Geometric Mean Calculator
Calculate the geometric mean of a set of positive numbers, the correct average for growth rates and ratios. Shows the product and nth root.
Last reviewed by the Radiatus Cloud team
Find the geometric mean, the right average for growth factors and percentage changes.
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Calculate the geometric mean
The geometric mean is the average found by multiplying all the values together and taking the nth root, where n is how many values there are. It is the correct average for quantities that multiply rather than add, such as growth factors, interest rates and ratios. The calculator computes it using logarithms for numerical stability, which avoids the overflow that can occur when multiplying many numbers directly.
All values must be positive, because the product of a negative number and the roots involved would not give a meaningful real average. The arithmetic mean is shown alongside for comparison.
When the geometric mean is right
If an investment grows by five percent one year, ten percent the next and falls five percent in the third, the average annual growth is the geometric mean of the growth factors, not the arithmetic mean of the percentages. Index construction, population growth over several periods, and any chain of percentage changes all call for the geometric mean.
A key property is that the geometric mean of a set of growth factors, raised to the power of the number of periods, reproduces the overall change, which the arithmetic mean cannot do. For any positive data the geometric mean never exceeds the arithmetic mean. All calculation runs locally in your browser.
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Frequently Asked Questions
What is the geometric mean?
It is the nth root of the product of n positive numbers. It averages quantities that combine by multiplication, such as growth rates.
When should I use the geometric mean?
Use it to average growth factors, rates of return or ratios over several periods, where the arithmetic mean would give a misleading figure.
Why must the numbers be positive?
The product and its root are only meaningful for positive numbers. Zero gives a geometric mean of zero, and negatives have no real root in this context.
How do I average percentage growth?
Convert each percentage to a growth factor, for example five percent to 1.05, take the geometric mean, then convert back to a percentage.
How does it compare to the arithmetic mean?
The geometric mean is always less than or equal to the arithmetic mean, with equality only when every value is identical.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Enter positive numbers separated by commas, spaces or new lines.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.
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