How to Calculate Historical Growth Rate

Historical Growth Rate (CAGR) Calculator

Calculation Results:

Compound Annual Growth Rate (CAGR):

Total Absolute Growth:

function calculateGrowth() { var startVal = parseFloat(document.getElementById("beginningValue").value); var endVal = parseFloat(document.getElementById("endingValue").value); var years = parseFloat(document.getElementById("numYears").value); var resultDiv = document.getElementById("resultDisplay"); if (isNaN(startVal) || isNaN(endVal) || isNaN(years) || startVal <= 0 || years <= 0) { alert("Please enter valid positive numbers. The beginning value and periods must be greater than zero."); return; } // CAGR Formula: [(Ending Value / Beginning Value) ^ (1 / Number of Years)] – 1 var cagr = (Math.pow((endVal / startVal), (1 / years)) – 1) * 100; // Total Growth Formula: ((Ending Value – Beginning Value) / Beginning Value) * 100 var totalGrowth = ((endVal – startVal) / startVal) * 100; document.getElementById("cagrResult").innerText = cagr.toFixed(2) + "% per period"; document.getElementById("totalGrowthResult").innerText = totalGrowth.toFixed(2) + "% total"; resultDiv.style.display = "block"; }

---

Understanding Historical Growth Rate

Historical growth rate is a critical metric used by investors, business owners, and analysts to determine how much a specific metric—such as revenue, earnings, or an investment portfolio—has grown over a set period of time. Unlike simple average growth, the historical growth rate is most commonly expressed as the Compound Annual Growth Rate (CAGR).

The CAGR Formula

The mathematical formula for calculating the historical compound growth rate is:

CAGR = [(Ending Value / Beginning Value)^{(1 / n)}] – 1

Where n represents the number of years or periods between the start and end dates.

Why Use Historical Growth Rate Instead of Average Growth?

Simple averages can be misleading when dealing with volatile numbers. For example, if an investment grows 100% in year one and drops 50% in year two, you are back to your original amount (0% total growth). However, the arithmetic average would suggest a 25% growth rate ((100 – 50) / 2). The CAGR correctly identifies the growth as 0%.

Real-World Example

Imagine you invested in a technology company five years ago. Your initial investment was 10,000. Today, that investment is worth 18,500. To find the historical growth rate:

• Beginning Value: 10,000
• Ending Value: 18,500
• Number of Years: 5

Using the calculator above, you would find that your investment had a CAGR of 13.10%. This means that, on average, your money grew by 13.10% every single year for five years.

Key Factors to Consider

1. Smoothing Volatility: CAGR provides a "smoothed" rate of return, ignoring the ups and downs of individual years.
2. Time Sensitivity: The longer the time period, the more "diluted" a single year's massive gain or loss becomes.
3. External Contributions: This calculation assumes no additional capital was added or withdrawn during the period. If you added money halfway through, a more complex "Internal Rate of Return" (IRR) calculation would be required.