Geometric Mean Calculator
Calculate the geometric mean of up to 8 positive growth factors, giving the equivalent constant compound growth rate.
Only the first this-many values below are included, e.g. yearly growth multipliers.
Your results
Calculation breakdown
- Geometric mean
- GM = ⁿ√(x₁ × x₂ × ... × xₙ) = exp(average of ln(xᵢ))
Worked example
An investment returns growth factors of 1.05, 1.08, 0.97 and 1.12 over four years (5%, 8%, −3% and 12%). The geometric mean of about 1.0546 shows an equivalent average annual growth rate of roughly 5.46%.
Assumptions
- Best used for growth rates, ratios or index values expressed as multiplying factors (e.g. 1.05 for +5%), not raw negative or zero-containing data.
- The geometric mean is always less than or equal to the arithmetic mean for the same positive dataset.
How this calculator works
Enter up to 8 positive values, typically growth factors like 1.05 for a 5% increase. The calculator returns the geometric mean and the equivalent compound growth rate, alongside the simple arithmetic mean for comparison.
Frequently asked questions
Why use a geometric mean instead of a simple average for growth rates?
The geometric mean correctly accounts for compounding across periods, while a simple average of percentage changes can overstate true growth.
Can I enter negative numbers or zero?
No, the geometric mean is undefined for zero or negative values; enter growth factors (like 1.05 or 0.97) instead of raw percentage changes if a period had a loss.
Is the geometric mean always smaller than the arithmetic mean?
For any set of positive numbers that aren't all identical, yes — the geometric mean is always less than or equal to the arithmetic mean.