How to use the Geometric Mean Calculator
Paste positive numbers separated by commas, spaces or new lines. The calculator multiplies them and takes the nth root, where n is how many numbers you entered.
Worked example with growth rates
An investment grows 10% one year and 50% the next. The growth factors are 1.10 and 1.50. Their geometric mean is the square root of 1.65, about 1.2845, so the average yearly growth is about 28.45%. The ordinary average of 30% would overstate what you actually earned.
When to use it
Use the geometric mean whenever values multiply rather than add: returns, growth rates, index numbers and ratios. For things that add up, such as test scores or heights, the ordinary arithmetic mean is the right choice. The geometric mean is always equal to or smaller than the arithmetic mean.
The formula
Geometric mean = (x₁ × x₂ × … × xₙ)^(1/n)
Examples
- 2, 4, 6, 8, 10
Geometric mean: 5.21034217
- Growth factors 1.10, 1.25, 0.95, 1.05
Geometric mean: 1.08219096
- 1, 10, 100
Geometric mean: 10
Limitations and assumptions
Every value must be greater than zero. For growth rates, enter growth factors such as 1.10 for 10% growth.
Frequently asked questions
What is the geometric mean?
The nth root of the product of n positive numbers.
When is it better than the arithmetic mean?
For multiplicative changes such as investment returns and growth rates.
Can it include zero or negatives?
No, values must be positive.
How does it compare with the arithmetic mean?
It is never larger than the arithmetic mean.