Use this calculator to determine the annual growth rate (CAGR) of a population over a specific period. Below the tool, you will find a detailed guide on how to perform this calculation manually or using Microsoft Excel.
Please enter valid positive numbers for all fields. Starting population cannot be zero.
Annual Growth Rate (CAGR):0.00%
Total % Growth:0.00%
Net Population Increase:0
function calculateGrowth() {
// Get input elements by ID strictly matching HTML
var initialInput = document.getElementById("initialPop");
var finalInput = document.getElementById("finalPop");
var yearsInput = document.getElementById("years");
var errorDiv = document.getElementById("errorMsg");
var resultDiv = document.getElementById("result");
// Parse values
var initial = parseFloat(initialInput.value);
var final = parseFloat(finalInput.value);
var years = parseFloat(yearsInput.value);
// Validation logic
if (isNaN(initial) || isNaN(final) || isNaN(years) || initial <= 0 || years <= 0) {
errorDiv.style.display = "block";
resultDiv.style.display = "none";
return;
}
errorDiv.style.display = "none";
// Calculation Logic
// 1. Net Population Change
var netChange = final – initial;
// 2. Total Percentage Growth
var totalGrowth = (netChange / initial) * 100;
// 3. Annual Growth Rate (CAGR)
// Formula: (Final / Initial)^(1/t) – 1
var growthRatio = final / initial;
var exponent = 1 / years;
var cagrDecimal = Math.pow(growthRatio, exponent) – 1;
var cagrPercent = cagrDecimal * 100;
// Display Results
document.getElementById("cagrResult").innerHTML = cagrPercent.toFixed(2) + "%";
document.getElementById("totalPercentResult").innerHTML = totalGrowth.toFixed(2) + "%";
document.getElementById("numericGrowthResult").innerHTML = netChange.toLocaleString();
resultDiv.style.display = "block";
}
How to Calculate Population Growth Rate in Excel
Calculating population growth is essential for city planners, demographers, and biology students alike. While the calculator above gives you instant results, performing this calculation in Excel allows you to manage large datasets of demographic information efficiently.
The Mathematical Formula
Before jumping into Excel, it is helpful to understand the underlying math. The standard metric for measuring population growth over several years is the Compound Annual Growth Rate (CAGR). This assumes the growth compounds year over year.
The formula is:
Rate = (End_Pop / Start_Pop)(1 / Years) – 1
Step-by-Step Excel Instructions
To calculate this in Excel, you do not need a specialized function. You can create a formula using the caret symbol (^) for exponents. Follow this setup:
Cell
Data Type
Example Value
A2
Starting Population
50000
B2
Ending Population
75000
C2
Number of Years
10
D2
The Formula
Result
The Excel Formula
In cell D2, type the following formula:
=((B2/A2)^(1/C2))-1
Important Formatting Step: By default, Excel might show the result as a decimal (e.g., 0.0413). To see it as a percentage:
Select cell D2.
Press Ctrl + Shift + % (or click the % icon in the Home ribbon).
The result will display as 4.14%.
Alternative: Using the RRI Function
If you have a newer version of Excel (2013 or later), you can use the RRI function, which is specifically designed to calculate the equivalent interest rate (growth rate) for the growth of an investment or population.
=RRI(C2, A2, B2)
Where:
C2 = Number of periods (Years)
A2 = Present Value (Starting Population)
B2 = Future Value (Ending Population)
Understanding the Metrics
When analyzing demographic data, it is crucial to distinguish between different types of growth:
Annual Growth Rate (CAGR): This smooths out the volatility and tells you what the steady growth rate would have been to get from the start point to the end point. This is what our calculator and the Excel formulas above provide.
Absolute Growth: This is simply the ending population minus the starting population.
Natural Increase: This specifically looks at (Births – Deaths), excluding migration. The formulas used here calculate total growth, which includes migration effects.
Example Calculation
Let's say a town had 50,000 residents in 2010 and grew to 75,000 by 2020 (a 10-year span).
Division: 75,000 / 50,000 = 1.5
Exponent: 1 / 10 = 0.1
Power: 1.50.1 ≈ 1.04138
Subtract 1: 1.04138 – 1 = 0.04138
Convert to %: 4.14%
This means the population grew by approximately 4.14% every year during that decade.