Mobile data traffic is increasing rapidly and wireless spectrum is becoming a more and more scarce resource. This makes it highly important to operate mobile networks efficiently. In this paper we are proposing a novel lightweight measurement technique that can be used as a basis for advanced resource optimization algorithms to be run on mobile phones. Our main idea leverages an original packet dispersion based technique to estimate per user capacity. This allows passive measurements by just sampling the existing mobile traffic. Our technique is able to efficiently filter outliers introduced by mobile network schedulers and phone hardware. In order to asses and verify our measurement technique, we apply it to a diverse dataset generated by both extensive simulations and a week-long measurement campaign spanning two cities in two countries, different radio technologies, and covering all times of the day. The results demonstrate that our technique is effective even if it is provided only with a small fraction of the exchanged packets of a flow. The only requirement for the input data is that it should consist of a few consecutive packets that are gathered periodically. This makes the measurement algorithm a good candidate for inclusion in OS libraries to allow for advanced resource optimization and application-level traffic scheduling, based on current and predicted future user capacity. pub