This paper addresses itself to evaluate quantitatively the severity of broken rotor bar (BRB) fault, i.e., the number of BRBs in induction motors. Sideband components are induced in stator current if BRB fault is present and commonly used for diagnosis purposes. Filippetti criterion has been proposed and developed in the literature to quantify the severity of BRB fault by using sideband components, however, with unsatisfactory universality/accuracy. This paper briefly analyzes Filippetti criterion, and mathematically derives a new criterion for the quantification of BRBs, based on the electromagnetic mechanism of sideband components. Comparing to Filippetti criterion, the universality and accuracy of the new criterion are both improved. Moreover, the new criterion includes the influence from the interbar currents associated with BRB fault. The related experiment on a 3-kW, 380-V, 50-Hz induction motor has been conducted, and results show the superiority of the new criterion over Filippetti criterion.