Sensorimotor information plays a fundamental role in cognition. However, the existing materials that measure the sensorimotor basis of word meanings and concepts have been restricted in terms of their sample size and breadth of sensorimotor experience. Here we present norms of sensorimotor strength for 39,707 concepts across six perceptual modalities (touch, hearing, smell, taste, vision, and interoception) and five action effectors (mouth/throat, hand/arm, foot/leg, head excluding mouth/throat, and torso), gathered from a total of 3,500 individual participants using Amazon's Mechanical Turk platform. The Lancaster Sensorimotor Norms are unique and innovative in a number of respects: They represent the largest-ever set of semantic norms for English, at 40,000 words × 11 dimensions (plus several informative cross-dimensional variables), they extend perceptual strength norming to the new modality of interoception, and they include the first norming of action strength across separate bodily effectors. In the first study, we describe the data collection procedures, provide summary descriptives of the dataset, and interpret the relations observed between sensorimotor dimensions. We then report two further studies, in which we (1) extracted an optimal single-variable composite of the 11-dimension sensorimotor profile (Minkowski 3 strength) and (2) demonstrated the utility of both perceptual and action strength in facilitating lexical decision times and accuracy in two separate datasets. These norms provide a valuable resource to researchers in diverse areas, including psycholinguistics, grounded cognition, cognitive semantics, knowledge representation, machine learning, and big-data approaches to the analysis of language and conceptual representations. The data are accessible via the Open Science Framework (http://osf.io/7emr6/) and an interactive web application (https://www.lancaster.ac.uk/psychology/lsnorms/).