Harmonic Mean Calculator
Calculate the harmonic mean of a data set, useful for averaging rates and speeds.
Enter your data set. All values must be positive numbers.
Harmonic Mean
Count (n)
Sum of Reciprocals
Calculation Steps
What the Harmonic Mean Measures
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 averaging rates or ratios, such as speeds, prices, or other quantities defined relative to a unit.
Formula
- Harmonic Mean: HM = n / Σ(1 / xᵢ)
When to Use It
The harmonic mean gives greater weight to smaller values and is always less than or equal to the geometric and arithmetic means for the same positive data. Because it relies on reciprocals, every value in the data set must be a positive number; zero or negative values are not allowed.