Harmonic Mean Calculator

Find the harmonic mean of positive values, ideal for averaging rates and ratios.

Harmonic Mean

48.0000

Arithmetic Mean (for comparison)50.0000

Harmonic Mean vs Value 1

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Formula

## How to Compute the Harmonic Mean ### Formula (for two values) **Harmonic Mean = 2 / (1/a + 1/b)** More generally for n values: **HM = n / (1/v1 + 1/v2 + ... + 1/vn)** The harmonic mean gives more weight to smaller values. It is the correct average to use when the quantities are defined in relation to a common unit, such as speed over the same distance at different rates.

Esempio Risolto

A car travels 100 km at 40 km/h and returns at 60 km/h. What is the average speed?

  1. 01Reciprocal sum = 1/40 + 1/60 = 0.025 + 0.01667 = 0.04167
  2. 02Harmonic Mean = 2 / 0.04167 = 48
  3. 03The average speed is 48 km/h (not 50 as the arithmetic mean would suggest)