Humans and other animals must often make decisions on the basis of imperfect evidence. Statisticians use measures such as P values to assign degrees of confidence to propositions, but little is known about how the brain computes confidence estimates about decisions. We explored this issue using behavioural analysis and neural recordings in rats in combination with computational modelling. Subjects were trained to perform an odour categorization task that allowed decision confidence to be manipulated by varying the distance of the test stimulus to the category boundary. To understand how confidence could be computed along with the choice itself, using standard models of decision-making, we defined a simple measure that quantified the quality of the evidence contributing to a particular decision. Here we show that the firing rates of many single neurons in the orbitofrontal cortex match closely to the predictions of confidence models and cannot be readily explained by alternative mechanisms, such as learning stimulus-outcome associations. Moreover, when tested using a delayed reward version of the task, we found that rats' willingness to wait for rewards increased with confidence, as predicted by the theoretical model. These results indicate that confidence estimates, previously suggested to require 'metacognition' and conscious awareness are available even in the rodent brain, can be computed with relatively simple operations, and can drive adaptive behaviour. We suggest that confidence estimation may be a fundamental and ubiquitous component of decision-making.