Formula of total fertility rate and gross fertility rate
Total Fertility Rate (TFR) is the average number of children a woman would have over her lifetime if current age-specific fertility rates remained constant. Gross Fertility Rate (GFR), also called the General Fertility Rate, measures births per 1,000 women of reproductive age in a given year.
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Here is a complete breakdown of both measures, drawn directly from Park's Textbook of Preventive and Social Medicine.
General Fertility Rate (GFR)
Definition: The number of live births per 1,000 women in the reproductive age group (15-44 or 15-49 years) in a given year.
Formula:
GFR = (Number of live births in a year / Mid-year female population aged 15-44 or 15-49) × 1000
Key points:
- It is a better measure than the crude birth rate because the denominator is restricted to women of childbearing age, not the whole population.
- Its main weakness is that not all women in the denominator are equally exposed to the risk of childbirth (e.g., unmarried women are included).
Total Fertility Rate (TFR)
Definition: The average number of children a woman would have if she passed through her entire reproductive lifespan bearing children at the same rates currently observed in each age group.
Formula:
TFR = (5 × ΣASFR) / 1000 (summed from age group 15-19 to 45-49)
Where ASFR = Age-Specific Fertility Rate for each 5-year age group, calculated as:
ASFR = (Live births in a particular age group / Mid-year female population of that age group) × 1000
Step-by-step:
- Calculate the ASFR for each 5-year age group from 15-19 up to 45-49 (7 groups total).
- Sum all ASFRs.
- Multiply the sum by 5 (the width of each age interval).
- Divide by 1000 (to convert per-1,000-women rates to a per-woman figure).
Example (illustrative):
| Age Group | Births | Women | ASFR |
|---|---|---|---|
| 15-19 | 34,772 | 860,698 | 40.4 |
| 20-24 | 117,697 | 759,335 | 155.0 |
| 25-29 | 85,664 | 507,188 | 168.9 |
| 30-34 | 56,565 | 422,755 | 133.8 |
| 35-39 | 37,072 | 454,870 | 81.5 |
| 40-44 | 14,448 | 401,344 | 36.0 |
| 45-49 | 1,436 | 319,017 | 4.5 |
| Sum | 620.1 |
TFR = (5 × 620.1) / 1000 = 3.10 children per woman
Key points:
- TFR gives the approximate "completed family size" for a hypothetical cohort.
- A TFR of ~2.1 is considered replacement-level fertility.
- It is an age-adjusted rate because it assumes equal numbers of women in each age group.
Quick Comparison
| Feature | GFR | TFR |
|---|---|---|
| Unit | Births per 1,000 women (15-44/49) | Average children per woman |
| Denominator | All women aged 15-44/49 | Age-specific groups summed |
| Age adjustment | No | Yes |
| Interpretation | Simpler, annual snapshot | Synthetic cohort lifetime estimate |
| Formula | (Births / Women 15-49) × 1000 | (5 × ΣASFR) / 1000 |
Source: Park's Textbook of Preventive and Social Medicine, p. 576
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