This harmonic mean calculator computes the harmonic average of a list of numbers – useful for averaging rates, speeds, and investment ratios.
Harmonic mean calculator
What is the harmonic mean?
The harmonic mean is n divided by the sum of reciprocals. It's the right average when you have a fixed quantity and varying rates.
harmonic\ mean = \frac{n}{\frac{1}{x_1}+\frac{1}{x_2}+...+\frac{1}{x_n}}The harmonic mean is especially useful for:
- Average speed - when traveling the same distance at different speeds
- Investment ratios - averaging P/E or P/S ratios across a portfolio
- Rates of work - filling/emptying containers at different rates
Example: average speed
You drive 50 miles to a city at 53 mph, then return at 31 mph. What's your average speed?
The harmonic mean gives 39.12 mph. The arithmetic mean would incorrectly show 42 mph... that's wrong because you spent more time driving slowly.
Using the calculator
Enter numbers separated by commas, spaces, or new lines. Results update instantly. The calculator also shows the geometric mean and arithmetic mean for comparison.
Note: The harmonic mean is undefined if any value is zero.
