Calculate the average number of daughters per woman accounting for mortality.
Age Group
Survivorship Probability ($l_x$) (0.0 to 1.0)
Annual Fertility Rate ($m_x$) (Daughters per woman per year)
15-19
20-24
25-29
30-34
35-39
40-44
45-49
Calculated Net Reproductive Rate ($R_0$)
0.00
Understanding Net Reproductive Rate (NRR)
The Net Reproductive Rate (NRR), often denoted as $R_0$, is a critical demographic metric used to measure the rate at which a cohort of females replaces itself in the next generation. Unlike the Gross Reproduction Rate (GRR), which assumes all women survive to the end of their childbearing years, the NRR accounts for **mortality**.
It represents the average number of daughters that would be born to a female (or a group of females) if she passed through her lifetime conforming to the age-specific fertility and mortality rates of a given year.
The Calculation Formula
The NRR is calculated using the summation of the product of survivorship and fertility for each age group. The simplified discrete formula used in this calculator is:
NRR = Σ ( n × l_x × m_x )
Where:
n: The width of the age interval (5 years in this standard model).
l_x: The probability of surviving from birth to the midpoint of age group $x$.
m_x: The annual age-specific fertility rate (daughters born per woman) for age group $x$.
Interpreting the Result
The value of the NRR indicates the future growth potential of a population:
NRR = 1 (Replacement Level): Each woman is replacing herself with exactly one surviving daughter. The population will remain constant in the long run.
NRR > 1 (Growing Population): Each woman is replaced by more than one surviving daughter. The population will grow over time.
NRR < 1 (Declining Population): Women are not replacing themselves sufficiently. The population will eventually decline unless offset by migration.
NRR vs. GRR
The Gross Reproduction Rate (GRR) is simply the NRR calculated assuming 100% survival (no mortality). Therefore, the NRR is always lower than or equal to the GRR. In countries with high mortality rates among young women, the gap between GRR and NRR is significant, indicating that fertility must be higher to achieve replacement levels.
Why "Daughters"?
Demographers focus on daughters because they are the potential mothers of future generations. Calculating total children would require adjusting for the sex ratio at birth. This calculator requires the fertility rate specifically for female births (daughters). If you only have the total fertility rate, a common approximation is to multiply the total rate by roughly 0.488 (assuming a sex ratio at birth of 1.05 boys per 1 girl).
function calculateNRR() {
// Define the age groups start indices
var ageStarts = [15, 20, 25, 30, 35, 40, 45];
var intervalWidth = 5; // Standard 5-year demographic cohorts
var totalNRR = 0;
var hasData = false;
// Loop through each age group input
for (var i = 0; i 1.05) {
interpretationDisplay.className = "result-status status-growth";
interpretationDisplay.innerText = "Population Growing";
summaryDisplay.innerText = "The NRR is greater than 1. This indicates that the generation of daughters is larger than the generation of mothers, leading to population growth.";
} else if (totalNRR < 0.95) {
interpretationDisplay.className = "result-status status-decline";
interpretationDisplay.innerText = "Population Declining";
summaryDisplay.innerText = "The NRR is less than 1. This indicates that the generation of daughters is smaller than the generation of mothers, leading to population decline.";
} else {
interpretationDisplay.className = "result-status status-stable";
interpretationDisplay.innerText = "Replacement Level (Stable)";
summaryDisplay.innerText = "The NRR is approximately 1. The population is replacing itself exactly, leading to population stability.";
}
}
function clearNRR() {
var ageStarts = [15, 20, 25, 30, 35, 40, 45];
for (var i = 0; i < ageStarts.length; i++) {
var idSuffix = ageStarts[i];
document.getElementById('lx_' + idSuffix).value = '';
document.getElementById('mx_' + idSuffix).value = '';
}
document.getElementById('resultBox').style.display = 'none';
}