Gear backlash is a quite serious problem in industrial robots, it causes vibrations and impairs the robot positioning accuracy. Backlash estimation allows targeted maintenance interventions, preserving robot performances and avoiding unforeseen equipment breakdowns. However, a direct measure of the backlash is hard to obtain, and dedicated auxiliary sensors are required for the measurement. This paper presents a method for estimating backlash in robotic joints that does not require the installation of extra devices. It only relies on data gathered from the motor encoder, which is always present in a robotic joint. The approach is based on the observation of a characteristic vibration pattern arising on the motor speed signal when backlash affects the joint transmission. By looking at the amplitude of this vibration some information about the entity of the backlash in the joint is gathered. Experimental results on simulated data are reported in the study to show the robustness of the method, also with respect of noise. Furthermore, tests on real-world data, gathered from robots installed in a production plant, demonstrate the efficacy of the technique. The approach is cost-effective, fast, and easily automatable, therefore convenient for the industrial world.