Math Calculators

Harmonic Mean Calculator

Calculate the harmonic mean of a list of positive numbers, ideal for averaging rates.

Harmonic mean —

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About the Harmonic Mean Calculator

The harmonic mean divides the count of values by the sum of their reciprocals. It gives more weight to smaller values, which makes it the correct average to use for rates, such as average speed over equal distances.

Formula: Harmonic Mean = n ÷ (1/x₁ + 1/x₂ + ... + 1/xₙ)

For example, averaging speeds of 10, 20 and 30 mph over equal distances uses the harmonic mean, not the arithmetic mean, to get the correct overall average speed.