Total fertility rate
The total fertility rate (TFR, sometimes also called the fertility rate, period total fertility rate (PTFR) or total period fertility rate (TPFR)) of a population is the average number of children that would be born to a woman over her lifetime if she were to experience the exact current age-specific fertility rates (ASFRs) through her lifetime. It is obtained by summing the age-specific rates for a given time-point.
The TFR is a synthetic rate, not something that is actually counted. It is not based on the fertility of any real group of women, since this would involve waiting until they had completed childbearing. Nor is it based on counting up the total number of children actually born over their lifetime, but instead is based on the age-specific fertility rates of women in their "child-bearing years," which in conventional international statistical usage is ages 15-44 or 15-49.
The TFR is therefore a measure of the fertility of an imaginary woman who passes through her reproductive life subject to all the age-specific fertility rates for ages 15-49 that were recorded for a given population in a given year. The TFR represents the average number of children a woman would have were she to fast-forward through all her childbearing years in a single year, assuming the all the age-specific fertility rates for that year. In other words, this rate is the number of children a woman would have if she was subject to prevailing fertility rates at all ages from a single given year, and survives throughout all her childbearing years.
An alternative fertility measure is the net reproduction rate (NRR), which measures the number of daughters a woman would have in her lifetime if she were subject to prevailing age-specific fertility and mortality rates in the given year. When the NRR is exactly one then each generation of women is exactly reproducing itself. The NRR is less widely used than the TFR, and the United Nations stopped reporting NRR data for member nations after 1998. But the NRR is particularly relevant where the number of male babies born is very high. The gross reproduction rate (GRR), is the same as the NRR, except that - like the TFR - it ignores life expectancy.
The TFR (or TPFR) is a better index of fertility than the Crude birth rate (annual number of births per thousand population) because it is independent of the age structure of the population, but it is a poorer estimate of actual completed family size than the total cohort fertility rate, which is obtained by summing the age-specific fertility rates that actually applied to each cohort as they aged through time. In particular, the TFR does not necessarily predict how many children young women now will eventually have, as their fertility rates in years to come may change from those of older women now. However, the TFR is a reasonable summary of current fertility levels.
Replacement fertility is the total fertility rate at which women would have only enough children to replace themselves and their partner. By definition, replacement is only considered to have occurred when the offspring reach 15 years of age. If there were no mortality in the female population until the end of the childbearing years (generally taken as 44 or 49, though some exceptions exist) then the replacement rate would be exactly 2, but in practice it is affected by mortality, especially childhood mortality. The replacement fertility rate is roughly 2.1 births per woman for most industrialized countries but ranges from 2.5 to 3.3 in developing countries because of higher mortality rates. Taken globally, the total fertility rate at replacement is 2.33 children per woman. At this rate, global population growth would trend towards zero.
Developed countries usually have a much lower fertility rate due to greater wealth and their individualistic culture. Mortality rates are low, birth control is easily accessible, and human beings are often deemed (by other human beings) as nothing but an economic drain, specially when they cannot produce income: because of education costs, clothing and feeding. Longer periods of time spent getting higher education often mean young people have children later in life. The result is the demographic-economic paradox.
In developing countries on the other hand, families desire children for their labour and as caregivers for their parents in old age. Fertility rates are also higher due to the lack of access to contraceptives, generally lower levels of female education, and lower rates of female employment in industry.
The total fertility rate in the United States after World War II peaked at about 3.8 children per woman in the late 1950s and by 1999 was at 2 children. This means that an imaginary woman (defined in the introduction) who fast-forwarded through her life in the late 1950s would have been expected to have about four children, whereas an imaginary woman who fast-forwarded through her life in 1999 would have been expected to have only about two children in her lifetime. The fertility of the population of the United States is below replacement among those native born, and above replacement among immigrant families. However, the fertility rates of immigrants to the U.S. has been found to decrease sharply in the second generation, as a result of improving education and income. 
The lowest TFR recorded anywhere in the world in recorded history is for Xiangyang district of Jiamusi city (Heilongjiang, China) which had a TFR of 0.41.  Outside china, the lowest TFR ever recorded was 0.80 for Eastern Germany in 1994.
A population that maintains a TFR of 3.8 over a long time would increase rapidly, whereas a population that maintains a TFR of 2.0 over a long time would decline (unless it had a large enough immigration). The TFR required for a closed population to eventually reach equilibrium in size ranges from 2.5 to 3.3 in developing countries and is near 2.1 in many developed countries (2.075 in the UK for example). However, it may take several generations for a change in the total fertility rate to be reflected in birth rate, because the age distribution must reach equilibrium. For example, a population that has recently dropped below replacement-level fertility will continue to grow, because the recent high fertility produced large numbers of young couples who would now be in their child-bearing years. This phenomenon carries forward for several generations and is called population momentum or population-lag effect. This time-lag effect is of great importance to the growth rates of human populations.
- Espenshade TJ, Guzman JC, and Westoff CF (2003). "The surprising global variation in replacement fertility". Population Research and Policy Review.
- "How Fertility Changes Across Immigrant Generations." Research Brief #58, Public Policy Institute of California, 2002.
- Crude birth rate
- List of countries and territories by fertility rate
- Demographic-economic paradox
- World Factbook table of Total Fertility Rate ordered by country rank
- Population Reference Bureau Glossary of Population Terms
- Java Simulation of Total Fertility.
- Java Simulation of Population Dynamics.
- How Fertility Changes Across Immigrant Generations.