Net Reproductive Rate Calculator
From a life table — survivorship and fecundity by age class — the net reproductive rate, the mean generation time, the intrinsic rate of increase and the doubling time of a population.
A life table lists, for each age class, the share of newborns surviving to it and the offspring each produces there.
How the net reproductive rate calculator works
A life table lists, for each age class, the share of newborns surviving to it and the offspring each produces there. Multiply and sum and you have R₀, the number of daughters a newborn is expected to leave over her life: above one the population grows, below one it shrinks. Weighting the same products by age gives the generation time, and the log of R₀ over the generation time is the intrinsic growth rate.
It is the calculation behind every population projection, pest forecast and conservation assessment.
Formula: R₀ = Σ lₓ mₓ; T = Σ x lₓ mₓ / R₀; r ≈ ln R₀ / T
Worked examples
| Inputs | Net reproductive rate R₀ | Note |
|---|---|---|
| A growing population | 1.905 | R₀ about 1.7 |
| Declining | 0.76 | R₀ below 1 |
| An insect, weekly classes | 20 | explosive growth |
FAQFrequently asked questions
What is the net reproductive rate?
The average number of offspring — conventionally daughters — an individual produces over its lifetime, allowing for the chance of dying first. Above one the population grows; below one it declines.
What is a life table?
A schedule of survivorship and fecundity by age: the share of a cohort alive at each age and the offspring each produces there. Ecologists build them by following a cohort or from age-structured census data.
What is generation time?
The mean age of the parents of a cohort — the l_x m_x-weighted mean age. Long generation times slow growth even when R₀ is high.
What is r?
The intrinsic rate of increase: the exponential growth rate per unit time. ln R₀ / T is an approximation; the exact value solves the Euler–Lotka equation and is close when growth is modest.
Why daughters only?
Because population growth is limited by females in most species. Using total offspring per individual doubles R₀ but does not change the trend.
Where these figures come from
- NCBI Bookshelf — Molecular Biology of the Cell — growth kinetics and molecular conventions
- National Human Genome Research Institute — the US genomics research institute
Last checked: September 2026. Formulas are the standard textbook forms; assumptions are stated on each page because they are where these models break.