Quick guide
How to use this calculator
- Enter one strictly positive value per line.
- Read the reduced exact fraction.
- Use the decimal representation only as a convenience when it repeats or is long.
Calculation method
Average the reciprocals, then invert
The harmonic mean of n positive values is n divided by the exact sum of their reciprocals.
Worked example
Harmonic mean of 2 and 3
The reciprocal sum is 1/2 + 1/3 = 5/6.
2 / (1/2 + 1/3) = 12/5 = 2.4
Supported inputs
Precision and limits
List size
Enter 1–100 values, one per line.
Decimal size
Each value may contain up to 200 digits and 100 decimal places.
Exactness
Exact rational results are never replaced by a rounded decimal; approximations are labelled.
Positive domain
Zero and negative values are rejected because the reciprocal formula would be undefined or outside this calculator's conventional domain.