What determines how much an organism can learn? One possibility is that the neural factors that limit sensory performance prior to learning, place an upper limit on the amount of learning that can take place. We tested this idea by comparing learning on a sensory task where performance is limited by cortical mechanisms, at two retinal eccentricities. Prior to learning, visual performance at the two eccentricities was either unmatched or equated in two different ways (through spatial scaling or visual crowding). The magnitude of learning was equivalent when initial levels of performance were matched regardless of how performance was equated. The magnitude of learning was a constant proportion of initial performance. This Weber-like law for perceptual learning demonstrates that it should be possible to predict the degree of perceptual improvement and the final level of performance that can be achieved via sensory training, regardless of what cortical constraint limits performance.