Rank Size Rule by GK Zipf

Many urban geographers have observed the existence of some kind of pattern in size and spacing of cities. Similarly, GK Zipf observed this pattern and propounded rank size rule. Rank Size Rule states that the population of all towns can be expressed in relation to the most populated city of a region. The rank size rule can be expressed as following.

Pn = P1/n

Pn denotes Population of nth town; P1 is the most populated city; n denotes the rank of city in terms of population.

Working of Rank Size Rule

One can use the following steps to arrive at the pattern of urban growth in a particular region.

  1. Collect the population data of all the cities of a country or region.
  2. Arrange the population of all the cities in descending order and assign rank (n) to them.
  3. Denote the city with largest population as P1.
  4. Divide the population of largest city (P1) with rank of each cities. Each city will get its own Pn value. For instance, if you divide the total population of First ranked city with 12, you will get the population of 12th ranked city. Similarly, we can calculate the population of all other cities.
  5. Once, we get the Pn value of all the cities, we have to plot the data on a graph at logarithmic scale.
  6. After we plot the data, we get the pattern of urban growth. The pattern is based on the shape of curve on the graph.

Pattern of Urban Growth

Based on rank size rule, we can classify the pattern of urban growth over space into four categories.

Fig. 1: Patterns of Urban Development

1. Primary Pattern

Primary pattern means that the curve on the graph is convex to the center. The population of second and third ranked city is far lower than the first ranked city. There is only one single dominant city in a region (see Fig. 1). It is primarily due to agglomeration of economic activities and non-ubiquitous nature of resource distribution.

2. Binary Pattern

Binary pattern means that the curve on the graph is concave to the center. The population of second ranked city is closer to the first ranked city. This means that the region is dominated by two large cities unlike the primary pattern (see Fig.1). Such pattern is found in a region where resources are concentrated in two places in such a manner that one city complements the other.

3. Stepped Pattern

Stepped pattern means that the curve on the graph is like a stair. The population of first and second, third and fourth, fifth and sixth cities is equal and so on. So, there are two cities with equal population at each lower level. An area with more or less ubiquitous resources has this pattern of city development because urban growth is closest to the rank size rule.

4. Rank Size Rule Pattern

This pattern conforms to the rank size rule. The curve is a negative sloping straight line. This type of urban development is found in areas with even distribution of resource (see Fig. 1).

Factors Controlling the Number and Distribution of Cities

1. Forces of Diversification

  • Forces of diversification envisage those forces which does not let the city growth concentrate at one place.
  • Land based activities such as agriculture and mining can not concentrate at one place. Therefore, a region will have greater number of cities scattered over larger land are.
  • If the transport network is well developed, the economic activities will not concentrate at one place.
  • Large number of towns: If a region has large number of towns, it means that resources are evenly distributed and cities will be evenly spaced too.

2. Forces of Unification

  • Forces of diversification envisage those forces which helps the concentration of urban growth at one place.
  • The proximity of production area with the markets promotes metropolitan centric urban growth.
  • If externalities are available in an urban system, it will promote the growth of large city.
  • Large settlements are themselves markets, therefore, the cumulative causation helps the growth of large urban agglomerations.

Assessment of Rank Size Rule

  • This principle is over-generalized.
  • Population of a city does not depend on population of largest city but on economic potential and many other factors.
  • This rule does not apply in India at national level because India has many large cities of same size.
  • It may apply only in an isolated region with export oriented industry which promotes large metropolitan near the coast.


In summary, rank size rule explains that the population of a city is dependent on the population size of the largest city of the region. Zipf did not explain any rationale behind putting this equation. This rule is application of a simple mathematical equation on a complex urban system. Hence, it has no practical or empirical validity.