We designate as an empire a state that stands out by area and population, as compared to most neighbors. The same population–technology interaction that enables world population to grow also enables states and then empires to form and expand, mostly by brutal force. Empires form where people are. The joint population share of the top five empires reached 50% of the world population by the year +1, and it did so on just 10% of the dry land area. The areas of top empires expanded in three phases, dependent on message speeds but also skills in delegation of power: Runner, Rider and Engineer Empires. The Rider age produced a new type of nomadic “area empires,” with low population density, in contrast with standard high-density “people empires.” The areas and populations of people empires tend to follow a square root relationship: Their share of world population is the square root of their share of dry land area.