The occurrence of faults in the power transmission network is inevitable due to the extensive nature of this network and the passage of transmission lines through areas with different weather and environmental conditions. One of the most important challenges faced by operators of these networks is to quickly and accurately determine the location of the fault occurrence in transmission lines, in order to expedite restoration operations and fault clearance. Various methods exist for locating faults on transmission lines. One common approach involves using distance relays and analyzing the impedance observed by these relays. However, several factors contribute to reduced fault locating accuracy by distance relays. The most significant of these factors include fault resistance, changes in network topology, and current injection from the remote end of the line to the fault location. In this research, a new fault location method based on estimating the network’s equivalent circuit has been introduced for single-phase-to-ground faults in two-terminal lines equipped with a communication system. The process of estimating the equivalent circuit impedances relies on online estimation of Thevenin impedances from the perspective of transmission line terminals, both before and after the fault occurrence. Additionally, if needed, offline data stored in the relay memory (including proposed equivalent circuit impedances for different network configurations, considering the N-1 criterion) is utilized. This method can promptly calculate fault location and fault resistance with high speed and accuracy, using local information and data received from the remote end of the transmission line. The proposed algorithm has been tested on the IEEE 39-bus standard network, and simulation results demonstrate its effectiveness in fault location and fault resistance calculation.