Numbers, Units & Calculators
Geometric Mean Calculator
Calculate the geometric mean of positive numbers using logarithms. Enter values and inspect the result without multiplying large inputs directly.
The geometric mean of n positive values is the nth root of their product: (x₁ × x₂ × … × xₙ)^(1/n). For 2 and 8, the product is 16 and the square root is 4. Use it for growth factors, ratios, and other values that combine by multiplication.
The result is JSON with two fields: geometricMean, the calculated mean, and count, the number of values read.
- Find the average annual growth rate from yearly growth factors.
- Average ratios or index values, such as benchmark speed-ups, without letting one large ratio dominate.
- Compare the geometric and arithmetic means of the same positive data. The geometric mean is never larger.
Instructions
- Enter positive values separated by commas, spaces, semicolons, or line breaks.
- For percentage changes, enter growth factors: +10% is 1.10, and -5% is 0.95.
- Select Calculate and check that count matches the number of values you entered.
- Subtract 1 from a geometric mean of growth factors to read the average change per period.
Example
Input: 1.10, 0.95, 1.20
Settings: Growth factors for +10%, -5%, and +20% over three years.
Result: geometricMean 1.078365153390936; count 3.
The product is 1.10 × 0.95 × 1.20 = 1.254, and its cube root is about 1.0784. The average growth is 7.84% per year, not the arithmetic 8.33%.
Limits
- Enter up to 1000 values, each between 1e-100 and 1e100. Percent signs and fractions such as 1/2 are rejected.
- Zero and negative values are rejected. A -100% change has growth factor 0, so this calculator cannot average it.
- A comma inside a number splits it. 1,000 is read as 1 and 000, and the zero causes an error.
- The calculator averages logarithms, so results carry tiny floating-point errors. 1e100 and 1e100 give 1.000000000000011e+100.