Harmonic Mean Calculator
The right average for rates, speeds and ratios.
Enter your values
ⓘ Live results
Results
- Harmonic mean
- 48.64865
- Geometric mean
- 49.32424
- Arithmetic mean
- 50
- Count
- 3
- Sum of reciprocals
- 0.061667
Quick answer
The harmonic mean is n divided by the sum of the reciprocals; it is the correct average when the values are rates over a fixed quantity, such as speeds over a fixed distance.
H = n ÷ Σ(1/xᵢ)
How to use the Harmonic Mean Calculator
- 1Enter the rates or speeds you want to average.
- 2Read the harmonic mean, not the arithmetic one, when each value applies to the same distance or workload.
- 3Compare all three means to see how skewed the data is.
Worked example
Using the values the calculator loads with:
Inputs
- Values60, 40, 50
Results
- Harmonic mean48.64865
- Geometric mean49.32424
- Arithmetic mean50
- Count3
- Sum of reciprocals0.061667
Frequently asked questions
Why is average speed a harmonic mean?
Driving 60 mph out and 40 mph back over the same distance averages 48 mph, not 50 — you spend more time at the slower speed.
Which mean is always largest?
Arithmetic ≥ geometric ≥ harmonic, with equality only when every value is identical.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.