Harmonic Mean Calculator
The right average for rates, speeds and ratios.
Enter your values
Enter the values you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)
At a glance
| What it does | The right average for rates, speeds and ratios. |
|---|---|
| Category | Math |
| Inputs needed | Values |
| Main output | Harmonic mean |
| Formula | H = n ÷ Σ(1/xᵢ) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Values
- Enter the values you are working with.
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.
What do I need to enter into the Harmonic Mean Calculator?
Just 1 value: values. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Harmonic Mean Calculator work out the 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. It applies the formula H = n ÷ Σ(1/xᵢ) and shows the working so you can check each step by hand.
Is the Harmonic Mean Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.