Harmonic Mean Calculator

Harmonic mean and interpretation

The harmonic mean retains the entered measurement unit. The comparison arithmetic mean uses the same observations and equal weights, making the difference between the two averaging methods visible.

To compare the arithmetic mean, median, and mode of observations, use the Mean, Median & Mode Calculator and follow its own input conventions.

The formula

Average the reciprocals and invert that average. The implementation scales the reciprocal sum by the smallest observation to avoid overflow for very small positive inputs.

How to use this calculator

1. Enter positive observations separated by commas, spaces, or new lines.
2. Use a common unit and equal reciprocal weights for all entries.
3. Read both means and confirm that the harmonic model fits the quantity you are averaging.

Harmonic Mean input conventions

Small positive entries have greater influence on the harmonic mean because their reciprocals are larger. This is useful for certain rates whose denominator changes while equal amounts of the numerator are combined. For two equal-distance journeys, the slower leg takes more time, which is why simply averaging the speeds gives the wrong overall speed.

Interpreting harmonic mean

Equal-distance and equal-time examples require different averages. If you drive for the same duration at each speed, the arithmetic mean is appropriate instead. This tool assigns each entered reciprocal the same weight; it does not accept unequal distance weights. All values must be positive, so zero rates and mixed signed values require a different model rather than being silently omitted.

Assumptions & limitations

What this calculation assumes

• Every entered positive reciprocal receives equal weight.

What to keep in mind

• Unweighted positive-data mean; no unequal-distance weights or reciprocal units are inferred.

Common questions