The geometric mean is the mathematically rigorous average for anything that compounds — investment returns, ratios, and growth rates.
The geometric mean formula
Instead of adding the numbers, you multiply all of them together, and then calculate the n-th root (where n is the quantity of numbers).
Geometric Mean = (x₁ × x₂ × ... × xₙ)^(1/n)
The classic investment trap of the arithmetic mean
Imagine you invest $10,000 in a stock portfolio. In Year 1, your portfolio gains +50%. Your balance rises to $15,000.
In Year 2, the market crashes and your portfolio drops by -50%. Half of $15,000 is lost, leaving you with $7,500.
If an advisor calculated the arithmetic mean of returns: (+50% + -50%) ÷ 2 = 0% average return. But in reality, you did not break even — you lost $2,500 (a 25% net capital loss)!
To calculate the geometric mean of growth multipliers: Year 1 multiplier is 1.50, Year 2 is 0.50.
Geometric Mean = √(1.50 × 0.50) = √0.75 ≈ 0.8660. Subtracting 1 gives -13.4% compound annual growth rate per year, reflecting the genuine financial reality.
Key limitations
This calculator requires strictly positive inputs. Some mathematical definitions allow zero, giving a geometric mean of zero, but signed data requires special care. Convert percentage returns to positive growth factors before using this tool.
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