Quantitative characterisation of the trajectories of moving animals is an important component of many behavioural and ecological studies, however methods are complicated and varied, and sometimes require well‐developed programming skills to implement. Here, we introduce trajr, an R package that serves to analyse animal paths, from unicellular organisms, through insects to whales. It makes a variety of statistical characterisations of trajectories, such as tortuosity, speed and changes in direction, available to biologists who may not have a background in programming. We discuss a range of indices that have been used by researchers, describe the package in detail, then use movement observations of whales and clearwing moths to demonstrate some of the capabilities of trajr. As an open‐source R package, trajr encourages open and reproducible research. It supports the implementation of additional methods by providing access to trajectory analysis “building blocks,” allows the full suite of R statistical analysis tools to be applied to trajectory analysis, and the source code can be independently validated.