution of localization error is matched to the Rician distribution whose K-factor value is given by the proposed formula as well. Finally, the normalized error function for the efficient localization network design is characterized.