Geometric Mean Calculator
GM = (x₁ · x₂ · ... · xₙ)^(1/n). Right "average" for ratios, growth rates, multiplicative quantities.
Result
Geometric mean
1.058253
Arithmetic mean (for comparison): 1.060000.
- n5
- GM1.058253
- AM1.060000
- GM ≤ AM (always)Confirmed
Step-by-step
- Use log form for numerical stability: GM = exp((log x₁ + log x₂ + … + log xₙ) / n).
- Sum of logs / n = 0.056619.
- GM = exp(0.056619) = 1.058253.
How to use this calculator
- Enter positive numbers (the calculator rejects zero or negative).
- Read GM and compare to AM.
About this calculator
The geometric mean is the right average for multiplicative quantities — investment returns, growth rates, or ratios. For a sequence of growth multipliers, GM gives the constant rate that would produce the same total growth. AM-GM inequality: GM ≤ AM, with equality only when all values are equal.
Frequently asked
For ratios, growth multipliers, percentages of change. If you grew 50% one year and 50% the next, the average growth isn't 50% (=AM); it's ~22.5% (=GM of 1.5 and 1.5 minus 1, sort of).
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