This paper proposes the rotor speed estimation of a squirrel cage induction motor fed by a sinusoidal power supply or an inverter based on the use of a Hall effect sensor installed between two stator slots of the machine. As well known in literature, inverter-fed induction motors usually contains a series of current harmonics and in case of rotor faults, such as broken bars, this operational condition becomes even more severe. The speed estimation has been extensively investigated for its use in control schemes, to compute output power or machine efficiency and particularly for fault diagnosis using motor current signature analysis. In this method, it is necessary an accurate speed estimation to prevent false positives and false negative indications. Therefore, the present research has been carried out by applying the Fast Fourier Transform and Hilbert Transform in the airgap signal measured by the Hall sensor, in order to estimate the rotational speed of the induction motor in a healthy condition and with broken rotor bars. This approach has been compared to the same signal processing techniques using the stator current phase, usually used for speed estimation in the state of the art solutions. The efficiency of this approach was evaluated from simulation and experimental tests, for motor running at distinct load torques, at very low slip conditions and considering a damaged rotor cage. The simulation and experimental results have shown a better accuracy with the measured or simulated speeds, using the airgap estimations when compared to those obtained from stator current processing.