Harmonic Mean Calculator

About this calculator

This calculator computes the harmonic mean, n / Σ(1/xᵢ) — the reciprocal of the average of the reciprocals — which, unlike the arithmetic mean, gives more weight to smaller values and is the mathematically correct way to average rates.

It's the standard tool for averaging speeds over equal distances (e.g., driving 60 km/h there and 40 km/h back doesn't average to 50 km/h — the harmonic mean gives the correct 48 km/h), for finance metrics like the average P/E ratio of a portfolio, and for computing the F1 score in machine learning, which harmonically averages precision and recall. The calculator flags when any input is zero, since the harmonic mean is undefined in that case (division by zero in the reciprocal).