Average Percentage Growth Calculator

Geometric Average Growth Formula:

\[ \text{Avg Growth %} = \left[ \prod_{i=1}^{n} (1 + r_i) \right]^{1/n} - 1 \times 100 \]

Average Growth Percentage:

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1. What is Average Percentage Growth?

The Average Percentage Growth calculates the geometric mean of multiple growth rates, providing a more accurate representation of compound growth over time compared to simple arithmetic average.

2. How Does the Calculator Work?

The calculator uses the geometric average formula:

\[ \text{Avg Growth %} = \left[ \prod_{i=1}^{n} (1 + r_i) \right]^{1/n} - 1 \times 100 \]

Where:

\( r_i \) — Individual growth rates (as percentages)
\( n \) — Number of periods
\( \prod \) — Product of all terms

Explanation: The formula calculates the constant growth rate that would yield the same final value as the actual varying growth rates over the same period.

3. Importance of Geometric Average

Details: Geometric average accounts for compounding effects and is essential for accurate financial analysis, investment returns, and business growth measurements where percentages compound over time.

4. Using the Calculator

Tips: Enter growth rates as percentages separated by commas. Positive values indicate growth, negative values indicate decline. At least one valid growth rate is required.

5. Frequently Asked Questions (FAQ)

Q1: Why use geometric average instead of arithmetic average?
A: Geometric average accounts for compounding effects, making it more accurate for growth rates over multiple periods. Arithmetic average overstates actual growth.

Q2: When should I use this calculator?
A: Use for investment returns, revenue growth, population growth, or any scenario where you need to find the average compound growth rate over multiple periods.

Q3: How do negative growth rates affect the calculation?
A: Negative rates are handled correctly in the geometric mean calculation. A mix of positive and negative rates will give an accurate average growth.

Q4: What's the difference between CAGR and this calculation?
A: This calculates average growth from multiple period rates, while CAGR calculates the rate from beginning and ending values over a time period.

Q5: Can I use this for monthly or daily growth rates?
A: Yes, the calculator works with growth rates of any time period as long as they're consistent (all monthly, all yearly, etc.).