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Math of Population

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There are several factors to keep in mind when thinking about population growth:

Birth Rate

This metric is the number of births per 1,000 persons in a population over a given period (usually a year). It excludes variation such as sex ratios, age distributions, and postponement or acceleration of marriage age, which all affect actual birth rates. Divide the number of births by the total population and multiply the quotient by 1,000.

\[\frac{births}{population} \times 1000 = \textit{birth rate}\]

Death Rate

This metric is calculated the same way as with birth rate, with deaths per 1,000 persons as the numerator.

\[\frac{deaths}{population} \times 1000 = \textit{death rate}\]

Natural Increase Rate

This metric represents the percentage by which a population is increasing or decreasing. Negative rates of natural increase indicate a declining population. To calculate, subtract death rate from birth rate, then divide the difference by 10 to express as a percentage.

\[\frac{\textit{birth rate}-{\textit{death rate}}}{10}=\textit{natural increase rate}\]

Doubling Time

This metric is the amount of time in years required for a population to double in size at a constant growth rate. To calculate doubling time for a population undergoing exponential growth, use the rule of 70. Divide 70 by the growth rate as a percentage (not as a decimal).

\[\frac{70}{\textit{growth rate %}}=\textit{doubling time}\]

Total Fertility Rate

The average number of children born per woman in her childbearing years according to a current schedule of age-specific fertility rates. Multiply by 1,000 to determine the number of children born per 1,000 women. Total fertiltiy rate is calculated as a sum of current age-specific fertility rates for single year age groups or x times the sum of current x-year group fertility rates.

\[\textit{total fertility rate}=\sum \textit{ASFR}_a \\
\text{for single-year age groups, or} \\
\textit{total fertility rate}=5 \sum \textit{ASFR}_a \\
\text{for 5-year age groups}\]

In the equations above, ASFRa represents the age-specific fertility rate for women in age group a (expressed as a rate per woman).

The United Nations Statistical Division collects a variety of demographic and social statistics from civil registries worldwide and publishes these data in annual Demographic Yearbooks and also in more specific occasional reports such as the World Fertility Report.

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