Harmonic Mean Calculator

About this calculator

The harmonic mean is the reciprocal of the arithmetic average of a set of numbers' reciprocals — for a list of n values, it is n divided by the sum of 1÷x for each value. Unlike the arithmetic mean, it gives proportionally more weight to smaller values, which makes it the mathematically correct way to average rates and ratios rather than simple counts.

The classic example is averaging speeds over equal distances: if you drive the first half of a trip at 60 mph and the second half at 30 mph, your true average speed is the harmonic mean of the two, 40 mph, not their arithmetic average of 45 mph, because you spend more time at the slower speed. Financial analysts apply the same logic to average price-to-earnings ratios across a portfolio of stocks, since P/E is itself a ratio of price over earnings, and the harmonic mean avoids the upward bias a simple average would introduce from high-P/E outliers.

Enter a list of positive numbers and this calculator returns their harmonic mean.