Geometric Mean Calculator
Paste positive numbers to get their geometric mean, with the arithmetic and harmonic means for comparison.
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Geometric Mean Calculator by TheCalcTools
How the Geometric Mean Calculator works
Multiply the n values together and take the n-th root. It is the right way to average growth factors: a gain of 10% then a loss of 5% is the same as a constant factor equal to the geometric mean each period.
To average percentage returns, enter them as growth factors: +10% is 1.10 and −5% is 0.95. Subtract 1 from the result to get the average rate. For positive data the geometric mean is never larger than the arithmetic mean.
The formula
Worked example
Using the default values shown in the calculator:
| Positive numbers | 1.10, 0.95, 1.20, 1.05 |
|---|
- Product: 1.10 × 0.95 × 1.20 × 1.05 = 1.3167.
- Fourth root: 1.0712, an average growth of about 4.9% per period.
Result:
| Geometric mean | 1.0712 |
|---|---|
| Arithmetic mean | 1.0750 |
| Harmonic mean | 1.0674 |
| Product of the values | 1.3167 |
Frequently asked questions
Why not just average the returns?
Returns compound. +50% then −50% averages 0% arithmetically, but you end with 75% of your money. The geometric mean, √(1.5 × 0.5) ≈ 0.866, shows a loss of about 13.4% per period.
Can I use negative numbers?
No. Convert returns to growth factors (1 + r) first, which are positive unless you lost everything.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.