Math

Harmonic Mean Calculator

Average positive rates using the reciprocal-based harmonic mean.

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How to use Harmonic Mean Calculator

The harmonic mean is count divided by the sum of reciprocal values. For speeds, it applies when the distance traveled at each speed is equal.

All values must be strictly positive. This is an unweighted harmonic mean; it does not average arbitrary journeys with unequal distances.
Decimal inputs have at most 120 characters and magnitude from 1e-100 to 1e15, or zero. Floating-point results are rounded to 12 significant digits; extreme derived results may underflow or be rejected. Exact integer results are identified separately.

What calculation does Harmonic Mean Calculator perform?

The harmonic mean is count divided by the sum of reciprocal values. For speeds, it applies when the distance traveled at each speed is equal.

Why does averaging 30 and 60 give 40?

For equal travel distances, more time is spent at the slower speed, so the harmonic mean is 40 rather than the arithmetic average of 45.

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