The three-phase induction machine is widely used in industry. Its equivalent circuit is essential in several applications, like performance evaluation, designing of speed/torque control loops, and failure diagnosis. This work establishes an analytical, non-iterative methodology to estimate the equivalent circuit parameters of this machine with high precision, using only data provided by the manufacturer catalog. The proposed methodology assessment is done by applying it to a total of 789 motors from 3 different manufacturers, with power range from 1 to 700 HP. Having the estimated equivalent circuit, the efficiency and power factor of three operating points (half, three quarters, and full load) are calculated and compared to the data available in the manufacturer catalog. These differences, so called errors, are small in a wide power range, roughly from 5 HP onwards. Also, by means of statistical analysis, the proposed method outperforms two other estimation methodologies, presenting lower errors for almost all considered machines. Finally, an illustrative case is made with a 5 HP machine. The three methods are used to estimate the efficiency and power factor curves of the motor from zero to 120% of the rated power, attesting to the quality of the proposed approach.