Harmonic Mean Calculator
Calculate the harmonic mean of a set of positive numbers, ideal for rates and ratios.
Inputs
Positive numbers only.
Harmonic Mean
48.000000
Count
2
Sum of Reciprocals
0.04166667
Step by step
Count of values
= 2
Sum of reciprocals
1/40 + 1/60
= 0.04166667
Harmonic mean = n / sum of reciprocals
2 / 0.04166667
= 48.000000
How it works
The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals. It is always ≤ the arithmetic mean and is the correct average for rates (like speed, efficiency, or price-to-earnings ratios).
Formula
Harmonic Mean
H = n / (1/x₁ + 1/x₂ + ... + 1/xₙ)
- H
- Harmonic mean
- n
- Number of values
- xᵢ
- Each positive value
Frequently Asked Questions
When is the harmonic mean useful?
Use it when averaging rates. For example, if you drive 40 km/h on the way out and 60 km/h on the return (same distance), the average speed is the harmonic mean: 2/(1/40+1/60) = 48 km/h, not the arithmetic mean of 50.
Why must all values be positive?
A zero value would make its reciprocal infinite, and negative values would cancel in ways that make the harmonic mean meaningless or undefined.