Harmonic Mean Calculator
H = n / Σ(1/xᵢ). Used for averaging rates and ratios.
Result
Harmonic mean
48.6486
Always ≤ geometric ≤ arithmetic.
- Count3
- Values60, 40, 50
- Σ(1/xᵢ)0.061667
- Harmonic48.648649
- Geometric49.324241
- Arithmetic50.000000
Step-by-step
- Σ(1/xᵢ) = 0.0167 + 0.0250 + 0.0200 = 0.061667.
- H = n / Σ(1/xᵢ) = 3 / 0.061667 = 48.6486.
How to use this calculator
- Enter positive values, comma-separated.
- Read all three means.
About this calculator
Harmonic mean: H = n / Σ(1/xᵢ). Always ≤ geometric ≤ arithmetic for positive values (AM-GM-HM inequality). Used for averaging rates: avg speed of round trip (60 mph there + 40 mph back is harmonic mean = 48 mph, NOT arithmetic 50). Also in p/r ratios, density of subscribers, parallel resistance (1/R = 1/R₁ + 1/R₂ + ...).
Frequently asked
Averaging rates of constant numerator (e.g. distance) where denominator varies (time). Round trip speed.
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