Geometric Mean Calculator
Enter a list of positive numbers to find their geometric mean.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- Geometric mean = (x₁ × x₂ × … × xₙ)^(1/n)
- The calculator averages the natural logs and converts back, which avoids overflow on long lists
- The arithmetic mean is shown for comparison
For a growth rate over time, try the CAGR calculator. For other averages, see the mean, median and mode calculator.
Worked example
For 4 and 9:
- Product = 36, and the square root of 36 = 6
- The arithmetic mean is 6.5
Why your number may differ
The geometric mean is always at or below the arithmetic mean. Rounding of very long lists can change the last digit.
Frequently asked questions
What is the geometric mean?
It is the nth root of the product of n numbers. It describes the typical size of values that multiply together, such as growth factors.
When should I use it instead of the average?
Use it for rates of growth, returns and ratios. The ordinary average overstates the result when values compound.
Why must the numbers be positive?
The calculation uses logarithms, which only exist for numbers above zero.