Harmonic Mean Calculator
The average built for rates — average speeds, P/E ratios, and anything measured per unit — worked out from your list in one step.
How it works
The harmonic mean flips every value, averages those reciprocals, then flips back. Put simply, it's the count divided by the sum of 1/x across your numbers. That structure gives smaller values more pull on the result.
It's the honest average for rates. If you drive somewhere at 40 mph and back at 60 mph over the same distance, your true average speed isn't 50 — it's the harmonic mean, 2 ÷ (1/40 + 1/60) = 48 mph.
The same logic covers things like average P/E ratios across a portfolio or throughput measured per unit of time. Any time the quantity is 'something per something,' the harmonic mean usually gives the number you actually want.
Frequently asked questions
When is the harmonic mean the right choice?
Use it for averaging rates and ratios, especially when each rate covers the same amount of the other quantity — equal distances at different speeds, equal dollars at different P/E ratios. In those setups the arithmetic mean quietly gives the wrong answer.
Why can't the list contain a zero?
The formula takes the reciprocal of every value, and 1 divided by zero is undefined. A single zero would break the whole calculation, so the tool shows a dash until you remove it.
How does it compare to the arithmetic and geometric means?
For any list of positive numbers the harmonic mean is the smallest of the three, the arithmetic mean the largest, and the geometric mean sits between them. They only all match when every value is identical.
Can I use negative numbers?
It's best avoided. The harmonic mean is defined for positive values, and mixing in negatives can produce a result that's meaningless or even undefined. Keep your inputs positive for a number you can trust.