How to Calculate Geometric Mean Growth Rate

Geometric Mean Growth Rate Calculator

Calculate the compounding growth rate over N periods.

How to Calculate Geometric Mean Growth Rate

The Geometric Mean Growth Rate (often referred to as CAGR in finance) is a measure used to determine the average growth rate of an investment or metric over multiple time periods. Unlike the arithmetic mean, which simply averages the periodic rates, the geometric mean accounts for the compounding effect of growth.

The Formula

To calculate the geometric mean growth rate based on the start and end values of a series, use the following formula:

Rate = (Ending Value / Beginning Value)^{(1 / n)} – 1

Where:

• Ending Value: The value at the end of the period.
• Beginning Value: The value at the start of the period.
• n: The total number of periods (usually years, months, or quarters).

Example Calculation

Suppose a company's revenue grew from 100 units to 180 units over 4 years. To find the geometric mean growth rate:

1. Divide Ending Value by Beginning Value: 180 / 100 = 1.8
2. Calculate the exponent (1/n): 1 / 4 = 0.25
3. Raise the result to the exponent: 1.8^0.25 ≈ 1.1583
4. Subtract 1: 1.1583 – 1 = 0.1583
5. Convert to percentage: 0.1583 * 100 = 15.83%

This means the revenue grew at a compounded annual rate of 15.83%.

Why use Geometric Mean instead of Arithmetic Mean?

The arithmetic mean (simple average) tends to overestimate growth when rates fluctuate significantly. The geometric mean provides a more accurate representation of the actual return or growth over time because it assumes the gains are reinvested (compounded). It smoothes out the volatility of the interim periods to show the steady rate required to get from the beginning value to the ending value.

' + s + '

' + e + '

' + n + '

' + formattedRate + '