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Mechanical properties of cells have been shown to have a significant role in disease, as in many instances cell stiffness changes when a cell is no longer healthy. We present a high-throughput microfluidics-based approach that exploits the connection between travel time of a cell through a narrow passage and cell stiffness. The system resolves both cell travel time and relative cell diameter while retaining information on the cell level. We show that stiffer cells have longer transit times than less stiff ones and that cell size significantly influences travel times. Experiments with untreated HeLa cells and cells made compliant with latrunculin A and cytochalasin B further demonstrate that travel time is influenced by cell stiffness, with the compliant cells having faster transit time.