Gravity Model of Migration: W.J. Reilly and G.K. Zipf

In the 1950s, Geographers and Demographers were increasingly attracted to methods of positivist sciences such as physics and mathematics. Therefore, they used different theories and models of these sciences in their own field to gain validation from the scientific community. This paradigm in social sciences is known as quantitative revolution. The Gravity Model of Migration is also an imitation of Newton’s Law of Gravitation. Based on this law, many scholars tried to provide explanations for human interaction over space e.g. W. J. Reily and G. K. Zipf tried to explain human migration.

The Law of Gravity

  • The law of gravity states that the gravitation between two objects is directly proportional to the product of their masses and inversely proportional to the square of distance between them. The formula for the gravitational force is as follows.

F = (m1.m2)/D²

  • Here, F is gravitational force, m1 is mass of the first object, m2 is mass of the second object and D² is square of distance between the two objects.
  • The above law denotes that greater the size of the objects, greater will be the gravitational pull between them. Further, if the distance is greater, less will be the gravitational pull.

Gravity Model by W. J. Reilly

W.J. Reilly was the first scholar who extended the law of gravity to human interactions in 1940. Reilly’s main objective was to draw the breaking point or boundaries around cities from which the customers are ready to come to the cities for the purchase of goods and services. Please note that the distance from which a customer is ready to travel to the city for purchasing goods and services is the breaking point or limit of the city’s gravitational pull. He chose many parameters such as market population, the size of the retail establishment, distance to the market, the distance between markets, and the location of competitors etc., to estimate the market area around each city. Based on these factors, Reilly propounded the The Law of Retail Gravitation as follows.

  • The law of retail gravitation states that the interaction between two adjacent markets is directly proportional to the product of population sizes of the those adjacent markets and inversely proportional to the square of distance between them. He chose population size as an indicator of the mass/size of a city.

Mi = K [(P1.P2)/D²]

  • Here, Mi is interaction between markets; K is the constant or minimum amount of interaction regardless of population size; P1 is the population size of the first market; P2 is the population size of the second market and is the square of distance between the two markets.
  • The above law denotes that greater the size of the population of cities, greater will be the interaction between them. Further, if the distance between two adjacent cities is greater, less will be the interaction between them. Greater interaction means a greater number of customers.

Assumption: Please note that the above theory is only valid when the topography is plain, other socio-economic and political factors remain constant.

Spatial Interaction and Breaking Points

  • In terms of customer base, the customers are more likely to visit a market which is closer to them. However, the influence of large markets is greater than the smaller markets according to this model. Therefore, the customers will visit the larger market from afar places. It is so because all the market goods and services are not available in small markets near the people. So, they travel long distances to purchase goods and services (See Fig. 1).

    Fig. 1: Gravity Model by Reilly
  • Take the example of two magnets, one is large and one is small. If we put an iron ball near the small magnet, it will get attracted to the large magnet because the pull of the large magnet is greater than the small one. Similarly, towns attract customers and migrants.
  • To draw the breaking point of the market’s gravitational force, Reilly used the size of the markets and the distance to the market from the customer base to calculate the limit of the market’s gravitational pull (Fig. 1). In Fig. 1, L is the large market, S is the small market and C is the customer base. When we apply the gravity formulae between C and L or C and S, we come to see that the gravitational force between C and L is greater than C and S. It is so because the size of L is greater than S whereas their distance from L is equal. Hence, customers will prefer L for their needs and L’s breaking point or area of influence extends up to C.

In short, this model points out that the size of immigration depends on the size of the economic base of a city or market area. This model is similar to Central Place Theory by Walter Christaller.

Principle of Least Effort by G.K. Zipf

Similar to Reilly, G. K. Zipf also theorized the volume of migration between two places through a gravity model. Zipf named this law as Principle of Least Effort or Inverse Distance Law.

Fig. 2: Principle of Distance Decay
  • This law states that people try to minimize total work in a system while moving from one place to another. In space, distance is the largest barrier. Therefore, people migrate greater to smaller distances.
  • Distance Decay: Principle of distance decay states that interaction of people between places is inversely proportional to distance between the places. The magnitude of migration between places decreases increasingly with increasing distance (Fig. 2).
  • Therefore, people interact more with the places closer to them and less with the places farther from them.

Criticism of Gravity Model

The use of the gravity model in social sciences was a novel idea during the quantitative revolution. However, the use of such a static model to predict dynamic social processes had many drawbacks.

  1. Ignores Human Agency: This model treats human beings as lifeless objects which will get attracted to large cities due to gravity. However, human beings make decisions based on their ethnicity, religion, economic status, liking etc. These characteristics affect migration behavior more than the size of the city.
  2. Geographic Undulations: This model neglects the topographic barriers and undulations. Therefore, this model does not present the space in true sense. The presence of rivers, mountains, political boundaries etc. act as barriers to migration.
  3. Marginal Transport Cost Declines: This means that the cost of migration per kilometer declines as the distance increases. Therefore, small differences in distance do not impact migratory behavior.
  4. People visit different cities for different purposes. They are not limited to one city as this model suggests.
  5. Intervening opportunities and Obstacles: This model does not acknowledge the presence of opportunities and obstacles between two cities. For detail read Intervening Model of Opportunities by Stouffer and Model of Intervening Obstacles by Lee.
  6. Ignores Composition of Migrants: This model puts too much focus on volume of migration and ignores the age-sex composition of migrants.
  7. Ignores impact of Technology: The gravity model of migration is very static. The migratory patterns and behavior changes with improvement in technology, transport and communication. For detail read Mobility Transition Model by Zelinsky.


To sum up, we can say that the gravity model of migration is too objective and rigid to explain a very dynamic process that is migration. It gives an overall correct viewpoint that migration is greater between large cities and markets. However, there are many deficiencies in this model which do not consider topographic undulations, social, economic and political factors. Overall, the gravity model is just one of the many principles of migration.