Harmonic Mean Calculator
Compute the harmonic mean of rates like speeds and learn when it beats the arithmetic mean.
Category: Statistics
About this tool
What Is the harmonic mean? Harmonic Mean Calculator. The harmonic mean calculator finds the typical value for rates, where distances and denominators carry equal weight. It is the correct mean for speeds, flow rates, and any ratio where each unit shares the same denominator. The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals: H = n ÷ Σ(1/xᵢ). It answers 'what constant rate gives the same total for equal-sized inputs'. Speeding the first half of a trip and cruising the second produces different average speeds depending on which mean you pick; the harmonic mean stays truthful when the journey legs are equal in distance, not time. H = n ÷ (1/x₁ + 1/x₂ + … + 1/xₙ). How to Use Enter the rates in the value fields; all inputs must be strictly positive. Read the harmonic mean together with the arithmetic mean to compare. Use the result whenever averaging speeds or efficiencies per unit. Worked Example Drive 60 km at 30 km/h and back at 60 km/h. The arithmetic mean says 45 km/h; the harmonic mean 2 ÷ (1/30 + 1/60) = 40 km/h, which is the true average speed because the distance, not time, is equal on each leg. Common Use Cases average speed and commute calculations flow rates in pipes and production lines power-system impedance averaging (parallel) machine efficiency per operating hour Important Notes Inputs must be positive — zero or negative rates break the r