Angle of rotation is a key parameter in motor fault diagnosis under varying speed conditions, and is usually measured by an optical encoder. However, the use of encoders is intrusive and in many scenarios its signal is difficult to access due to technical or commercial reasons. In this study, a novel rotation angle measurement method based on stray flux analysis is proposed and applied to bearing fault diagnosis of brushless direct-current (BLDC) motors. The measurement accuracy of the proposed method is comparable to that from an encoder. The developed method is flexible, noninvasive, and nondestructive. It is easy to implement and eliminates the need for long cables and access of the motor control system. The proposed method can be extended to the diagnosis of motor electrical and drive faults. If implemented with an Internet of Things (IoT) or a hand-held device, it can further improve the reliability of sensorless motor drive systems in industrial automation so as to meet Industry 4.0 requirements.