Harmonic Mean Calculator
Calculate the harmonic mean, the correct average for rates and speeds.
What the Harmonic Mean Calculator does
The harmonic mean is the reciprocal of the average of reciprocals. It is the correct average for rates measured over a constant quantity — driving 60 mph out and 40 mph back averages 48 mph, not 50, because you spend more time at the slower speed.
Formula
Harmonic mean = n ÷ Σ(1 ÷ xᵢ)Weighted: Σwᵢ ÷ Σ(wᵢ ÷ xᵢ)
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Values | text | Yes | Separate values with commas, spaces or new lines. |
| Weights | text | Optional | Optional — for a weighted harmonic mean. |
How to use it
- Enter Values.
- Optionally add Weights.
- Select Calculate.
Worked example
Driving one leg at 60 mph and the return at 40 mph over the same distance.
- Values
- 60, 40
2 ÷ (1/60 + 1/40) = 48 mph average, not the 50 that arithmetic averaging suggests.
Frequently asked questions
When should I use harmonic instead of arithmetic mean?
When the values are rates and the quantity in the denominator is held constant. Equal distances at different speeds is the canonical case.
Why is it always the smallest mean?
Because taking reciprocals gives disproportionate weight to small values. This is exactly the behaviour you want when slow rates dominate the total time.