acalculator

What is the rate of natural increase?

Enter the births and deaths in a year and the population, or the crude birth and death rates per 1,000. The rate of natural increase calculator shows how fast the population grows from births and deaths alone, as a percent.

Your numbers

I know the
Rate of natural increase
0.4%

The rate of natural increase is 0.4%, or 4 per 1,000 people in the year.

Natural increase per 1,000 people
4
Natural increase (births − deaths)
4,000
Crude birth rate (per 1,000)
12
Crude death rate (per 1,000)
8

Rate of natural increase: 0.4%. The rate of natural increase is 0.4%, or 4 per 1,000 people in the year.

How to calculate

Computes the rate of natural increase (RNI): births minus deaths as a percent of the population, from counts or from the crude birth and death rates per 1,000.

Example with the default inputs (I know the Births and deaths, Live births in the year 12,000, Deaths in the year 8,000, Population 1,000,000): The rate of natural increase is 0.4%, or 4 per 1,000 people in the year.

Method: RNI (%) = (births − deaths) ÷ population × 100. From rates per 1,000: RNI (%) = (crude birth rate − crude death rate) ÷ 10. Crude birth rate = births ÷ population × 1,000; crude death rate = deaths ÷ population × 1,000.

  • Births and deaths are for one year, and the population is the one the rates are based on, usually at midyear.
  • Migration is left out: natural increase counts only births and deaths.
  • Arithmetic is exact on the typed decimals; the RNI shows to 3 decimals and the rates to 2, halves up.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. I know the Births and deaths, Live births in the year 12,000, Deaths in the year 8,000, Population 1,000,000 gives Rate of natural increase 0.4%, Natural increase per 1,000 people 4, Natural increase (births − deaths) 4,000, Crude birth rate (per 1,000) 12, Crude death rate (per 1,000) 8.Source: Population Reference Bureau, Glossary of Demographic Terms (rate of natural increase: the rate at which a population is increasing or decreasing in a year due to a surplus or deficit of births over deaths, as a percentage of the base population; birth rate and death rate: live births and deaths per 1,000 population in a year). https://www.prb.org/resources/glossary/
  2. I know the Births and deaths, Live births in the year 9,500, Deaths in the year 11,200, Population 850,000 gives Rate of natural increase −0.2%, Natural increase per 1,000 people −2, Natural increase (births − deaths) -1,700, Crude birth rate (per 1,000) 11.18, Crude death rate (per 1,000) 13.18.Source: Population Reference Bureau, Glossary of Demographic Terms (rate of natural increase: the rate at which a population is increasing or decreasing in a year due to a surplus or deficit of births over deaths, as a percentage of the base population; birth rate and death rate: live births and deaths per 1,000 population in a year). https://www.prb.org/resources/glossary/
  3. I know the Rates per 1,000, Crude birth rate (per 1,000) 17, Crude death rate (per 1,000) 8 gives Rate of natural increase 0.9%, Natural increase per 1,000 people 9.Source: Population Reference Bureau, Glossary of Demographic Terms (rate of natural increase: the rate at which a population is increasing or decreasing in a year due to a surplus or deficit of births over deaths, as a percentage of the base population; birth rate and death rate: live births and deaths per 1,000 population in a year). https://www.prb.org/resources/glossary/
  4. I know the Rates per 1,000, Crude birth rate (per 1,000) 9.2, Crude death rate (per 1,000) 10.6 gives Rate of natural increase −0.14%, Natural increase per 1,000 people −1.4.Source: Population Reference Bureau, Glossary of Demographic Terms (rate of natural increase: the rate at which a population is increasing or decreasing in a year due to a surplus or deficit of births over deaths, as a percentage of the base population; birth rate and death rate: live births and deaths per 1,000 population in a year). https://www.prb.org/resources/glossary/
  5. I know the Births and deaths, Live births in the year 25,481, Deaths in the year 21,736, Population 2,345,678 gives Rate of natural increase 0.16%, Crude birth rate (per 1,000) 10.86, Crude death rate (per 1,000) 9.27.Source: Population Reference Bureau, Glossary of Demographic Terms (rate of natural increase: the rate at which a population is increasing or decreasing in a year due to a surplus or deficit of births over deaths, as a percentage of the base population; birth rate and death rate: live births and deaths per 1,000 population in a year). https://www.prb.org/resources/glossary/

How it works

From births and deaths:

  • Natural increase = births − deaths
  • Rate of natural increase (%) = (births − deaths) ÷ population × 100
  • Natural increase per 1,000 people = (births − deaths) ÷ population × 1,000
  • Crude birth rate = births ÷ population × 1,000; crude death rate = deaths ÷ population × 1,000

From rates per 1,000:

  • Rate of natural increase (%) = (crude birth rate − crude death rate) ÷ 10
  • Natural increase per 1,000 people = crude birth rate − crude death rate

Rules:

  • Births and deaths are 0 or more; the population must be more than 0. Each count is at most 1 trillion. Rates per 1,000 are 0 to 1,000.
  • The rate is negative when deaths outnumber births (a natural decrease).
  • A result too large to show as a number gives no answer. So does a result that is not 0 but too small to show as a number.
  • The arithmetic is exact on the numbers you type. The RNI shows to 3 decimals and the rates per 1,000 to 2 decimals; the natural increase shows up to 6 decimals (6 significant figures below 0.0001 in size). Halves round away from 0.

Assumptions

  • Births and deaths are counted over one year. The population is the base the rate is measured against, usually the population at midyear.
  • Migration is left out. Natural increase counts births and deaths only.

Worked examples by hand

A town of a million. Natural increase = 12,000 − 8,000 = 4,000. RNI = 4,000 ÷ 1,000,000 × 100 = 0.4%, or 4 per 1,000. Birth rate = 12 and death rate = 8 per 1,000.

A natural decrease. Natural increase = 9,500 − 11,200 = −1,700. RNI = −1,700 ÷ 850,000 × 100 = −0.2%. Birth rate = 11.18 and death rate = 13.18 per 1,000.

From rates per 1,000. Birth rate 17, death rate 8: RNI = (17 − 8) ÷ 10 = 0.9%.

A death rate above the birth rate. RNI = (9.2 − 10.6) ÷ 10 = −0.14%.

A city of 2,345,678. Natural increase = 25,481 − 21,736 = 3,745. RNI = 3,745 ÷ 2,345,678 × 100 = 0.15966%, shown as 0.16%. Birth rate = 10.86 and death rate = 9.27 per 1,000.

Other questions people ask

What is the rate of natural increase?

The rate of natural increase (RNI) is the rate at which a population grows, or shrinks, in a year from the surplus or deficit of births over deaths, as a percent of the population. It leaves out migration.

How do I calculate the rate of natural increase?

Subtract deaths from births, divide by the population and multiply by 100. A town of 1,000,000 with 12,000 births and 8,000 deaths has an RNI of (12,000 − 8,000) ÷ 1,000,000 × 100 = 0.4%.

How do I get the RNI from birth and death rates?

Crude birth and death rates are per 1,000 people, so subtract the death rate from the birth rate and divide by 10 to get a percent. A birth rate of 17 and a death rate of 8 give (17 − 8) ÷ 10 = 0.9%.

Why divide by 10?

A rate per 1,000 people becomes a percent, which is per 100 people, by dividing by 10: 9 per 1,000 is 0.9 per 100, or 0.9%.

Can the rate of natural increase be negative?

Yes. When deaths outnumber births the population shrinks naturally, a natural decrease. A birth rate of 9.2 and a death rate of 10.6 per 1,000 give an RNI of −0.14%.

How is the RNI different from the population growth rate?

The growth rate also counts net migration, the people moving in minus the people moving out. A country can have a negative RNI and still grow if more people move in than the natural decrease takes away.