The relation between flow and density is an essential quantitative characteristic to describe the efficiency of traffic systems. We have performed experiments with single-file motion of bicycles and compared the results with previous studies for car and pedestrian motion in similar setups. In the space–time diagrams we observe three different states of motion (free flow state, jammed state and stop-and-go waves) in all these systems. Despite their obvious differences they are described by a universal fundamental diagram after proper rescaling of space and time which takes into account the size and free velocity of the three kinds of agents. This indicates that the similarities between the systems go deeper than expected.