Many decisions must be made with incomplete information. The ability to evaluate the resulting uncertainty is a key aspect of metacognition. As both confidence judgments and reaction times are expected to be closely related to sensory uncertainty, a mathematical model of human perceptual decision-making should be able to explain them both. Here, we propose the new dynamical evidence and visibility model (dynWEV), an extension of the drift diffusion model of decision making, to account for choices, reaction times, and confidence at the same time. The decision process in a binary perceptual task is described as a Wiener process accumulating sensory evidence about the choice options bounded by two constant thresholds. To account for confidence judgments, we assume a period of postdecisional accumulation of sensory evidence and parallel accumulation of information about the reliability of the present stimulus. We examined model fits in two experiments, a motion discrimination task with random dot kinematograms and a post-masked orientation discrimination task. A comparison between the dynamical evidence and visibility model, two-stage dynamical signal detection theory, and several versions of race models of decision making showed that only dynWEV produced acceptable fits of choices, confidence, and reaction time. This finding suggests that confidence judgments not only depend on choice evidence, but also on a parallel estimate of sensory uncertainty as well as postdecisional accumulation of evidence.