The evaluation of an arc quenching medium in circuit breakers usually requires the experimental investigation or the 2D or 3D magnetohydrodynamics simulation of switching arcs, which are expensive and time-consuming. In this work, a fast method is proposed for evaluating the arc quenching performance of gases. In this method, the arc decaying process is divided into three stages based on the results of 1D arc decaying modeling, including the thermal recovery stage, the predielectric recovery stage, and the postdielectric recovery stage. Compared to the previous method, the present method is improved mainly in the three aspects: the thermal recovery stage is featured by the average radial temperature instead of the axial temperature; the criterion of dividing the dielectric recovery stage into the pre- and postdielectric recovery stages is validated by the average electron number density instead of choosing arbitrarily; and the postdielectric recovery stage is characterized by the critical electric field strength Ecr instead of the reduced critical electric field strength (E/N)cr. The case study of SF6, CO2, CF4, and air arcs indicates that the present method yields the same descending order of the thermal recovery rate and the predielectric recovery rate for the four gases as the previous method. Moreover, the present method can avoid negative postdielectric recovery rates, which means that it is more reasonable than the previous method.