Incidental waits are an unavoidable element of the consumer experience on any digital platform. Firms typically utilize no animation or single-speed, repeated animations during these waits. How might the use of such animations and their visual qualities influence perceived waiting time? Can simple design changes by managers influence the customer experience? Although prior research suggests a linear relationship where faster animations reduce perceived waiting time, we find a convex relationship between animation speed and time perception: moderate-speed animations minimize perceived waiting time compared to no, slow-moving, or fast-moving animations (experiments 1a-1c). We refer to this effect as the convex effect of animation speed. This effect occurs when people use animation speed to infer wait time (experiment 2a) and because moderate-speed animations draw more attention than static images or faster animations (experiment 2 b). Animations that introduce dual-attention elements (experiment 3a) or atypical animations (experiment 3 b) shift attention away from movement speed, attenuating this effect. Finally, this effect extends to website click-to-landing rates (experiment 4), conversion rates (experiment 5), and product evaluations during mobile shopping (experiment 6). These findings highlight the practical value of optimizing animation speed in user interface design to enhance both customer experience and business outcomes.