Geometric Mean Calculator
Enter a list of positive numbers to calculate their geometric mean — the appropriate type of average for rates of change, growth rates, and ratios, where a simple arithmetic average can be misleading.
How the Geometric Mean formula works
The geometric mean formula:
Geometric mean = (x₁ × x₂ × ... × xₙ)^(1/n)
Step-by-step calculation
- Multiply all the values together.
- Take the nth root of that product, where n is the count of values.
Worked example
Annual growth rates of 1.10, 1.20, and 1.05 (representing 10%, 20%, and 5% growth): Geometric mean = (1.10 × 1.20 × 1.05)^(1/3) ≈ 1.1156, or about 11.56% average annual growth.
Frequently asked questions
Why not just use a regular (arithmetic) average for growth rates?
Arithmetic averages of percentage growth rates overstate actual compound growth, because they don't account for compounding effects across periods. Geometric mean correctly reflects the actual average multiplicative growth rate over time.
Can geometric mean handle negative or zero values?
No — geometric mean requires all positive values, since it involves taking roots of a product; zero or negative numbers make the calculation undefined or nonsensical for this purpose.