The Tor network uses a measurement system to estimate its relays' forwarding capacity and to balance traffic among them. This system has been shown to be vulnerable to adversarial manipulation. Moreover, its accuracy and effectiveness in benign circumstances has never been fully quantified. We first obtain such a quantification by analyzing Tor metrics data and performing experiments on the live network. Our results show that Tor currently underestimates its true capacity by about 50% and improperly balances its traffic by 15-25%. Then, to solve the problems with security and accuracy, we present FlashFlow, a system to measure the capacity of Tor relays. Our analysis shows that FlashFlow limits a malicious relay to obtaining a capacity estimate at most 1.33 times its true capacity. Through realistic Internet experiments, we find that FlashFlow measures relay capacity with at least 89% accuracy 95% of the time. Through simulation, we find that FlashFlow can measure the entire Tor network in less than 5 hours using 3 measurers with 1 Gbit/s of bandwidth each. Finally, simulations using FlashFlow for load balancing shows that, compared to TorFlow, network weight error decreases by 86%, while the median of 50 KiB, 1 MiB, and 5 MiB transfer times decreases by 15%, 29%, and 37%, respectively. Moreover, FlashFlow yields more consistent client performance: the median rate of transfer timeouts decreases by 100%, while the standard deviation of 50 KiB, 1 MiB, and 5 MiB transfer times decreases by 55%, 61%, and 41%, respectively. We also find that the performance improvements increase relative to TorFlow as the total client-traffic load increases, demonstrating that FlashFlow is better suited to supporting network growth.