About the Geometric Mean Calculator

The geometric mean multiplies n values and takes the nth root, where the arithmetic mean adds and divides. For the pair 2 and 8, the geometric mean is √16 = 4 — the "fair middle" for multiplicative quantities. It is always less than or equal to the arithmetic mean, equal only when every value is identical.

Where it is indispensable

Any quantity that compounds over time averages geometrically, not arithmetically. A portfolio returning +50% then −50% has an arithmetic average of +0% but an actual result of −25% — the geometric mean correctly reports −13.4% per period. The same logic governs inflation, population growth, currency exchange, and lens aperture scales, which is why the geometric mean is the default for ratios.