How to Calculate a Growth Rate
Understanding growth rates is fundamental in business, economics, and personal finance. Whether you are tracking the increase in your website traffic, the revenue of a startup, or the growth of a plant, the math remains consistent.
1. The Basic Growth Rate Formula
The standard growth rate (percentage change) calculates the difference between two values as a percentage of the initial value. This is best used for single-period comparisons.
Growth Rate = ((Final Value – Initial Value) / Initial Value) × 100
2. Compound Annual Growth Rate (CAGR)
If you are looking at growth over several years, the total growth percentage can be misleading due to the effects of compounding. CAGR provides a smoothed annual rate that represents the geometric progression of growth over time.
CAGR = [(Final Value / Initial Value)^(1 / Number of Periods)] – 1
Practical Example
Imagine your business had 10,000 subscribers at the start of year 1 and grew to 25,000 subscribers by the end of year 3 (a 2-year period).
- Total Growth: ((25,000 – 10,000) / 10,000) = 150% total increase.
- CAGR: [(25,000 / 10,000)^(1/2)] – 1 = 58.11% average annual growth.
Why Track Growth?
Growth rates allow for "apples-to-apples" comparisons between different entities. A company growing by 5,000 units might seem successful, but if they started with 1,000,000 units, their growth rate is only 0.5%. Conversely, a company growing by 5,000 units starting from 5,000 units has a 100% growth rate, indicating much higher momentum.
function calculateStandardGrowth() {
var start = parseFloat(document.getElementById('startValue').value);
var end = parseFloat(document.getElementById('endValue').value);
var display = document.getElementById('growthResultDisplay');
var resultText = document.getElementById('resultText');
var detailText = document.getElementById('detailText');
var resultTitle = document.getElementById('resultTitle');
if (isNaN(start) || isNaN(end) || start === 0) {
alert("Please enter valid numbers. Initial value cannot be zero.");
return;
}
var growth = ((end – start) / start) * 100;
var difference = end – start;
display.style.display = 'block';
display.style.borderColor = '#27ae60';
resultTitle.innerText = "Total Growth Rate";
resultText.innerText = growth.toFixed(2) + "%";
resultText.style.color = growth >= 0 ? "#27ae60" : "#e74c3c";
detailText.innerText = "The value " + (growth >= 0 ? "increased" : "decreased") + " by " + Math.abs(difference).toLocaleString() + " units from the initial starting point.";
}
function calculateCAGR() {
var start = parseFloat(document.getElementById('startValue').value);
var end = parseFloat(document.getElementById('endValue').value);
var periods = parseFloat(document.getElementById('periods').value);
var display = document.getElementById('growthResultDisplay');
var resultText = document.getElementById('resultText');
var detailText = document.getElementById('detailText');
var resultTitle = document.getElementById('resultTitle');
if (isNaN(start) || isNaN(end) || isNaN(periods) || start <= 0 || end <= 0 || periods <= 0) {
alert("For CAGR, please enter positive numbers for all fields. Initial and Final values must be greater than zero.");
return;
}
var cagr = (Math.pow((end / start), (1 / periods)) – 1) * 100;
display.style.display = 'block';
display.style.borderColor = '#2980b9';
resultTitle.innerText = "Annual Growth (CAGR)";
resultText.innerText = cagr.toFixed(2) + "% per period";
resultText.style.color = "#2980b9";
detailText.innerText = "Over " + periods + " periods, your value grew at a compounded annual rate of " + cagr.toFixed(2) + "%.";
}