Quick answer
The geometric mean is (Πx)^(1/n) for positive values. For 2 and 8 it is √16 = 4.
Enter positive data values. The calculator returns the geometric mean.
Related tools: Mean Calculator: Mean of a data set. Mean Median Mode Calculator: Mean, median and mode of a data set. Mean Absolute Deviation Calculator: Average distance of values from the mean.
How to use the Geometric Mean Calculator
- Type data set, for example 4, 8, 15, 16, 23, 42.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Data set | Text, such as 4, 8, 15, 16, 23, 42 | — |
Formula and method
Formula
(Πx)^(1/n) (positive values only)
IEEE-754 double precision; shown to at most 6 decimal places.
Computed directly from the sorted or raw values.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Data set = 2, 8.
| Result | Value |
|---|---|
| Geometric mean | 4 |
Example 2
Inputs: Data set = 1 10 100.
| Result | Value |
|---|---|
| Geometric mean | 10 |
The first line is the headline result (geometric mean). IEEE-754 double precision; shown to at most 6 decimal places.
When to use it
Use the geometric mean for growth rates and ratios. Growth of +10% then +20% averages (1.1 × 1.2)^(1/2) − 1 = 14.9% a year, not the arithmetic 15%. It is always no more than the arithmetic mean.
Requirements
All values must be positive; zero or negative values break the formula. At least one value is needed. Taking logs: the geometric mean is the exponential of the mean of the logarithms.
Average growth over several periods
For growth factors, the geometric mean gives the steady rate that produces the same result. Growth of 10% then 30% has factors 1.10 and 1.30, whose geometric mean is √1.43 ≈ 1.1958, a steady 19.58% per period, not the 20% the arithmetic mean suggests.
Convert percentages to factors first (add 100% and divide by 100). Values must be positive: a zero makes the product zero, and negative values can make the root undefined.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Data set: left empty shows "Enter data set." beside that field and no result.
Choosing between the Geometric Mean Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Mean Calculator](/statistics/mean/) | data set | Mean |
| [Mean Median Mode Calculator](/statistics/mean-median-mode-calculator/) | data set | Mean |
| [Mean Absolute Deviation Calculator](/statistics/mean-absolute-deviation-calculator/) | data set | Mean absolute deviation |
| [Harmonic Mean Calculator](/statistics/harmonic-mean-calculator/) | data set | Harmonic mean |
| [Mean Median Mode Range Calculator](/statistics/mean-median-mode-range-calculator/) | data set | Mean |
Background: descriptive statistics
Population statistics divide by n and sample statistics divide by n − 1 (Bessel's correction), because a sample tends to understate variability. Use the population version when your data is every value in the group, and the sample version when it is a subset.
Defaults differ between tools, and so do quartile conventions, which can give slightly different values for small data sets; this page states the method it uses.
Assumptions and limitations
- At least one value
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for data set to confirm this.
Frequently asked questions
What is the geometric mean of 1, 10, 100?
The geometric mean of 1, 10 and 100 is (1 × 10 × 100)^(1/3) = 10.
Is it smaller than the arithmetic mean?
Yes, unless all values are equal.
Where is it used?
Index numbers and investment returns.
How do I average percentage growth rates?
Convert each rate to a factor such as 1.10, find the geometric mean of the factors, then subtract 1.
Why must the values be positive?
A zero collapses the product to zero and negative values can make the root undefined, so the geometric mean is only defined for positive numbers.
What does the Geometric Mean Calculator calculate?
Geometric mean of a data set. It returns Geometric mean.
What formula does the Geometric Mean Calculator use?
(Πx)^(1/n) (positive values only). Computed directly from the sorted or raw values.
What is an example of a geometric Mean result?
With data set 2, 8, the geometric mean is 4.
Related calculators
- Mean Calculator — Mean of a data set.
- Mean Median Mode Calculator — Mean, median and mode of a data set.
- Mean Absolute Deviation Calculator — Average distance of values from the mean.
- Harmonic Mean Calculator — Harmonic mean of a data set.
- Mean Median Mode Range Calculator — Mean, median, mode and range of a data set.
- Standard Deviation Calculator — Sample or population standard deviation with variance and mean.
- Coefficient of Variation Calculator — Standard deviation relative to the mean.
- Midrange Calculator — Midpoint between the smallest and largest value.
- Outlier Calculator — Find outliers with Tukey's 1.5 × IQR fences.
Sources
- OpenStax, Introductory Statistics 2e (Rice University): measures of center and spread, correlation and regression
- NIST/SEMATECH e-Handbook of Statistical Methods (nist.gov), Exploratory Data Analysis chapter
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.