If you drive to work at 60 km/h and back at 40 km/h, your average speed is not 50 km/h but the harmonic mean, 48 km/h, because you spend longer at the slower speed. The harmonic mean is also used for P/E ratios and the F1 score in machine learning.
How to use the Harmonic Mean Calculator
- Type the numbers separated by commas, spaces or new lines.
- Read the result – it updates as you type.
Results update as you type, and everything is calculated in your browser.
How it works
The calculator takes the reciprocal of each value, averages them and takes the reciprocal of the result. All values must be positive.
What each result means
- Harmonic mean = hmean([Values (positive numbers)])
- Arithmetic mean = mean([Values (positive numbers)])
- Geometric mean = gmean([Values (positive numbers)])
Formula
H = n ÷ (1/x₁ + 1/x₂ + … + 1/xₙ)
Worked example
Inputs — Values (positive numbers): 60, 40.
Results — Harmonic mean = 48; Arithmetic mean = 50; Geometric mean = 48.98979486.
Key terms
- Harmonic mean
- The reciprocal of the mean of the reciprocals.
Frequently asked questions
When should I use the harmonic mean?
When averaging rates over equal distances or amounts, such as speeds over equal distances.
Why is the average speed 48 km/h, not 50?
You spend 1.5 times as long at 40 km/h as at 60 km/h.
Can the harmonic mean be larger than the arithmetic mean?
No, it is always less than or equal to it.
What is the harmonic mean of two numbers?
2ab/(a + b).