function calculateGrowthRate() {
var start = parseFloat(document.getElementById('initialValue').value);
var end = parseFloat(document.getElementById('finalValue').value);
var n = parseFloat(document.getElementById('timePeriods').value);
var resultBox = document.getElementById('growthResultBox');
var rateDisplay = document.getElementById('growthRateResult');
var totalDisplay = document.getElementById('totalGrowthResult');
if (isNaN(start) || isNaN(end) || isNaN(n) || start <= 0 || n <= 0) {
alert("Please enter valid positive numbers. The initial value and number of intervals must be greater than zero.");
return;
}
// CAGR Formula: [(End/Start)^(1/n)] – 1
var periodicRate = (Math.pow((end / start), (1 / n)) – 1) * 100;
var totalGrowth = ((end – start) / start) * 100;
rateDisplay.innerHTML = periodicRate.toFixed(2) + "%";
totalDisplay.innerHTML = "Total cumulative growth over " + n + " intervals: " + totalGrowth.toFixed(2) + "%";
resultBox.style.display = 'block';
}
Understanding Average Growth Rate
Calculating the average growth rate over regular time intervals is essential for understanding performance trends in business, population studies, or investment portfolios. Unlike a simple arithmetic average, the Compound Annual Growth Rate (CAGR) provides a smoothed representation of growth, accounting for the effects of compounding over time.
The Formula for Average Growth Rate
To find the geometric average growth rate (CAGR), we use the following mathematical formula:
Rate = [(Final Value / Initial Value) ^ (1 / Number of Intervals)] – 1
This formula determines the constant rate at which an amount would have grown if it had grown at a steady rate each year (or month) during the specified period.
Why Use Geometric Mean Instead of Arithmetic Mean?
If you simply average the percentage changes from year to year, you may get a distorted view of actual progress. For example, if a value drops by 50% and then grows by 50%, an arithmetic average suggests 0% growth, but you actually have 25% less than you started with. The average growth rate calculation used here correctly accounts for these fluctuations.
Step-by-Step Example
Step
Description
Example Calculation
1. Identify Start & End
Define your beginning and ending data points.
Start: 1,000 | End: 2,500
2. Count Intervals
Determine the number of regular time steps (e.g., 4 years).
n = 4
3. Divide and Power
Divide final by initial, then raise to the power of (1/n).
(2,500 / 1,000) ^ (1/4) = 1.2589
4. Final Percentage
Subtract 1 and multiply by 100.
(1.2589 – 1) * 100 = 25.89%
Practical Applications
Business Revenue: Assessing how quickly a company is expanding its sales year-over-year.
User Growth: Measuring the increase in active users for a software platform over several months.
Inventory Levels: Tracking the rate of stock accumulation or depletion over fiscal quarters.
Demographics: Analyzing population changes in a specific region over decades.
Interpreting the Results
A positive average growth rate indicates an upward trend, while a negative rate signifies a decline. It is important to remember that this calculator assumes "regular intervals." If your time steps are inconsistent (e.g., 3 months then 6 months), you must first normalize the intervals to a standard unit before using this specific logic.