Fault location on a dc microgrid feeder needs to be extremely fast to protect the circuit breaker and converter-source components. This paper develops a seminal theoretical foundation for fast fault location on a dc feeder that uses only single-ended local measurements in time domain. The theory provides a closed-form deterministic solution for fault location, making the resulting fault location method agnostic to system-topology and immune to fault resistance. The theory is developed with ideal dc voltage sources, and extended to practical converter-sources. The performance of the resulting method is demonstrated by simulating a dc feeder with converters connected at both ends, modeled in PSCAD.