Geometric Mean Calculator – Growth Rates

The geometric mean multiplies the values and takes the n-th root, which is the correct average for factors applied in sequence. For 4 and 9: √(36) = 6, sitting between the two as every mean should. For investment growth of +10%, +20% and +30% across three years, the multipliers 1.1, 1.2, 1.3 multiply to 1.716, and the cube root gives ≈ 1.1972 — a steady 19.72% per year would land on the same final value (1.1972³ ≈ 1.716). The calculator shows the product, the root, and the equivalent steady rate, and contrasts the arithmetic mean (1.2, which would claim 20% and overshoot the true return). It requires positive inputs — the even root of a negative product does not exist — and it links to log-space averaging: GM = exp(mean of ln x), the method spreadsheets use.

1. 1

   Enter positive values

   Growth multipliers like 1.1, 1.2, 1.3 — or plain numbers

2. 2

   Multiply them all

   The running product is displayed

3. 3

   Take the n-th root

   ⁿ√(product) is the geometric mean

4. 4

   Read the steady rate

   Subtract 1 for the average growth per period

• 1

  Multiplicative data (rates, ratios) needs the geometric mean

• 2

  GM of 4 and 9 is 6; arithmetic would say 6.5 and overshoot

• 3

  Log shortcut: GM = exp( average of ln x )

• Averaging percentage returns arithmetically: +50% then −50% leaves GM = √(1.5×0.5) ≈ 0.866, a 13.4% loss

• Including zero or negative multipliers, which kills the root

• Forgetting to subtract 1: GM 1.1972 means 19.72% growth, not 119.72

• Mixing periods (monthly and yearly factors) in one product