Harmonic Mean Calculator

This calculator finds the harmonic mean of a set of numbers, the correct average to use for rates, speeds and ratios where the quantity is measured per unit of something. Of the three classical averages, the harmonic mean is the least familiar but the most appropriate in a surprising number of situations. It is defined as the number of values divided by the sum of their reciprocals, which gives more weight to the smaller values and is exactly what you need when averaging things like speeds over equal distances, prices in cost-per-unit terms, or rates of work. The classic example is average speed: if you drive somewhere at 40 kilometres an hour and back at 60, your average speed for the round trip is not 50 but the harmonic mean of 40 and 60, which is 48, because you spend more time at the slower speed. Getting this wrong is a common mistake, and the harmonic mean fixes it. This tool computes it for you. You paste or type your numbers, which should be positive, and the calculator returns the harmonic mean, along with the arithmetic and geometric means for comparison and the count of values. For any set of positive numbers, the harmonic mean is the smallest of the three, the arithmetic the largest, and the geometric in between. The results update as you type. Use it to average speeds or rates correctly, to combine ratios, in finance for averaging price multiples, or for statistics study. The key is to reach for the harmonic mean whenever you are averaging quantities expressed as something per unit, especially over equal amounts of the denominator, where the ordinary average would mislead.

Harmonic mean = n / sum of reciprocals. Best for averaging rates and speeds over equal distances. Always the smallest of the three classical means.