This paper presents an analytical equation that relates the number of broken bars in the rotor of an induction machine to the vibrations of its stator. The relation is given in terms of both amplitudes and frequencies and is validated by numerical and experimental investigations. The amplitude of vibrations of some frequency components is shown to increase quadratically with the number of broken bars when the motor is operated at rated load. The frequency components of interest are in the range of two to four times the value of the supply frequency, which simplifies the implementation with relatively low-cost instrumentation. The main focus and innovation of this paper is on the derivation of the analytical equations and their verification with numerical analysis, and the comparison of both results to the experimental measurements.