function calculateGrowth() {
// Clear errors
document.getElementById('startError').style.display = 'none';
document.getElementById('endError').style.display = 'none';
document.getElementById('periodError').style.display = 'none';
document.getElementById('calcResult').style.display = 'none';
// Get values
var startValue = parseFloat(document.getElementById('startVal').value);
var endValue = parseFloat(document.getElementById('endVal').value);
var years = parseFloat(document.getElementById('timePeriod').value);
var hasError = false;
// Validation
if (isNaN(startValue) || startValue === 0) {
document.getElementById('startError').style.display = 'block';
hasError = true;
}
if (isNaN(endValue)) {
document.getElementById('endError').style.display = 'block';
hasError = true;
}
if (isNaN(years) || years <= 0) {
document.getElementById('periodError').style.display = 'block';
hasError = true;
}
if (hasError) return;
// Formula: (Ending / Beginning)^(1/n) – 1
var growthRatio = endValue / startValue;
// Handle negative growth base scenarios if needed, but standard CAGR assumes positive start
if (growthRatio <= 0) {
alert("The ratio of Ending Value to Beginning Value must be positive to calculate a standard annual growth rate.");
return;
}
var exponent = 1 / years;
var cagrDecimal = Math.pow(growthRatio, exponent) – 1;
var cagrPercentage = cagrDecimal * 100;
// Formating
var formattedPercentage = cagrPercentage.toFixed(2) + "%";
var totalGrowth = ((endValue – startValue) / startValue) * 100;
// Update DOM
document.getElementById('resultPercentage').innerHTML = formattedPercentage;
document.getElementById('resultExplanation').innerHTML =
"Over " + years + " years, the value grew from " + startValue.toLocaleString() +
" to " + endValue.toLocaleString() + "." +
"Total absolute growth: " + totalGrowth.toFixed(2) + "%.";
document.getElementById('calcResult').style.display = 'block';
}
Understanding Expected Annual Growth Rate
The Expected Annual Growth Rate, often referred to in finance and statistics as the Compound Annual Growth Rate (CAGR), provides a smoothed representation of growth over a specific period. Unlike a simple average, which can be misleading due to volatility, this metric assumes the investment or value grew at a steady rate every single year to reach the final figure.
The Growth Formula
To calculate the annual growth rate, we use the following mathematical formula:
Ending Value: The value of the asset or metric at the end of the period.
Beginning Value: The initial value at the start of the period.
n: The number of years or periods over which the growth occurred.
Why Use This Calculator?
Calculating expected growth is crucial for performance analysis in various fields:
Investment Analysis: Determine the true annual return of a portfolio that fluctuates in value.
Business Planning: Analyze revenue or user base growth to forecast future trends.
Population Studies: Estimate the annual percentage increase in demographic data.
Example Calculation
Suppose a company had a revenue of 50,000 in Year 1 (Beginning Value) and it grew to 85,000 by Year 4 (Ending Value). The time period is 3 years (Year 4 minus Year 1).
Applying the formula:
Divide Ending by Beginning: 85,000 / 50,000 = 1.7
Raise to power of (1/3): 1.70.3333 ≈ 1.1935
Subtract 1: 1.1935 – 1 = 0.1935
Convert to Percentage: 19.35%
This means the company grew at an effective rate of 19.35% per year.
Frequently Asked Questions
Can the Annual Growth Rate be negative?
Yes. If the Ending Value is lower than the Beginning Value, the calculation will result in a negative percentage, indicating an annual rate of decline.
How is this different from Average Annual Growth Rate (AAGR)?
AAGR is the arithmetic mean of a series of growth rates. It does not account for the compounding effect. The metric calculated here (CAGR) is geometric and is generally considered more accurate for measuring returns over time because it links the beginning and ending values directly.