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Harmonic Mean Calculator

Compute the harmonic mean: the correct average for speeds, rates, and ratios over equal distances.

Harmonic Mean

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Arithmetic mean
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Formula: Harmonic mean = n / (1/x1 + 1/x2 + ... + 1/xn). Values must be positive and non-zero.
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Reciprocals do the work

The harmonic mean averages the reciprocals and flips the result: n divided by the sum of 1/x. Driving 60 km/h one way and 40 km/h back over the same distance averages 48 km/h, not 50, because more time is spent at the slower speed.

The smallest of the means

For any positive dataset: harmonic <= geometric <= arithmetic. The harmonic mean is pulled toward small values, which is exactly right for rates: the slowest leg dominates the total time.

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Harmonic Mean FAQs

What is the average speed of 60 km/h one way and 40 back?
48 km/h. The harmonic mean 2 / (1/60 + 1/40) = 48 accounts for the extra time at 40.
What is the harmonic mean formula?
n / (1/x1 + 1/x2 + ... + 1/xn). Average the reciprocals, then take the reciprocal of that.
When do I use harmonic instead of arithmetic mean?
For rates over equal distances or equal amounts: speeds, fuel economy per fixed distance, parallel resistors, price-to-earnings ratios.
Why must values be positive?
Zero or negative values make the reciprocals undefined or misleading. Rates like speed are naturally positive.
Is my data uploaded?
No. The calculation runs fully in your browser.
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