Experimental design and computational modelling across the cognitive sciences often rely on measures of semantic similarity between concepts. Traditional measures of semantic similarity are typically derived from distance in taxonomic databases (e.g. WordNet), databases of participant-produced semantic features, or corpus-derived linguistic distributional similarity (e.g. CBOW), all of which are theoretically problematic in their lack of grounding in sensorimotor experience. We present a new measure of sensorimotor distance between concepts, based on multidimensional comparisons of their experiential strength across 11 perceptual and action-effector dimensions in the Lancaster Sensorimotor Norms. We demonstrate that, in modelling human similarity judgements, sensorimotor distance has comparable explanatory power to other measures of semantic similarity, explains variance in human judgements which is missed by other measures, and does so with the advantages of remaining both grounded and computationally efficient. Moreover, sensorimotor distance is equally effective for both concrete and abstract concepts. We further introduce a web-based tool (https://lancaster.ac.uk/psychology/smdistance) for easily calculating and visualising sensorimotor distance between words, featuring coverage of nearly 800 million word pairs. Supplementary materials are available at https://osf.io/d42q6/.