Geometric Mean Calculator
The average that fits growth rates, ratios, and compounding better than the everyday mean — paste your positive numbers and get it instantly.
How it works
The geometric mean multiplies all your values together and takes the nth root, where n is how many numbers you have. Under the hood we sum the natural logs and exponentiate the average — same result, but it stays stable even when the product would be huge.
It shines whenever things multiply rather than add: investment returns, population growth, price ratios. Because it accounts for compounding, it never overstates an average the way the plain arithmetic mean can when values swing.
Take 2, 8, 32, 4, and 1.5. Their product is 3,072, and the fifth root of 3,072 is about 4.97 — the single factor that, applied five times, matches the combined effect of the whole list.
Frequently asked questions
When should I use the geometric mean instead of the regular average?
Reach for it when your numbers represent rates of change or things that multiply — annual returns, growth percentages, scaling factors. In those cases the arithmetic mean overstates the true average, while the geometric mean reflects the actual compounded outcome.
Why can't I include zero or negative numbers?
The geometric mean relies on multiplying everything and taking a root. A single zero drags the whole product to zero, and negatives can produce roots that aren't real numbers. So the calculation only makes sense for strictly positive values.
Is the geometric mean always smaller than the arithmetic mean?
For any list of positive numbers that aren't all identical, the geometric mean comes out less than or equal to the arithmetic mean. They're only equal when every value is the same. That gap grows as your data becomes more spread out.
How does it handle growth rates given as percentages?
Convert each rate to a growth factor first — a 10% gain becomes 1.10, a 5% loss becomes 0.95 — then take the geometric mean of those factors. Subtract one from the result to read it back as an average percentage.