Tor is a popular network for anonymous communication. The usage and operation of Tor is not well-understood, however, because its privacy goals make common measurement approaches ineffective or risky. We present PrivCount, a system for measuring the Tor network designed with user privacy as a primary goal. PrivCount securely aggregates measurements across Tor relays and over time to produce differentially private outputs. PrivCount improves on prior approaches by enabling flexible exploration of many diverse kinds of Tor measurements while maintaining accuracy and privacy for each. We use PrivCount to perform a measurement study of Tor of sufficient breadth and depth to inform accurate models of Tor users and traffic. Our results indicate that Tor has 710,000 users connected but only 550,000 active at a given time, that Web traffic now constitutes 91% of data bytes on Tor, and that the strictness of relays’ connection policies significantly affects the type of application data they forward.