In touch as in vision, perceptual acuity improves with training to an extent that differs greatly across people; even individuals with similar initial acuity may undergo markedly different improvement with training. What accounts for this variability in perceptual learning? We hypothesized that a simple physical characteristic, fingertip surface area, might constrain tactile learning, because previous research suggests that larger fingers have more widely spaced mechanoreceptors. To test our hypothesis, we trained 10 human participants intensively on a tactile spatial acuity task. During 4 d, participants completed 1900 training trials (38 50-trial blocks) in which they discriminated the orientation of square-wave gratings pressed onto the stationary index or ring finger, with auditory feedback provided to signal correct and incorrect responses. We progressively increased task difficulty by shifting to thinner groove widths whenever participants achieved ≥90% correct block performance. We took optical scans to measure surface area from the distal interphalangeal crease to the tip of the finger. Participants' acuity improved markedly on the trained finger and to a lesser extent on the untrained finger. Crucially, we found that participants' tactile spatial acuity improved toward a theoretical optimum set by their finger size; participants with worse initial performance relative to their finger size improved more with training, and posttraining performance was better correlated than pretraining performance with finger size. These results strongly support the hypothesis that tactile perceptual learning is limited by finger size. We suspect that analogous physical constraints on perceptual learning will be found in other sensory modalities.