Please enter valid numeric values for all fields. Initial value must be greater than zero and days must be positive.
Absolute Return (Total ROI):0.00%
Annualized Rate of Return:0.00%
Compound Annual Growth Rate (CAGR):0.00%
How to Calculate Annualized Rate of Return
Understanding the performance of an investment is crucial for making informed financial decisions. While calculating a simple total return tells you how much money you made in absolute terms, it fails to account for the most critical factor in investing: time. The Annualized Rate of Return (often synonymous with CAGR in multi-year contexts) solves this by standardizing your returns to a yearly basis.
Why Annualization Matters
Imagine two investments:
Investment A returns 20% over 5 years.
Investment B returns 20% over 6 months.
While the total return (ROI) is identical (20%), Investment B is significantly superior because it generated that return much faster. The Annualized Rate Calculator allows you to compare these two investments "apples-to-apples" by expressing their performance as if it occurred over a standard one-year period.
The Formula
The calculation for the annualized rate of return uses the following geometric average formula:
Annualized Rate = ((Ending Value / Beginning Value) ^ (365 / Days Held)) – 1
This formula accounts for compounding, assuming that the gains are reinvested at the same rate over the standardized year.
Example Calculation
Let's say you purchased a stock for $10,000 (Beginning Value) and sold it 450 days later for $12,500 (Ending Value).
Calculate the ratio: 12,500 / 10,000 = 1.25
Calculate the time exponent: 365 / 450 = 0.8111
Apply the exponent: 1.25 ^ 0.8111 = 1.198
Subtract 1 and convert to percentage: (1.198 – 1) * 100 = 19.8%
Even though your total gain was 25%, your annualized rate is roughly 19.8% because it took longer than a year to achieve that gain.
Key Considerations
Short-term Extrapolation: Be cautious when annualizing returns for periods shorter than one year (e.g., a 10% gain in one month annualized to over 200%). This assumes you can repeat that performance every month for a year, which is often unrealistic.
Negative Returns: This calculator also works for losses. If the ending value is lower than the beginning value, the annualized rate will show the yearly rate of decline.
function calculateAnnualizedRate() {
// Get input values
var startVal = parseFloat(document.getElementById('initialValue').value);
var endVal = parseFloat(document.getElementById('finalValue').value);
var days = parseFloat(document.getElementById('holdingDays').value);
// Get UI elements
var errorDiv = document.getElementById('arcError');
var resultsDiv = document.getElementById('arcResults');
var totalRoiDisplay = document.getElementById('totalRoiResult');
var annualRateDisplay = document.getElementById('annualizedRateResult');
var cagrDisplay = document.getElementById('cagrResult');
// Validation logic
if (isNaN(startVal) || isNaN(endVal) || isNaN(days)) {
errorDiv.style.display = 'block';
resultsDiv.style.display = 'none';
return;
}
if (startVal <= 0 || days <= 0) {
errorDiv.style.display = 'block';
errorDiv.innerHTML = "Beginning value must be greater than zero and days held must be positive.";
resultsDiv.style.display = 'none';
return;
}
// Hide error if valid
errorDiv.style.display = 'none';
// 1. Calculate Absolute Return (Total ROI)
// Formula: (End – Start) / Start
var absoluteReturnDecimal = (endVal – startVal) / startVal;
var absoluteReturnPercent = absoluteReturnDecimal * 100;
// 2. Calculate Annualized Rate
// Formula: ((End / Start) ^ (365 / Days)) – 1
// Use Math.pow(base, exponent)
var ratio = endVal / startVal;
var exponent = 365.0 / days;
var annualizedDecimal = Math.pow(ratio, exponent) – 1;
var annualizedPercent = annualizedDecimal * 100;
// Display Results
// We use toFixed(2) for standard financial precision
totalRoiDisplay.innerHTML = absoluteReturnPercent.toFixed(2) + "%";
annualRateDisplay.innerHTML = annualizedPercent.toFixed(2) + "%";
// CAGR is mathematically the same as Annualized Return for the specific period,
// but labeling it clarifies for users looking for that term.
cagrDisplay.innerHTML = annualizedPercent.toFixed(2) + "%";
// Show results container
resultsDiv.style.display = 'block';
}