We use cookies.This website uses essential cookies to operate core features. With your consent, we also use analytics cookies to understand traffic and improve the service. For more details, see our .
We use cookies.This website uses essential cookies to operate core features. With your consent, we also use analytics cookies to understand traffic and improve the service. For more details, see our .
Was this tool helpful to use?
Your feedback helps us make it better
Input a set of positive numbers, one-click calculation of geometric mean, commonly used for average growth rate, investment return and other scenarios.
Separate by commas, spaces, semicolons, or newlines. Whitespace and non-numeric content are ignored. (In simple terms: the geometric mean is the nth root of the product of n numbers, commonly used for average growth rates and compound returns.)
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
The geometric mean of n positive values is the nth root of their product: G = (x₁ × x₂ × … × xₙ)^(1/n). Equivalently, it is exp[(ln x₁ + … + ln xₙ) / n]. The National Institute of Standards and Technology gives the product-and-root definition. This mean is useful when values combine by multiplication, such as comparable ratios or period growth factors, rather than by addition.
The calculator requires every parsed number to be greater than zero. It reports the geometric mean, arithmetic mean, number of values, and product. The arithmetic mean is a comparison statistic; it is not substituted into the geometric-mean formula.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Separate values with commas, spaces, semicolons, tabs, or line breaks. Non-numeric pieces are ignored, so check that the data count matches the values you intended to include.
Confirm the count, then read the geometric mean as the primary result. The displayed product and arithmetic mean help you audit the input and compare the two kinds of average.
For 4, 9, 16, 25, the product is 14,400 and the geometric mean is about 10.954451; the arithmetic mean is 13.5. Displayed values are rounded to at most six decimal places.
Use cases
See how the tool fits into real work and everyday tasks.
For factors applied successively over equal-length periods, the geometric mean is the constant per-period factor that gives the same overall product. Convert percentage returns first: +8% is a factor of 1.08, and −5% is 0.95.
A researcher can use it to summarize positive measurements when relative, multiplicative differences are meaningful. Keep units and definitions consistent across the input set.
For a sequence of period returns, enter each gross growth factor, not the percentage number by itself. If the resulting average factor is 1.02, the corresponding average rate is 1.02 − 1 = 0.02, or 2% per period. This summarizes the entered observations; it does not forecast future results.
Q&A
Find concise answers to common questions and confusing cases.
This calculator accepts strictly positive values. If the values are returns, convert each rate into a growth factor first; a loss of 5% becomes 0.95, not −5.
No. Enter the factor 1.08 for an 8% gain. The tool averages the numbers exactly as entered and does not infer percentage notation.
Empty pieces and text that cannot be parsed as finite numbers are skipped. Check the separators and the displayed count; any non-positive parsed value prevents a result for the set.
The results are rounded to at most six decimal places for display. A rounded value may differ from the full-precision internal calculation.
Notes
Review scope, result limitations, and important precautions before use.
Use the geometric mean only when the values are positive and their multiplicative relationship answers the question. Do not combine unlike units or unrelated measures. For returns, use comparable periods and gross growth factors; the result describes the supplied history and is not investment advice or a prediction. Large inputs can also exceed the range of a displayed product even when the logarithm-based mean remains calculable, so retain the original data and independently verify results needed for precision reporting.
Related
Discover related tools, collections, and available API capabilities.