Geometric Mean Calculator
Find the geometric mean of positive numbers, with the arithmetic mean for comparison.
Change the values and press Calculate to work out your own figures.
Enter positive numbers to find their geometric mean.
Show the working
- Multiply the 8 values and take the 8th root
- = exp(mean of ln x) = 17.1198517261
How to use it
Enter positive numbers to find their geometric mean.
Paste or type the numbers separated by commas, spaces or new lines. Results are worked out exactly and shown to 12 significant figures; Show the working lists each step.
Key facts
geometric mean = (x₁ × x₂ × … × xₙ)^(1/n)
Growth rates
The geometric mean is the right average for rates of growth: an investment that rises 50% then falls 50% has a geometric mean return of about −13%, not 0%.
Questions
When should I use the geometric mean?
For quantities that multiply together, such as growth rates and ratios.
Why can't it use negative numbers?
The nth root of a negative product isn't a real number in general.
Formulas
geometric mean = (x₁ × x₂ × … × xₙ)^(1/n)
Sources
Limitations
- Up to 5,000 values. Values are separated by commas, spaces or new lines, so write 1250 rather than 1,250.