Harmonic Mean Calculator

Calculate the harmonic mean - the right average to use for rates like speed over equal distances.

n/Σ(1/x)
Harmonic Mean-
Arithmetic Mean (for comparison)-
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What Is the Harmonic Mean?

The harmonic mean is the appropriate average for rates - most famously average speed when traveling equal distances at different speeds, where a simple average would overstate the true result.

Formula

Harmonic Mean = n ÷ Σ(1/xᵢ), where n is the count of numbers.

How to Use This Calculator

Example

Traveling equal distances at 60, 40, and 80 mph gives a harmonic mean (true average speed) of about 56.47 mph - noticeably lower than the arithmetic mean of 60 mph.

Frequently Asked Questions

How is harmonic mean calculated?

Harmonic mean = n ÷ (sum of the reciprocals of each value), where n is the count of values.

When is harmonic mean more appropriate than arithmetic mean?

It's preferred when averaging rates or ratios, like speeds over equal distances, since it correctly weights the different times each rate applies to.

What's a classic example where harmonic mean matters?

Averaging speeds for a round trip covering the same distance at different speeds (e.g. 60 mph one way, 40 mph the other) — the true average speed is the harmonic mean, not the simple average.

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