Zipf's law

"Zipf's Law" is the name of a remarkable regularity in the distribution of city sizes all over the world, also known as the "Rank-Size Distribution". Take, for example, Amsterdam, the largest city in the Netherlands and give it rank number 1. Then take the second largest city, Rotterdam, and give it rank number 2. Keep on doing this for those cities for which you have data available, possibly selecting only cities exceeding a certain minimum size. If you calculate the natural logarithm of the rank and of the city size (measured in terms of the number of people) and plot the resulting data in a diagram you will get a remarkable log-linear pattern, this is the Rank-Size Distribution. If the slope of the line equals minus 1, as is for example approximately the case for the USA, India, and France, the relationship is known as Zipf's Law.

The remarkable log-linear relationship of the city-size distribution holds for virtually all countries. To demonstrate this, we have collected data on the city-size distribution for many countries, calculated Zipf's Law, and illustrated it in a figure. The results, containing cities with more than 100,000 inhabitants, are made in the Microsoft Office Excel '97 files downloadable below. The files distinguish between measurements of the "city proper" and the urban agglomeration When available the latter estimates of city sizes gives a more reliable view of Zipf's Law.

To use the files below you must have available a version of Microsoft Office Excel '97, or a more recent version. Download all files and place them in the same folder. Opening the file will make the data available in the other files easily accessible.

1) Index: (Excel 237kB)
2) America: (Excel 405kB)
3) Europe: (Excel 531kB)
4) Asia: (Excel 658kB)
5) Africa: (Excel 211kB)

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Oxford University Press, Online Resource Centre, Zipf's law.

Zipf's law