When making decisions, combining multiple pieces of information can increase the probability of making the right choice. A decision maker's estimate of this probability, referred to as decision confidence (Hangya et al., 2016), is useful for guiding subsequent actions and learning improvements in the decision policy (Drugowitsch et al., 2019). But studies of the neural computations that give rise to confidence have been limited by the difficulty of measuring confidence in animal subjects. One promising approach uses willingness to wait for reward after choice as a proxy for confidence (Lak, 2014). While rats can learn to modulate wait time as a function of the probability that they've chosen correctly (Lak et al., 2014; Joo et al., 2021), it is unclear how subjects transform confidence into wait time. Here, we show that a drift diffusion to bound model can generate optimal wait times using a tractable update rule to a confidence variable whose initial value is set by the choice process. In this model, each time step that elapses without reward is treated as evidence that reward will not be delivered on that trial. Correspondingly, confidence decreases with time until the expected value of waiting falls to the expected value of starting a new trial. We trained rats to wait for randomly delayed rewards after trials of an auditory evidence accumulation task (Brunton et al., 2013). We used an extensively studied model of the choice process (Brunton et al., 2013; Piet et al., 2018) as the initial point of a drift diffusion process controlling the wait time decision. Fitting the parameters of the wait time model, we find that rats can learn the optimal drift rate for the wait time decision process, but that not all do. Our model offers a strategy for performing this task, unifying the side choice and wait time decisions into a single process and producing a dynamic view of decision confidence.