The geometric mean is the right average for quantities that multiply: growth rates, investment returns, ratios and index numbers. If an investment grows 10% one year and falls 10% the next, the geometric mean growth factor shows the true average change.
How to use the Geometric Mean Calculator
- Type the numbers separated by commas, spaces or new lines.
- Read the result – it updates as you type.
Results update as you type, and everything is calculated in your browser.
How it works
To avoid overflow with many large numbers, the calculator averages the logarithms and exponentiates. All values must be positive.
What each result means
- Geometric mean = gmean([Values (positive numbers)])
- Arithmetic mean = mean([Values (positive numbers)])
- Harmonic mean = hmean([Values (positive numbers)])
- Number of values = count([Values (positive numbers)])
Formula
GM = (x₁ × x₂ × … × xₙ)¹/n) = exp(mean of ln xᵢ)
Worked example
Inputs — Values (positive numbers): 1.10, 0.90, 1.25, 1.05.
Results — Geometric mean = 1.06766161; Arithmetic mean = 1.075; Harmonic mean = 1.06028152; Number of values = 4.
Key terms
- Geometric mean
- The n-th root of the product of n numbers.
Frequently asked questions
When should I use the geometric mean?
For averaging rates of growth, ratios or numbers on very different scales.
Why must the values be positive?
Roots of negative products are not real, and a zero makes the mean zero.
How do the three means compare?
Harmonic ≤ geometric ≤ arithmetic, with equality only when all values are equal.
How do I average percentage returns?
Convert them to growth factors (1 + r), take the geometric mean and subtract 1.