Harmonic Mean Calculator
Calculate the harmonic mean of a set of numbers.
A mean for rates
The harmonic mean is a particular kind of average, found from the reciprocals of the numbers, that is the right choice for certain situations where the ordinary average would mislead. This calculates it for your data.
Enter your numbers to find the harmonic mean.
When the ordinary average is wrong
The harmonic mean matters because there are real cases where the familiar arithmetic mean gives the wrong answer, particularly with rates. The classic example is average speed over equal distances: if you drive one way at 30 and back at 60, your average speed for the trip is not 45, the simple average, but the harmonic mean, which is lower, because you spend more time at the slower speed. Averaging rates like speed, or prices per unit, or rates of work, often calls for the harmonic mean rather than the arithmetic one. It is always the smallest of the common means, pulled down by small values. Knowing that different situations call for different kinds of average, and that using the wrong one quietly gives a wrong answer, is a genuinely useful and often-overlooked piece of statistical literacy.
Harmonic Mean Calculator FAQ
When should I use the harmonic mean?
For averaging rates — like average speed over equal distances, or rates of work — where the ordinary average gives a wrong answer.
Why isn't average speed just the simple average of the speeds?
Because you spend more time at the slower speed, so the true average is the harmonic mean, which is lower than the simple average.
Is anything uploaded?
No. The calculation happens in your browser.