Harmonic Mean Calculator

Paste positive values to calculate the harmonic mean, reciprocal sum, related means, and a clear formula summary in your browser.

Positive non-zero values

The harmonic mean is useful for averaging rates in appropriate equal-weight settings. This calculator requires positive non-zero values.

Harmonic mean

7.8689

n ÷ Σ(1/x)

4Count

—Reciprocal sum

—Geometric mean

—Arithmetic mean

Ready

Core describe → test → interpret workflows

Use descriptive context first, choose the method that matches the design, then keep inputs, settings and result evidence reproducible instead of copying a p-value without its analysis recipe.

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Interpret statistical results in context

Use plots and descriptive summaries before formal tests. Check the sampling/design assumptions that matter for the chosen method, report effect size and uncertainty where available, and avoid treating a threshold such as p < .05 as proof of importance, causation, or truth. Browser calculations are educational/planning utilities, not domain-specific professional advice.

How to use this Harmonic Mean Calculator

Paste positive non-zero values to calculate n divided by the sum of reciprocals, with geometric and arithmetic means for comparison.

What the result means

Paste positive values to calculate the harmonic mean, reciprocal sum, related means, and a clear formula summary in your browser.

Practical guide and verification

Use the tool first, then use these checks to interpret, verify and hand off the result without displacing the primary workflow.

Use the harmonic mean for rates with the right denominator

The harmonic mean is especially useful when averaging rates or ratios across equal amounts of the numerator quantity, such as speeds over equal distances. It is not a universal replacement for the arithmetic mean. Write down what is being held equal before deciding which average answers the real question.

Check for zero and negative values

The ordinary harmonic mean uses reciprocals, so zero is undefined and values near zero can dominate the result. Negative values may be mathematically possible in some specialized contexts but often make a simple rate interpretation meaningless. Review every input before accepting a single summary number.

Compare with the arithmetic mean as a diagnostic

For positive values, the harmonic mean cannot exceed the arithmetic mean. If your computed harmonic mean is larger, recheck the inputs or method. The difference between the two can also reveal how strongly small rate values pull down the reciprocal-based average.

Preserve weighting information

If observations represent unequal distances, quantities, exposures, or other weights, the unweighted harmonic mean may not be appropriate. Record the weighting rule and use a weighted harmonic mean when the underlying problem requires it. A clean result from the wrong weighting model is still misleading.