🎵 Harmonic Mean Calculator
Calculate the harmonic mean of a set of positive numbers: n / (1/x₁ + 1/x₂ + ... + 1/xₙ).
What Is the Harmonic Mean?
The harmonic mean of n positive numbers is defined as n divided by the sum of their reciprocals: HM = n / (1/x₁ + 1/x₂ + ... + 1/xₙ). It is always the smallest of the three Pythagorean means (HM ≤ GM ≤ AM).
When to Use Harmonic Mean
The harmonic mean is appropriate when averaging rates or ratios. Common applications include calculating average speed when distances are equal, averaging P/E ratios in finance, and computing the F1 score in machine learning (which is the harmonic mean of precision and recall).
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