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Converting km/h and m/s: speed from a short measurement segment

Deriving the m/s to km/h conversion, the uncertainty of short measurements, and correctly combining two road sections with different speeds.

DG Kalkulátor5 min read
Converting km/h and m/s: speed from a short measurement segment
qimono / Pixabay

For speed conversion, the 3.6 factor is sufficient, but to interpret the measurement you must also clarify the meaning of distance and time. Twenty metres in five seconds is 4 m/s, which is 14.4 km/h as a segment average. This data does not show the maximum speed reached in the meantime.

Where does 3.6 come from?

One hour is 3600 seconds, and one kilometre is 1000 metres. An object travelling at 1 m/s for one hour covers 3600 metres, which is 3.6 kilometres. Therefore, to convert from m/s to km/h you multiply by 3.6, and to convert in the reverse direction you divide by the same amount.

72 km/h is thus 20 m/s. As a check, consider this: twenty metres per second is 1200 metres in one minute, and 72 kilometres in one hour. The 3.6 factor is for expressing the same speed in a different unit; it does not create an instantaneous value from an average.

What does the measurement result mean?

In the illustrative twenty-metre measurement, v = 20 / 5 = 4 m/s. This is the average for the entire segment. The object may have accelerated and decelerated in the meantime; this cannot be determined from a single time datum. Therefore, record the number as a segment average.

If you measure 4.8 seconds instead of five seconds, the result is approximately 4.17 m/s, which is 15 km/h. A difference of two tenths of a second already causes a visible difference in such a short measurement. A longer measurement segment or multiple repetitions can help assess how constant the result is.

Pace and speed

Pace given in minutes per kilometre is inversely related to speed. 12 km/h means five minutes per kilometre: 60 / 12 = 5. For paces, therefore, the simple arithmetic mean can only be used under appropriate conditions. In the calculator, first standardise the speeds, and for a complex route, divide the total distance by the total time.

Average of two equal distances

On an illustrative route, you travel 1 kilometres at 10 km/h, then another 1 kilometres at 20 km/h at a constant speed. The first segment takes 6 minutes, and the second 3 minutes. The total 2 km takes 9 minutes, which is 0.15 hours, so the average is 13.33 km/h. The arithmetic mean of 15 km/h would be incorrect for these two segments of equal distance.

However, for segments of equal duration, the arithmetic mean of the two speeds is correct: in 6–6 minutes you would cover 1 and 2 km, a total of 3 km in 0.2 hours, which is 15 km/h. So first check whether you kept time or distance constant. At stops, add the waiting time to the denominator if you are looking for the average of the entire journey. Do not calculate speed from zero duration; you must correct a measurement error or incomplete data.

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Source and methodological background

The numerical examples are illustrative calculations prepared for this article.

Three-question knowledge test

Choose one answer for each question. Each correct answer earns 1 point; an incorrect answer, a skipped question or more than one selected answer earns 0 points. You can score 0–3 points in total. Read the solutions after answering.

1. How much is 10 m/s?

  • A) 36 km/h
  • B) 3.6 km/h
  • C) 100 km/h

2. What does total distance divided by total time show?

  • A) The average speed
  • B) The acceleration
  • C) The maximum speed

3. You travel two 1 km segments at 10 and then 20 km/h, without stopping. What is the average?

  • A) 15 km/h
  • B) 13.33 km/h, approximately
  • C) 30 km/h

Solutions and self-scoring

Each correct answer is worth 1 point; an incorrect or skipped answer is worth 0 points. A maximum of 3 points can be obtained. 3 points: You correctly handled both the conversion and the time weighting of the segments. 2 points: Review the section named in the missed question and recalculate its example. 0–1 points: Go through the three solutions, then solve the questions again. This short test checks your understanding of the article's connections.

1. Solution

A) 36 km/h – 10 × 3.6 = 36 km/h. If you gave a different answer or skipped it, review this section: Where does 3.6 come from?.

2. Solution

A) The average speed – You get the average for the entire segment, not the changes in between. If you gave a different answer or skipped it, review this section: What does the measurement result mean?.

3. Solution

B) 13.33 km/h, approximately – Adding 6 and 3 minutes gives you 9 minutes; 2 / (9/60) ≈ 13.33 km/h. More time passed during the slower segment. If you gave a different answer or skipped it, review this section: Average of two equal distances.

Translated and adapted from the Hungarian article: Hungarian original.