Math
Harmonic mean of three values
Average three positive values through their reciprocals; this harmonic mean gives greater influence to the smaller values.
Calculators / Math / Weighted harmonic mean
Weighted harmonic mean calculator
Combine two positive rates using weights on their reciprocals.
On this page
Weighted harmonic mean26.67
Calculator controls
How to calculate
Combine two positive rates using weights on their reciprocals.
Weighted harmonic mean =
(w1+w2)/(w1/a+w2/b)Worked example
- First positive value: 20
- Second positive value: 40
- First weight: 1
- Second weight: 1
- Weighted harmonic mean: 26.67
Assumptions and limits
Weights must be nonnegative with at least one positive weight. This is appropriate for equal-quantity rate comparisons, not every average of rates.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Combine two positive rates using weights on their reciprocals. For speeds, distance weights support an average-speed calculation; time weights instead call for an arithmetic mean.
When this tool is useful
For speeds, distance weights support an average-speed calculation; time weights instead call for an arithmetic mean.
Understanding your inputs
| Input | Example |
|---|---|
First positive value a | 20 |
Second positive value b | 40 |
First weight w1 | 1 |
Second weight w2 | 1 |
Frequently asked questions
Which assumptions matter for this result?
Weights must be nonnegative with at least one positive weight. This is appropriate for equal-quantity rate comparisons, not every average of rates.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.