How this calculator works
The harmonic mean averages reciprocal quantities before taking a reciprocal again. It is useful for positive rates applied over equal quantities, such as speeds over equal distances. The implementation scales reciprocals by the smallest input so very small rates remain usable. Every input must be strictly positive.
Formula
Arithmetic: A = sum(x)/n. Geometric: G = (product(x))^(1/n). Harmonic: H = n/sum(1/x).
Worked example
Equal distances travelled at 30 and 60 km/h give a harmonic mean speed of 40 km/h. The harmonic mean of 2 and 6 is 3.
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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.