Calculate the harmonic mean, the correct average for rates and ratios.
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.
Harmonic Mean Rate
Harmonic mean = n ÷ Σ(1 ÷ xᵢ)
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.
Averaging speeds arithmetically overstates the true average whenever the distances rather than the times are equal, which is the usual case.
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.