Harmonic Mean Calculator
Calculate the harmonic mean of positive numbers, rates or ratios.
How to Use the Harmonic Mean Calculator
Enter two or more positive rates or ratios. The calculator divides the number of observations by the sum of their reciprocals.
Practical Example
For speeds of 30 and 60 over equal distances, the harmonic mean is 2 ÷ (1/30 + 1/60) = 40.
Factors That Affect the Result
The harmonic mean is most appropriate for rates with a common numerator or equal-distance comparisons. Using it for unrelated additive values can be misleading.
Related Tools
Average Calculator · Weighted Average Calculator · Geometric Mean Calculator · Unit Rate Calculator · Ratio Calculator
Frequently Asked Questions
Can I enter zero?
No. The reciprocal of zero is undefined.
When is harmonic mean useful?
It is commonly used for rates, speeds and ratios.
Is it usually smaller than the arithmetic mean?
For positive values, it is no greater than the arithmetic mean.
When to Use the Harmonic Mean
The harmonic mean is the reciprocal of the arithmetic mean of reciprocals. For positive values x₁ through xₙ, it is n / (1/x₁ + … + 1/xₙ). It is especially useful for averaging rates when the same quantity or distance is involved.
A Common Example
If equal distances are traveled at two different speeds, the simple arithmetic average of the speeds can be misleading. The harmonic mean gives the appropriate average speed for equal-distance segments because slower rates consume more time.
The harmonic mean is strongly influenced by small values and is not defined in the ordinary formula when an input is zero. It also serves a different purpose from the arithmetic and geometric means. Before choosing an average, identify whether values combine additively, multiplicatively, or as rates over a common numerator.