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Evolving faults are faults beginning in one phase of a distribution circuit and spreading to another phase after a few cycles. This paper develops a time-domain algorithm for estimating the location of such faults. The algorithm is divided into two parts, namely, the single line-to-ground portion of the fault and the line-to-line-to-ground portion of the fault. The arc voltage that exists during faults is taken into consideration while deriving this methodology. For the single line-to-ground portion of the fault, the distance to the fault is estimated in terms of the loop or self-reactance between the monitor and the fault. On the other hand, for the line-to-line-to-ground and line-to-line portion of the fault the distance is estimated in terms of the positive-sequence reactance. The reactance-to-fault estimate is more robust than that of the resistance-to-fault, because it is unaffected by fault resistance. Two evolving fault cases and two line-to-line fault cases are analyzed in detail and the error in the location estimates is found to be below 10% in each case. Ten additional cases are analyzed and linear regression analysis is conducted to demonstrate the accuracy of the fault location estimates.