Rank a country's cities from largest to smallest, and a striking regularity shows up across an enormous range of countries and historical periods: the second-largest city tends to sit at roughly half the population of the largest, the third at roughly a third, the fourth at roughly a quarter — a city's population landing close to the largest city's population divided by its own rank. It's called the rank-size rule, first documented for cities by the linguist George Zipf in the 1940s, who noticed the same kind of pattern turning up in word frequency and city size alike, and it shows up with striking consistency in national urban systems around the world despite nobody designing it.
A pattern nobody planned, showing up anyway
No planning authority sets out to make a country's second city exactly half the size of its capital or largest metropolis, and no law requires it. Yet plotted on a graph, many national urban systems track the rank-size rule closely enough to be genuinely surprising. Not every country fits it, though, and the exceptions are informative: some nations have a single "primate city" that dwarfs the rank-size prediction entirely — a capital, often with a history of centralised colonial or political administration, that concentrates a hugely disproportionate share of a country's population, economy and infrastructure, leaving every other city far smaller than the rule would predict.
The best explanation is really a description, not a mechanism
Economists and geographers have proposed generative explanations for why the pattern emerges rather than just documenting that it does. One influential idea, sometimes called Gibrat's law, models city growth as random and proportional — each city's population changing by a percentage rate each year that's independent of how big it already is — and shows mathematically that this simple growth rule tends to produce a rank-size, Zipf-like distribution over time, purely as a statistical outcome of many cities growing at random, unrelated rates. That's a real mechanism, but it explains the shape of the pattern without explaining why city growth would actually behave that randomly and independently in the first place.
What we're still unsure about
The rank-size rule is a strong empirical regularity, not a strict law — plenty of real countries deviate meaningfully from it, primate-city cases especially. And there's genuine, ongoing disagreement in urban economics about what the pattern actually reflects: whether it points to some deep, shared underlying process governing how cities grow everywhere, or whether it's closer to a statistical artifact that different countries' very different underlying growth processes just happen to converge on. The pattern itself is thoroughly documented. Why it holds as often as it does remains an active research question rather than settled theory.
This sits inside Urbanisation & City Systems, one of seven topics in Human Geography, one of five domains in Geography, one of seventeen subjects the app can quiz you on.