A population as a system
Two inputs, two outputs and one storage. Set the three rates and watch fifty years happen, with natural increase, growth rate and doubling time recalculating as you move.
Set the flows
The storage at year 0: 10 million.
Births per 1,000 people in the population each year. An input.
Deaths per 1,000 people each year. An output.
Immigration minus emigration. Positive means more people arriving than leaving; negative means the other way round.
Or load a real country
Source: Country Profiles, read on 19 September 2026. Population 2025, birth and death rates 2024, net migration 2025 (Niger -7,704, Switzerland +37,253). Each published count is converted to a rate per 1,000 so that all three flows share one unit.
1.20 %
12.0 per 1,000
Natural increase counts only births and deaths. It ignores migration entirely.
1.20 %
12.0 per 1,000
Births minus deaths, plus net migration.
58.3 years
Doubling time tells you when the population would double if the current rate continued unchanged for that whole period. Rates rarely do.
18.2 million
from 10 million
This is a model, not a prediction. It assumes the three rates you have set stay exactly the same for every one of these years. Real birth rates, death rates and migration rates change constantly, which is why even the UN publishes several different projections rather than one.
The same projection as a table
| Year | Population |
|---|---|
| 0 | 10 million |
| 1 | 10.1 million |
| 2 | 10.2 million |
| 3 | 10.4 million |
| 4 | 10.5 million |
| 5 | 10.6 million |
| 6 | 10.7 million |
| 7 | 10.9 million |
| 8 | 11 million |
| 9 | 11.1 million |
| 10 | 11.3 million |
| 11 | 11.4 million |
| 12 | 11.5 million |
| 13 | 11.7 million |
| 14 | 11.8 million |
| 15 | 12 million |
| 16 | 12.1 million |
| 17 | 12.2 million |
| 18 | 12.4 million |
| 19 | 12.5 million |
| 20 | 12.7 million |
| 21 | 12.8 million |
| 22 | 13 million |
| 23 | 13.2 million |
| 24 | 13.3 million |
| 25 | 13.5 million |
| 26 | 13.6 million |
| 27 | 13.8 million |
| 28 | 14 million |
| 29 | 14.1 million |
| 30 | 14.3 million |
| 31 | 14.5 million |
| 32 | 14.6 million |
| 33 | 14.8 million |
| 34 | 15 million |
| 35 | 15.2 million |
| 36 | 15.4 million |
| 37 | 15.5 million |
| 38 | 15.7 million |
| 39 | 15.9 million |
| 40 | 16.1 million |
| 41 | 16.3 million |
| 42 | 16.5 million |
| 43 | 16.7 million |
| 44 | 16.9 million |
| 45 | 17.1 million |
| 46 | 17.3 million |
| 47 | 17.5 million |
| 48 | 17.7 million |
| 49 | 17.9 million |
| 50 | 18.2 million |
Natural increase 1.20 per cent, overall growth rate 1.20 per cent, doubling time 58.3 years. After 50 years the population is 18.2 million.
Three things to try
- 1
Set a birth rate and a death rate, with no migration, that give a doubling time of about 35 years.
- 2
Build a population that is shrinking through natural decrease but growing overall.
- 3
Load the Niger preset. Find the birth rate that would hold the population steady.
Load Switzerland. More people are being born than are dying, but only just: natural increase is 0.07 %, which on its own would take a thousand years to double the population. The overall growth rate is several times that. Every bit of the difference is migration, and no amount of staring at the birth and death rates will explain it.
Natural increase is not the growth rate
Natural increase is births minus deaths, and nothing else. A country can have a negative natural increase and a growing population, or a positive natural increase and a shrinking one. The two figures sit side by side in the readout for exactly that reason: when they disagree, the gap is the migration flow.
The rule of 70 is an approximation
Divide 70 by the growth rate as a percentage and you get the doubling time. It is what the syllabus asks for and what the headline figure here uses. Set a growth rate that doubles the population inside the projection and the chart also shows the year the model actually crosses the line: close, but not identical, which is worth a sentence in an exam answer about models.
Niger and Switzerland are the same model
One doubles in about twenty years, the other in about a hundred and fifty, and both are four numbers in the same four boxes. Then find the birth rate that would hold Niger still: it is around 9 per 1,000, against the 41.4 it actually has. That gap is what a population policy is arguing about.
What this model leaves out
Every rate here is frozen for the whole projection, which no real country manages for fifty years. There is no age structure, so nothing here can tell you how many of the people are children or how that shapes what happens next. Those are the questions the next lessons ask. This one is about the four flows and the storage they fill.