Population Growth Rate
Births minus deaths is the natural increase. Dividing by the population turns it into a rate you can compare across countries.
Three rates, one percentage
Demographers describe a population's change with crude rates: births, deaths and net migration per 1,000 people per year. "Crude" means the rate is divided by the whole population, not by the group that can actually give birth or die. That keeps the arithmetic simple and makes countries comparable, at the cost of hiding age structure.
growth rate (%) = (births − deaths + net migration) ÷ 10A birth rate of 17 and a death rate of 8 give a natural increase of 9 per 1,000, or 0.9% a year. Add net migration of 2 per 1,000 and the rate becomes 1.1%. Subtract an emigration flow of 3 and it falls to 0.6%.
Natural increase is not the whole story
Natural increase is births minus deaths. It ignores people crossing borders, which for some countries is the dominant term. The Gulf states, Canada and Australia have grown faster than their natural increase for decades because of immigration; several eastern European countries have shrunk faster than their birth deficit because of emigration.
When a news report says a country's population "fell", check which measure it used: natural increase, total change, or a projection. The three can point in different directions in the same year.
Doubling time and the rule of 70
At a constant growth rate r, the number of years needed to double is ln(2) ÷ ln(1 + r). For small r, ln(1 + r) is close to r, so the answer is approximately 0.693 ÷ r, or 69.3 ÷ (r as a percentage). The rule of 70 is the rounded version.
| Growth rate | Rule of 70 | Exact |
|---|---|---|
| 0.5% | 140 years | 139.0 years |
| 1% | 70 years | 69.7 years |
| 2% | 35 years | 35.0 years |
| 3% | 23.3 years | 23.4 years |
| 5% | 14 years | 14.2 years |
The same arithmetic works in reverse: a population shrinking at 1% a year halves in about 69 years. A negative rate is not symmetric in its consequences, because the age structure changes as the population shrinks.
Replacement fertility is about 2.1
A woman needs to have about 2.1 children on average for a population to replace itself without migration, because some children die before adulthood and because not everyone has children. A fertility rate below that does not produce an immediate decline: the children already born keep entering childbearing age, so the population can grow for decades after fertility falls below replacement. That lag is population momentum.
Conversely, a population that has had low fertility for a long time can keep shrinking even if fertility rises back to replacement, because there are fewer women of childbearing age. Age structure is a stock, and births are a flow into it.
Why a constant-rate projection is a scenario
Holding three rates constant for 30 years is a strong assumption. Fertility responds to housing, childcare, employment and policy; mortality improves with medicine; migration responds to borders and economies. A straight-line projection is useful for showing what a rate implies, not for telling you what will happen.
A cohort-component projection does the work properly: it tracks each age group, applies age-specific fertility and mortality, and adds migration by age. That needs a lot more data than three numbers, and it is what statistical agencies publish.
Reading a projection in the news
- Check the base year. A projection from 2020 and one from 2024 use different starting populations and different assumptions.
- Check the variant. The UN publishes low, medium and high fertility variants; the medium variant is usually the headline, not a certainty.
- Check the horizon. A five-year projection is much more reliable than a fifty-year one, because fewer assumptions have time to break.
- Check whether migration is included. A natural-increase-only projection can be far from the total change.
The calculator works from annual counts rather than rates: enter the births, deaths and net migration you can find for a country, and it shows what those numbers imply. This page explains the crude rates behind those counts, and why a fixed-rate or fixed-count scenario is not a forecast.