Calculate the harmonic mean of any dataset. The harmonic mean is particularly useful for averaging
rates, ratios, and speed calculations. Enter your numbers separated by commas, spaces, or line breaks.
What is the Harmonic Mean?
The harmonic mean is a type of average that is calculated by dividing the number of values by the sum
of the reciprocals of those values. It is most appropriate when dealing with rates and ratios.
Formula
The harmonic mean H of n numbers x₁, x₂, ..., xₙ is calculated as:
H = n / (1/x₁ + 1/x₂ + ... + 1/xₙ)
When to Use Harmonic Mean
Averaging speeds or rates over the same distance
Calculating average price to earnings ratios in finance
Finding average rates when the denominator is constant
Financial analysis when working with multiples
Computer science (e.g., F1 score in machine learning)
How to Use This Calculator
Enter your numbers in the text area above
Separate numbers with commas, spaces, or place each on a new line
Click "Calculate Harmonic Mean" to see the result
View detailed reciprocal calculations to understand how the result was obtained
Important Notes
All numbers must be positive and non-zero for harmonic mean calculation
The harmonic mean is always less than or equal to the arithmetic mean
This calculator shows step-by-step reciprocal calculations for transparency
Results are rounded to 6 decimal places for precision