A compound unit such as km/h contains two units, distance and time, and converting it means converting both. This appears in speed questions where the data is in one unit and the answer is required in another.
It is the first lesson in rates, time and compound quantities, and every later lesson relies on it.
How do you convert a speed unit safely?
A speed unit is a fraction: distance over time. To change it, treat the distance part and the time part separately.
For km/h to m/s: the distance changes from km to m (× 1000) and the time changes from hours to seconds (÷ 3600 to express per second). Together that is × 1000 ÷ 3600, which simplifies to ÷ 3.6.
For m/s to km/h: reverse it, so × 3.6.
A quick sense check: a speed in m/s always gives a larger number in km/h. One m/s is a slow walk, yet 3.6 km/h.
Worked example
A cyclist rides at 18 km/h. Give the speed in m/s.
Step 1, distance unit: 18 km = 18 × 1000 = 18 000 m.
Step 2, time unit: 1 hour = 3600 s, so the speed is 18 000 m per 3600 s.
Step 3, divide: 18 000 ÷ 3600 = 5 m/s.
Step 4, check with the shortcut: 18 ÷ 3.6 = 5. The two routes agree.
Now reverse it. A runner moves at 8 m/s. In km/h: 8 × 3.6 = 28.8 km/h.
Check by parts: 8 m/s is 8 × 3600 = 28 800 m per hour, which is 28.8 km per hour.
The mistake to watch for
A common slip is to convert the distance and leave the time alone.
Mistaken answer: 72 km/h = 72 × 1000 = 72 000 m/s
The student changed km to m but forgot that the time is still in hours. The result claims a speed faster than sound, which a bus cannot reach.
The correction is to ask what the time unit is in the answer you want. Here it is seconds, so divide by 3600 as well: 72 000 ÷ 3600 = 20 m/s.
A second check stops this every time: decide beforehand whether the number should get bigger or smaller. Going from km/h to m/s, the number must get smaller.
Check yourself
Try these, then open each answer.
1. Convert 108 km/h to m/s.
Show answer
108 ÷ 3.6 = 30 m/s. Check: 30 × 3.6 = 108.
2. Convert 12.5 m/s to km/h.
Show answer
12.5 × 3.6 = 45 km/h. Check: 45 ÷ 3.6 = 12.5.
3. A cyclist travels 4.5 km in 15 minutes. Find the speed in km/h, then in m/s.
Show answer
15 min = 0.25 h, so speed = 4.5 ÷ 0.25 = 18 km/h. Then 18 ÷ 3.6 = 5 m/s.
Where this leads next
With units under control, move on to reading a distance-time graph, then try the rates mixed practice set. The non-calculator working trainer and the percentage-base explorer are useful for checking method on your own numbers.
Some students know the conversion rule but choose the wrong direction under pressure. That is the kind of pattern our teachers look for in online one-to-one Mathematics tuition.