Statistics

Harmonic Mean Calculator

Calculate harmonic mean for rates and ratios.

Last validated: 2026-02-14

Harmonic Mean Calculator computes the harmonic mean for rate-like quantities. It is useful for averaging speeds, ratios, and per-unit metrics where reciprocal weighting matters. The tool gives the correct mean for many rate aggregation cases. Use it instead of arithmetic mean for rate datasets.

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Input Pattern

Enter values in the left panel, keep units explicit, run the calculation, then copy or share the result. Invalid fields are highlighted immediately.

Harmonic Mean Inputs

Enter positive numbers separated by commas.

Result

Harmonic mean: 17.14285714

How to use this tool

Enter positive rate values.
Run the calculator to compute harmonic mean.
Apply result in rate-comparison or efficiency analysis.

Worked Example

Auto-generated from the tool's current default or entered inputs.

Example Inputs

Values: 10, 20, 40

Expected Outputs

Parsed values 0: 10
Parsed values 1: 20
Parsed values 2: 40
Harmonic mean: 17.142857

Interpretation

Parsed values 0 is 10.0. Use this as a decision input, not as a standalone conclusion.
Parsed values 1 is 20.0. Use this as a decision input, not as a standalone conclusion.
Parsed values 2 is 40.0. Use this as a decision input, not as a standalone conclusion.
Interpret this value alongside sample quality and assumptions to avoid overconfidence.

Scenario Compare (A vs B)

Use this to compare two input sets and quantify change in key outputs.

Confidence and limitations

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Interpretation depends on assumptions (distribution, independence, sample quality).

Formula References

Frequentist estimation and hypothesis-test formulas used in standard textbooks.
Interpretation depends on sample quality and assumptions.

Assumptions

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Interpretation depends on assumptions (distribution, independence, sample quality).

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