Geometric Mean Calculator
Calculate the geometric mean of positive datasets—the nth root of the product of n values. Essential for compounding growth rates, financial portfolio returns, and proportional scaling factors.
List of strictly positive numbers separated by commas or spaces
Nth root of the product of all positive values
How to Use This Calculator
- Enter positive numbers separated by commas or spaces.
- Inspect the calculated geometric mean.
- Compare with the arithmetic mean to observe the AM-GM gap.
Formula & Calculation Methodology
The geometric mean multiplies all n values together and takes their nth root. Logarithmic transformation prevents numerical floating overflow.
Worked Example
Evaluating 2, 8, 32 (Product = 512, n = 3)
Evaluating investment multipliers 1.10, 1.20, 0.90
Frequently Asked Questions
Why must geometric mean inputs be strictly positive?↓
Zero forces the product to 0, rendering the calculation meaningless. Negative numbers can lead to imaginary roots when n is even.
What is the AM-GM Inequality?↓
The Arithmetic Mean is always greater than or equal to the Geometric Mean (AM ≥ GM). They are equal if and only if all numbers in the sample are identical.
Why is geometric mean used for investment returns instead of arithmetic mean?↓
Compound interest multiplies wealth over time. A 100% gain followed by a 50% loss yields an arithmetic average of +25%, but the true wealth change is 0% (GM = 1.0).
What is a limitation of the geometric mean?↓
It cannot accommodate datasets containing zero or negative numbers without artificial shifting or offsets.
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Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.