Misperceptions of the size of demographic groups are one of the most prevalent instances of citizen ignorance. Americans are often accused of being ignorant of basic demographic facts, such as the size of the black, Hispanic, and foreign-born populations in the United States. Research over the past two decades has documented the tendency for citizens to overestimate the size of minority populations and underestimate the size of majority populations in over a dozen countries. While public opinion scholars have proposed a multiple explanations for these misperceptions, they are limited both by inconsistent empirical support and the number of instances of demographic misperceptions they fail to explain. In this paper we provide an alternative explanation for demographic misperceptions, one that is rooted in the psychology of individual decision-making under uncertainty and applies to misperceptions regardless of who they are about or who holds them. We aggregate estimates of a wide variety of groups from a collection of existing surveys, published studies, and original data to evaluate the extent to which our model accounts for demographic misperceptions. We then evaluate our explanation alongside existing theories using a rich dataset containing estimates of racial and ethnic groups at the national and local level, as well as measures of perceived threat and contact. Our findings strongly suggest that demographic misperceptions are an instance of a broader pattern of cognitive errors people make when interpreting and estimating quantities, and have implications for our understanding of both where demographic misperceptions originate and how they should be interpreted.