# Total fertility rate

This article describes an attempt to use behavior of multiple birth cohorts in a single period and extrapolate from that to consider the outcomes for a hypothetical individual, who, at each age, behaves like the birth cohort for that age.

## Definition

The total fertility rate (TFR), also called the period fertility rate or period fertility of a population is defined in the following equivalent ways:

• It is the sum of the age-specific fertility rates for females at all ages. Note that only birth cohorts of females in their childbearing years are expceted to have age-specific fertility rates that are noticeably different from zero, so we can also define TFR as the sum of age-specific fertility rates for all ages that fall within the defined span for childbearing years. Note that we use age-specific fertility rates scaled to a denominator of 1 rather than to a denominator of 1000 for this definition.
• It is the expected value of the fertility that a female would have if, at every age, she had the age-specific fertility rate observed for the current year (rather than the year when she'd actually be that age).

We use the term period fertility to describe the TFR because it is a form of period analysis: we are aggregating over people of different ages, all in a given period of time. This is in contrast with cohort analysis, where we are looking at people who share a common temporal experience (such as birth, school attendance, or marriage) and study their behavior over their whole lifetime or a long part thereof.

### Total fertility rate for a particular birth order

Suppose $i$ is a positive integer. The total fertility rate at birth order $i$ is defined in the following equivalent ways:

• It is the sum of the age-specific fertility rates at birth order $i$.
• It is the probability that a female would have a birth at birth order $i$ if, at every age, she had the age-specific fertility rate observed for the birth order $i$.

Note that the total fertility rate at any particular birth order is bounded between 0 and 1: it is at least 0 and at most 1.

## Distinction between total fertility rate and general fertility rate

Further information: general fertility rate, total fertility rate versus general fertility rate

The reason TFR and GFR are different is because, whereas the TFR is the total of age-specific fertility rates and it weighs the birth cohort for each year with a weight of 1 per birth cohort, the GFR is the average of age-specific fertility rates weighted by the population sizes for the ages.

TFR and GFR would be easily related in the following two cases:

• All the age-specific fertility rates are the same. In this case, the GFR would equal all the equal age-specific fertility rate values, and the TFR would be the product of that value and the number of childbearing years.
• The population size is the same for each age. In this case, the GFR would equal the average of the age-specific fertility rate values, and the TFR would be the sum of the age-specific fertility rate values. In this case again, the TFR would equal the product of the GFR and the number of childbearing years.

Of course, neither case occurs in practice: there is considerable variation in the age structure of the female population (see the population pyramid for more), and considerable variation in the age-specific fertility rates.

Note also that, whereas TFR numbers are scaled to 1 (i.e., they represent actual numeric values), GFR numbers are scaled to a denominator of 1000. If the GFR numbers were not scaled to a denominator of 1000, they would be much smaller than TFR values. Both the above points about the relationship in special cases become valid only after we rescale the GFR and ASFR values to a denominator of 1.