Geometric mean calculator

The geometric mean is the nth root of the product: GM = (x₁ · x₂ · … · xₙ)1/n. It's the right average for quantities that multiply, like growth rates and interest — so for multi-year returns, use the geometric, not the arithmetic mean.

The error this prevents

An investment gains 100% one year and loses 50% the next. The arithmetic mean of those returns is +25% a year — a figure that turns up in marketing material. The real result is zero: $100 becomes $200 and returns to $100. The geometric mean gives exactly that: √(2.00 × 0.50) = 1.00, or 0% a year.

Working with negative returns

The geometric mean cannot take a negative value directly — the root of a negative product is not real. So with returns you work with growth factors (1 + return): a 20% loss becomes 0.80, not −0.20. Multiply the factors, take the nth root, then subtract 1 to get back to a percentage.

Where it also applies

Anywhere values chain by multiplication: accumulated inflation, population growth, bacterial counts, and index construction. It is also the correct average for ratios expressed on different scales — which is why composite indices built from normalised indicators use it rather than a simple mean.