The size of states, including empires, is measured by two crude measures: their area and their population. Areas graphed over time represent the growth–decline curves of empires. These are the basic portraits of empires, showing at a glance how rapidly they formed, how large they became, and how long they lasted. Measuring areas in historical atlases supplies most data. Rome, Ottoman, and Manchu Qing offer examples of completed life cycles. Russia and the USA show curves still incomplete. The beginnings of these curves often approximate the “simple logistic” pattern typical of growth of bacteria colonies when they have plenty of food but space is limited. A table lists the following characteristic of 98 major empires during the last 5000 years: maximum size, duration at least at one-half of maximum size, and rise time from 20−80% of maximum size. Of these, 20 are Runner Empires (3000 to 600 BCE), 66 are Rider Empires (600 BCE to 1800 CE), and 12 are Engineer Empires (from 1800 on).