How many disappeared in the Rwandan civil war and genocide, and during the long, bloody aftermath? Scholars, international bodies, and Rwandan sources have come up with widely diverging estimates. However, these estimates are either limited to a subpopulation; have a truncated timeframe; or border on propaganda. More fundamentally, they lack a rigorous methodology and fail to fully exploit the wealth of pre- and post-conflict demographic data on Rwanda. A new approach is therefore proposed. We use 50 years of Rwandan population data; work with a reference population (which includes Rwandan refugees) instead of a resident population (Rwandans inside Rwanda); consider age-sex cohorts instead of overall values; and extrapolate excess mortality on the basis of intercensal survival rates. We estimate that between 1994 and 2002 more than 1.5 million Rwandans – or 20% of the pre-conflict population – disappeared. In a second article we will disaggregate the missing according to age, sex, and ethnicity; differentiate between direct and indirect conflict deaths; interpret the results; and reconcile them with historical sources.