Traditional impedance-based fault-locating methods implemented in modern overcurrent protection relays require voltage and current measurements to provide reasonable fault-location estimates. Although they capture voltage and current, depending on field condition or due to equipment failure, relays may record current measurements only. Voltage measurements are thus missing or unavailable. The objective of this paper is to develop practical impedance-based fault-locating algorithms with current data (magnitude or phasors) as the only input and demonstrate the efficacy of the algorithms with simulated and actual field data. These algorithms use the circuit model of the distribution feeder and Kirchhoff's circuit laws in estimating the fault voltage at the relay location and then use impedance-based methods for fault location. Based on the analysis conducted on actual fault data, error in estimation is generally less than 0.5 mi from the actual location of the fault.