Confidence is the 'feeling of knowing' that accompanies decision making. Bayesian theory proposes that confidence is a function solely of the perceived probability of being correct. Empirical research has suggested, however, that different individuals may perform different computations to estimate confidence from uncertain evidence. To test this hypothesis, we collected confidence reports in a task where subjects made categorical decisions about the mean of a sequence. We found that for most individuals, confidence did indeed reflect the perceived probability of being correct. However, in approximately half of them, confidence also reflected a different probabilistic quantity: the perceived uncertainty in the estimated variable. We found that the contribution of both quantities was stable over weeks. We also observed that the influence of the perceived probability of being correct was stable across two tasks, one perceptual and one cognitive. Overall, our findings provide a computational interpretation of individual differences in human confidence.