SME
Human Geography
Urbanization
Use this for “A country’s largest city has 8,400,000 people. How big should its third city be by the rank–size rule, and how does 2,100,000 compare?”
Chart
8,400,000
2,100,000
This is an example. Type your own values to start a new problem.
Pₙ
=
P₁
÷
n
Aₙ
Actual size
example
R
Actual ÷ expected
calculated
Formulas
Pₙ
=
P₁
n
2,800,000
=
8,400,000
3
R
=
Aₙ
Pₙ
0.75
=
2,100,000
2,800,000
Assumptions
•
Rank–size rule: the city ranked n has about 1 ÷ n of the largest city’s people.
•
It fits many countries’ city systems; a primate city is far more than twice the second.
•
A ratio R near 1 fits the rule; below 1 the city is smaller than the rule expects.
Step-by-step
WE KNOW
P₁ = 8,400,000, n = 3, Aₙ = 2,100,000
FIND
expected size (Pₙ), actual ÷ expected (R)
Step 1 · Find expected size (Pₙ)
Use Pₙ = P₁ ÷ n
The rule shares out the largest city’s size by rank: the second has half, the third a third.
Pₙ
=
8,400,000
3
Pₙ = 2,800,000
Step 2 · Find actual ÷ expected (R)
Use R = Aₙ ÷ Pₙ
Compare the real city with the rule’s size: 1 means it fits exactly.
R
=
2,100,000
2,800,000
R
=
0.75
Check
Put the numbers back in. Both sides should match.
2,800,000
=
8,400,000
3
✓
0.75
=
2,100,000
2,800,000
✓
← Previous lesson
Stages of the demographic transition
Next lesson →
Population density away from the centre
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
Population density away from the centre
Use this for “A city’s centre has 20,000 people per km² and a density gradient of 0.2 per km. How dense is it 10 km out?”
A city’s growth rate and doubling time
Use this for “A city grew from 1,200,000 to 3,000,000 people in 25 years. What was its yearly growth rate, and how fast does it double?”
Models of a city’s land use
Use this for “A city’s richest neighbourhoods run in a wedge along the lakeshore. Which urban model does that fit?”