Travel speed (average speed of travel while active) and day range (average speed over the daily activity cycle) are behavioural metrics that influence processes including energy use, foraging success, disease transmission and human-wildlife interactions, and which can therefore be applied to a range of questions in ecology and conservation. These metrics are usually derived from telemetry or direct observations. Here, we describe and validate an entirely new alternative approach, using camera traps recording passing animals to measure movement paths at very fine scale. Dividing the length of a passage by its duration gives a speed observation, and average travel speed is estimated by fitting size-biased probability distributions to a sample of speed observations. Day range is then estimated as the product of travel speed and activity level (proportion of time spent active), which can also be estimated from camera-trap data. We field tested the procedure with data from a survey of terrestrial mammals on Barro Colorado Island, Panama. Travel speeds and day ranges estimated for 12 species scaled positively with body mass, and were higher in faunivores than in herbivores, patterns that are consistent with those obtained using independent estimates derived from tracked individuals. Comparisons of our day range estimates with independent telemetry-based estimates for three species also showed very similar values in absolute terms. We conclude that these methods are accurate and ready to use for estimating travel speed and day range in wildlife. Key advantages of the methods are that they are non-invasive, and that measurements are made at very high resolution in time and space, yielding estimates that are comparable across species and studies. Combined with emerging techniques in computer vision, we anticipate that these methods will help to expand the range of species for which we can estimate movement rate in the wild.