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

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

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.*