This study describes two new methods of sensing the speed of a pulse-width modulation-driven brushed DC motor based on measuring the inductive spikes generated when the motor is turned off. The research has studied the relationship between the rise time or duration of the inductive spike, and the motor current and speed. Computationally inexpensive algorithms have been developed that use either rise time or duration to estimate speed. The algorithms have been implemented on an inexpensive microprocessor and show a speed error of approximately 10% over most of the motor's range of operation. The spike rise time implementation requires an analog-to-digital converter (ADC) as found in many microprocessors, while the spike duration implementation requires only a single digital input thus reducing the cost of the controlling microprocessor. This work has shown that sensorless speed measurement can be based on the inductive spike and has also raised future research questions, such as to the best way to optimise the speed measurement in dynamic situations, and measurement errors to be expected in a mass production environment.