Harmonic Mean Calculator
The harmonic mean averages positive values through their reciprocals and is often useful for rates under compatible weighting assumptions.
How to use this calculator
- Enter positive values with commas, semicolons or spaces. Compare the output with the arithmetic mean before choosing a method.
- Check the labels and units before using a result outside this page.
- Change one input at a time if you want to compare scenarios.
Formula and method
HM = n ÷ Σ(1 ÷ xᵢ)
- HM = n ÷ Σ(1 ÷ xᵢ)
- Only positive values are accepted; using the harmonic mean for incompatible or differently weighted rates can mislead.
Worked examples
Worked example
Find the harmonic mean of 2, 4 and 8.
HM = 3 ÷ (1/2 + 1/4 + 1/8) ≈ 3.4286.
HM = 3 ÷ (1/2 + 1/4 + 1/8) ≈ 3.4286.
Understanding the result
The harmonic mean averages positive values through their reciprocals and is often useful for rates under compatible weighting assumptions.
Only positive values are accepted; using the harmonic mean for incompatible or differently weighted rates can mislead.
Important notes
Only positive values are accepted; using the harmonic mean for incompatible or differently weighted rates can mislead.
Displayed outputs are rounded for readability; preserve full precision when continuing a calculation.
Frequently asked questions
What does this harmonic mean calculator show?
The harmonic mean averages positive values through their reciprocals and is often useful for rates under compatible weighting assumptions.
Which inputs should I check first?
Enter positive values with commas, semicolons or spaces. Compare the output with the arithmetic mean before choosing a method.
Can the result be used as a final professional specification?
Only positive values are accepted; using the harmonic mean for incompatible or differently weighted rates can mislead.
Related calculators
- Average Calculator — Calculate the mean, median, mode, and range of any set of numbers.
- Weighted Average Calculator — Calculate a weighted average from values and their weights.
- Geometric Mean Calculator — Calculate the geometric mean of positive values and compare it with their arithmetic mean.
- Trimmed Mean Calculator — Calculate a trimmed mean by removing a chosen percentage of observations from both tails.
- Confidence Interval for Mean Calculator — Estimate a normal-approximation confidence interval around a sample mean from its spread and sample size.
- Mean Absolute Deviation Calculator — Measure the average absolute distance of data values from their arithmetic mean.
Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.