Decision making between several alternatives is thought to involve the gradual accumulation of evidence in favor of each available choice. This process is profoundly variable even for nominally identical stimuli, yet the neuro-cognitive substrates that determine the magnitude of this variability are poorly understood. Here, we demonstrate that arousal state is a powerful determinant of variability in perceptual decision making. We measured pupil size, a highly sensitive index of arousal, while human subjects performed a motion-discrimination task, and decomposed task behavior into latent decision making parameters using an established computational model of the decision process. In direct contrast to previous theoretical accounts specifying a role for arousal in several discrete aspects of decision making, we found that pupil diameter was uniquely related to a model parameter representing variability in the rate of decision evidence accumulation: Periods of increased pupil size, reflecting heightened arousal, were characterized by greater variability in accumulation rate. Pupil diameter also correlated trial-by-trial with specific patterns of behavior that collectively are diagnostic of changing accumulation rate variability, and explained substantial individual differences in this computational quantity. These findings provide a uniquely clear account of how arousal state impacts decision making, and may point to a relationship between pupil-linked neuromodulation and behavioral variability. They also pave the way for future studies aimed at augmenting the precision with which people make decisions. 