How this calculator works
Choose an arithmetic, geometric or harmonic mean, or compare all three. Arithmetic means combine additive values; geometric means describe multiplicative scale; harmonic means suit positive rates over equal quantities. Arithmetic accepts any real values, geometric accepts non-negative values, and harmonic or combined mode requires positive values.
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 arithmetic mean is 5, the geometric mean is 4 and the harmonic mean is 3.2. For 3 and 12, they are 7.5, 6 and 4.8.
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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.