Pragmatic abilities are fundamental to successful language use and learning. Individual differences studies contribute to understanding the psychological processes involved in pragmatic reasoning. Small sample sizes, insufficient measurement tools, and a lack of theoretical precision have hindered progress, however. Three studies addressed these challenges in three- to 5-year-old German-speaking children (N = 228, 121 female). Studies 1 and 2 assessed the psychometric properties of six pragmatics tasks. Study 3 investigated relations among pragmatics tasks and between pragmatics and other cognitive abilities. The tasks were found to measure stable variation between individuals. Via a computational cognitive model, individual differences were traced back to a latent pragmatics construct. This presents the basis for understanding the relations between pragmatics and other cognitive abilities. Research Highlights: Individual differences in pragmatic abilities are important to understanding variation in language development. Research in this domain lacks a precise theoretical framework and psychometrically high-quality measures. We present six tasks capturing a wide range of pragmatic abilities with excellent re-test reliability. We use a computational cognitive model to provide a substantive theory of individual differences in pragmatic abilities.