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Fast, accurate algorithms to compute network capabilities are indispensable for transfer-based electricity markets. Most transfer studies involve contingencies and multipattern scenarios that often can only be performed in reasonable time with the use of linear methods. One of the limitations of linear ATC is the error produced by neglecting the effect of reactive power flows in line loading. This paper describes a fast algorithm to incorporate this effect. The estimation of the line post-transfer complex flow is based on circle equations and a megavar-corrected megawatt limit. The method can be easily integrated into existing linear ATC software because the computation remains based on active power distribution factors. The algorithm is illustrated in a small example and the error correction demonstrated for transfers in larges systems.