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Harmonic Mean Rate Calculator

Calculate the harmonic mean, the correct average for rates and ratios.

About Harmonic Mean Rate Calculator

When equal distances are covered at different speeds, the average speed is the harmonic mean, not the arithmetic mean. The harmonic mean is always the smallest of the three classical means. Averaging speeds arithmetically overstates the true average whenever the distances rather than the times are equal, which is the usual case.

Formula

Harmonic Mean Rate

Harmonic mean = n ÷ Σ(1 ÷ xᵢ)

harmonic mean
Correct average when each rate applies over the same quantity, not the same time

Worked example

With the default values below, Harmonic Mean Rate Calculator returns Harmonic Mean of 48.64865. Change any input above and every figure here is recalculated in your browser.

Inputs used

Rate 1minimum 0
60
Rate 2minimum 0
40
Rate 3minimum 0
50
Equal quantity covered at each rateminimum 0
100

Results

Harmonic Mean
48.64865
Arithmetic Mean for Comparison
50.00000
Geometric Mean
49.32424
Total Time Across the Legs
6.16667
Amount the Arithmetic Mean Overstates
1.35135

Step by step

  1. 1Values used
  2. 2Harmonic Mean Rate
  3. 3Harmonic Mean= 48.64865
  4. 4Arithmetic Mean for Comparison= 50.00000
  5. 5Geometric Mean= 49.32424
  6. 6Total Time Across the Legs= 6.16667
  7. 7Amount the Arithmetic Mean Overstates= 1.35135

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Harmonic Mean Rate calculated?

Harmonic mean = n ÷ Σ(1 ÷ xᵢ) When equal distances are covered at different speeds, the average speed is the harmonic mean, not the arithmetic mean. The harmonic mean is always the smallest of the three classical means.

Why does Harmonic Mean Rate matter?

Averaging speeds arithmetically overstates the true average whenever the distances rather than the times are equal, which is the usual case.

What values do I need to enter?

This calculator takes 4 inputs: Rate 1, Rate 2, Rate 3, Equal quantity covered at each rate. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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Harmonic Mean Rate Calculator – Calculate Harmonic Mean