Round Trip Average Speed (Harmonic Mean)

Find the true average speed of a round trip over equal distances from your outbound and return speeds, using the harmonic mean.

Input

When you travel the same distance out and back, the overall average speed is the harmonic mean 2 v1 v2 ÷ (v1 + v2). Enter your outbound and return speeds.

Speed unit

Outbound speed v1

km/h

Return speed v2

km/h

The distance does not affect the result. No matter how long each leg is, the average speed depends only on the two speeds.

Result

Round trip average speed (harmonic mean)

km/h

Simple arithmetic mean

50 km/h

Difference from arithmetic mean

2 km/h

Slower than arithmetic mean

4 %

Average speed = 2 v1 v2 ÷ (v1 + v2). This is the harmonic mean of the outbound speed v1 and return speed v2, and it is always at most the arithmetic mean (v1 + v2) ÷ 2. They are equal only when v1 equals v2.

How it works

For a round trip over equal distances, the average speed is the total distance divided by the total time. With outbound speed v1 and return speed v2, the average speed equals 2 v1 v2 ÷ (v1 + v2), which is the harmonic mean of v1 and v2.
The average speed does not depend on the distance. The distance cancels out of the formula, so the result is the same whether each leg is short or long.
The harmonic mean is always at most the arithmetic mean (v1 + v2) ÷ 2. A faster leg takes less time, so the slower leg dominates the total time and pulls the average down. The two means are equal only when v1 equals v2.
For example, going at 60 km/h and returning at 40 km/h gives an average of 48 km/h, which is below the arithmetic average of 50 km/h.
Speeds must be positive. Zero or negative values do not represent real motion and cannot be used. Keep both legs in the same unit.

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