Harmonic Mean Calculator
Calculate the harmonic mean of a list of positive numbers — commonly used for averaging rates, such as speeds over equal distances.
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Your result
48
Harmonic mean
AI explanation
Formula
Harmonic mean = n / (1/x₁ + 1/x₂ + ... + 1/xₙ)Worked example
Equal distances at 60 and 40 (e.g. km/h)
| Field | Value |
|---|---|
| Numbers (all positive) | 60, 40 |
| Harmonic mean | 48 |
| Count of numbers | 2 |
Assumptions
- All numbers must be positive, since the formula divides by each value.
- Best suited for averaging rates (like speed) rather than general-purpose averaging.
Frequently asked questions
When should I use harmonic mean instead of arithmetic mean?
Use harmonic mean when averaging rates over a fixed quantity — the classic example is average speed over equal distances traveled at different speeds, where the simple arithmetic mean would give an incorrect (too high) answer.
Why is the answer for 60 and 40 not simply 50?
Because more time is spent traveling at the slower speed (40) for the same distance, the true average speed weights toward the slower value — harmonic mean captures this correctly, giving 48, not the arithmetic mean of 50.
Is harmonic mean always smaller than arithmetic mean?
Yes, for any set of positive numbers that aren't all identical, harmonic mean ≤ geometric mean ≤ arithmetic mean.