Geometric Mean Growth Rate Calculator
Calculate the average compounded growth rate over specific periods.
What is Geometric Mean Growth Rate?
The Geometric Mean Growth Rate (GMGR) represents the average rate of return of a set of values calculated using the products of the terms. In finance and business, it is most commonly known as the Compounded Annual Growth Rate (CAGR) when applied to annual data.
Unlike the Arithmetic Mean (simple average), which can be misleading when calculating growth rates over time due to the effects of compounding and volatility, the Geometric Mean provides a "smoothed" annual rate. It answers the question: "What constant growth rate would take me from the starting value to the ending value over this time period?"
The Formula
The calculator uses the standard formula for compounded growth over $n$ periods:
Where:
- Ending Value: The value at the end of the period.
- Beginning Value: The value at the start of the period.
- n: The number of periods (typically years).
Example Calculation
Imagine a company's revenue grew from $100,000 to $180,000 over 4 years.
Step 1: Divide End by Start: $180,000 / 100,000 = 1.8$
Step 2: Raise to the power of (1/4): $1.8^{(0.25)} \approx 1.158$
Step 3: Subtract 1: $1.158 – 1 = 0.158$
Result: The Geometric Mean Growth Rate is 15.8%.
If you had used a simple arithmetic average, you might simply calculate the total growth (80%) and divide by 4 to get 20%, which significantly overstates the actual compounded performance. This is why the Geometric Mean is the gold standard for investment performance and long-term business metrics.
When to Use This Calculator
This tool is essential for:
- Investment Analysis: Comparing the historical performance of different funds or stocks.
- Business Metrics: Tracking revenue, user base, or profit growth over multiple years.
- Economics: Analyzing GDP or population growth rates.