Population Growth Rate Calculator
How to Calculate Annual Growth Rate of Population
Understanding population dynamics is crucial for city planning, resource allocation, and biological studies. The annual growth rate tells you the average percent by which a population has increased (or decreased) for each year within a specific time period.
Unlike a simple percentage increase, the annual growth rate accounts for the compounding effect—the idea that growth happens on top of the previous year's growth.
The Annual Growth Rate Formula
To find the Compound Annual Growth Rate (CAGR) of a population, we use the following mathematical formula:
Growth Rate = ( ( P_end / P_start ) ^ ( 1 / t ) ) – 1
- P_end: The population at the end of the period.
- P_start: The population at the beginning of the period.
- t: The number of years between the start and end dates.
The result is a decimal, which is then multiplied by 100 to get a percentage.
Step-by-Step Calculation Example
Let's say a small town had a population of 50,000 people in the year 2015. By the year 2020 (5 years later), the population grew to 65,000.
- Determine the ratio: Divide the final population by the initial population.
65,000 / 50,000 = 1.3 - Apply the exponent: Raise this ratio to the power of one divided by the number of years (1/5 = 0.2).
1.3 ^ 0.2 ≈ 1.05387 - Subtract 1:
1.05387 – 1 = 0.05387 - Convert to Percentage: Multiply by 100.
0.05387 * 100 = 5.39%
This means the town's population grew by approximately 5.39% every single year.
Why Not Just Use Simple Percentage?
If you simply took the total growth (15,000) divided by the start (50,000), you get 30% total growth. Dividing that by 5 years gives 6%. However, 6% is inaccurate because it assumes linear growth. Real populations grow exponentially. The compound formula (giving us 5.39%) is more accurate for demographic projections.
Factors Influencing Population Growth
When analyzing these numbers, keep in mind the core components of demographic change:
- Birth Rate: The number of live births per 1,000 people.
- Death Rate: The number of deaths per 1,000 people.
- Net Migration: The difference between immigrants moving in and emigrants moving out.
Please fill in all fields.
";
return;
}
var pStart = parseFloat(startVal);
var pEnd = parseFloat(endVal);
var t = parseFloat(timeVal);
if (pStart <= 0 || t <= 0) {
resultBox.style.display = "block";
resultBox.innerHTML = "Starting population and years must be greater than zero.
";
return;
}
// 1. Calculate Total Numerical Change
var absoluteChange = pEnd – pStart;
// 2. Calculate Total Percentage Change
var totalPercentChange = ((pEnd – pStart) / pStart) * 100;
// 3. Calculate Annual Growth Rate (CAGR Formula)
// Formula: ( (End / Start) ^ (1 / t) ) – 1
var growthRatio = pEnd / pStart;
// Handle negative growth or zero growth correctly
var annualRateDecimal;
if (growthRatio > 0) {
annualRateDecimal = Math.pow(growthRatio, (1 / t)) – 1;
} else {
// Edge case if population drops to 0 or below (unlikely but possible in models)
annualRateDecimal = -1; // -100%
}
var annualRatePercent = annualRateDecimal * 100;
// Formatting Numbers
var formattedAnnual = annualRatePercent.toFixed(2) + "%";
var formattedTotalPct = totalPercentChange.toFixed(2) + "%";
var formattedAbs = Math.round(absoluteChange).toLocaleString();
// Determine descriptive text (Growth or Decline)
var trend = absoluteChange >= 0 ? "Growth" : "Decline";
var colorClass = absoluteChange >= 0 ? "#27ae60" : "#c0392b";
// Build Result HTML
var htmlContent = `
Annual Growth Rate:
${formattedAnnual}
Total Population Change:
${formattedAbs} people
Total Percentage Change:
${formattedTotalPct}
The population ${trend.toLowerCase()}s by an average of ${formattedAnnual} per year.
`;
resultBox.innerHTML = htmlContent;
resultBox.className = "result-box active";
}