This paper presents a new numerical algorithm for the fault location estimation and arcing fault detection when a single-phase arcing ground fault occurs on a transmission line. The proposed algorithm derived in the spectrum domain is based on the synchronized voltage and current samples measured from the PMUs(Phasor Measurement Units) installed at both ends of the transmission lines. In this paper, the algorithm uses DFT(Discrete Fourier Transform) for estimation. The algorithm uses a short data window for real-time transmission line protection. Also, from the calculated arc voltage amplitude, a decision can be made whether the fault is permanent or transient. The proposed algorithm is tested through computer simulation to show its effectiveness.