How this calculator works
The geometric mean is the common multiplicative scale of a list. This tool averages logarithms to avoid overflowing a direct product, then exponentiates. Non-negative inputs are accepted; if any input is zero, the mean is zero. Convert growth percentages to growth factors before averaging them.
Formula
Arithmetic: A = sum(x)/n. Geometric: G = (product(x))^(1/n). Harmonic: H = n/sum(1/x).
Worked example
For 2 and 8, the geometric mean is sqrt(16) = 4. For 1, 4 and 16, it is the cube root of 64, also 4.
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Frequently asked questions
Must the values use the same units?
Yes. Convert every measurement to a consistent unit before calculating a mean.
How do zeros and negatives work?
Arithmetic means allow both. Geometric means here allow zero but no negatives. Harmonic means and the all-means comparison require strictly positive values.
Can an average hide important variation?
Yes. These means summarize location, not spread or uncertainty. Review the original observations as well as the result.