The Size & Distribution
of Cities
Explore how cities vary in population size, why some grow into megacities while others stay small, and the models geographers use to explain urban hierarchies.
What Is an Urban Hierarchy?
Cities are not all the same size. In every country, a few large cities sit at the top of the hierarchy, while many smaller cities and towns fill the base. This pattern of size distribution is one of the most consistent findings in geography.
Why City Size Matters
Understanding urban size distribution helps geographers and policymakers predict migration patterns, allocate infrastructure investment, and assess how economic development spreads across a country.
Measuring City Size
The Rank-Size Rule
Proposed by George Zipf, the rank-size rule states that in an ideal system, a city's population is inversely proportional to its rank among all cities in a country:
If the largest city has 10 million people, the 2nd city should have about 5 million, the 3rd about 3.33 million, and so on.
Visualizing the Rank-Size Rule
The Primate City Concept
Mark Jefferson (1939) observed that in many countries, the largest city is disproportionately larger than the second-largest: at least twice the size and more than twice as significant culturally and economically.
Primate City vs. Rank-Size
| Primate City | Rank-Size | |
|---|---|---|
| Distribution | One city dominates | Smooth hierarchy |
| 2nd City Size | < half of 1st | ≈ half of 1st |
| Typical Countries | UK, France, Thailand | USA, Brazil, India |
| Development | Often developing nations | Often large/mature economies |
Christaller's Central Place Theory
Walter Christaller (1933) proposed that cities exist to provide services to surrounding areas. Larger cities offer more specialized services and serve wider market areas, while smaller towns provide everyday goods to nearby residents.
Hexagonal Market Areas
The Gravity Model
Inspired by Newton's law of gravitation, the gravity model predicts the interaction between two cities based on their populations and the distance between them:
How to Analyze City Distribution
Example: Rank-Size in Country X
Country X's largest city has a population of 8 million. If the rank-size rule applies, predict the populations of the 2nd through 5th largest cities.
| Rank | Formula | Predicted Population |
|---|---|---|
| 1st | \( 8{,}000{,}000 / 1 \) | 8,000,000 |
| 2nd | \( 8{,}000{,}000 / 2 \) | 4,000,000 |
| 3rd | \( 8{,}000{,}000 / 3 \) | 2,667,000 |
| 4th | \( 8{,}000{,}000 / 4 \) | 2,000,000 |
| 5th | \( 8{,}000{,}000 / 5 \) | 1,600,000 |
Example: Is Bangkok a Primate City?
Thailand's largest cities by population:
Example: Gravity Model Calculation
City A has 500,000 people and City B has 200,000 people. They are 100 km apart. City C has 500,000 people and is 200 km from City A. Which pair interacts more?
Common Mistakes
Key Models Summary
| Model | Key Idea | Formula / Rule | Best Example |
|---|---|---|---|
| Rank-Size Rule | Smooth hierarchy | \( P_n = P_1 / n \) | USA, Brazil |
| Primate City | One dominant city | \( P_1 > 2 \times P_2 \) | UK, Thailand |
| Central Place | Service hierarchy | Hexagonal markets | Flat farmlands |
| Gravity Model | Interaction strength | \( P_1 P_2 / d^2 \) | Trade flows |
Question 1 of 5
According to the rank-size rule, if a country's largest city has 12 million people, what is the expected population of the 4th-largest city?
Question 2 of 5
Which of the following best describes a primate city?
Question 3 of 5
In the gravity model, what happens to the predicted interaction between two cities if the distance between them is tripled?
Question 4 of 5
Christaller's central place theory assumes hexagonal market areas rather than circular ones because:
Question 5 of 5
A country has the following largest cities: Capital (15M), City B (2M), City C (1.5M), City D (1.2M). This pattern most closely reflects: