What this speed converter does
This tool converts between the five speed units that appear most often in Pakistani school problems and everyday contexts: metres per second (m/s), kilometres per hour (km/h), miles per hour (mph), knots (nautical miles per hour) and feet per second (ft/s). Every conversion goes through the SI base unit (m/s) internally. The article explains the 5/18 factor that every BISE student needs to memorise, the difference between the statute mile used in mph and the nautical mile used in knots, and a real-world reference table with speeds ranging from walking (1.4 m/s) up through the Pakistani motorway limit (120 km/h) to the cruising speed of a PIA jet (900 km/h) and the speed of sound (1234.8 km/h).
The 5/18 factor — why it works
The most important speed conversion in school physics is between km/h and m/s. It reduces to the fraction 5/18 (or its reciprocal, 3.6), and both are worth memorising.
The reason is simple: in one hour there are 3600 seconds, and in one kilometre there are 1000 metres. So 1 m/s means 3600 metres per hour = 3.6 km/h. Reading it the other way, 1 km/h means 1000 metres per 3600 seconds = 5/18 m/s.
Worked examples
Example 1: 72 km/h to m/s (the classic)
- Multiply by 5/18.
- Result = 72 × 5/18 = 72 / 3.6 = 20 m/s.
- The most common conversion in BISE motion problems.
Example 2: 20 m/s to km/h (reverse)
- Multiply by 3.6.
- Result = 20 × 3.6 = 72 km/h.
- Confirms the previous example in the other direction.
Example 3: 100 km/h to m/s
- 100 × 5/18 = 500 / 18.
- Result = 27.78 m/s.
- A car at motorway speed covers about 28 metres every second.
Example 4: 8 m/s to km/h (sprinting athlete)
- 8 × 3.6.
- Result = 28.8 km/h.
- The fastest human sprint is about 12 m/s = 43 km/h (Usain Bolt).
Example 5: 60 mph to km/h
- 1 mph = 1.609344 km/h.
- Result = 60 × 1.609344 = 96.56 km/h.
- A common US highway speed — just under the Pakistani motorway limit.
Example 6: 30 knots to km/h (marine / aviation)
- 1 knot = 1.852 km/h.
- Result = 30 × 1.852 = 55.56 km/h.
- A speedboat cruising at 30 knots. A ship's log or aircraft airspeed indicator uses knots.
Example 7: 343 m/s to km/h (speed of sound)
- 343 × 3.6.
- Result = 1234.8 km/h.
- Speed of sound in dry air at 20 °C. Supersonic aircraft fly faster than this (Mach 1 = speed of sound).
Example 8: 32 ft/s to m/s (imperial gravity)
- 1 ft = 0.3048 m.
- Result = 32 × 0.3048 = 9.754 m/s.
- Approximately the acceleration due to gravity in imperial units (32 ft/s² ≈ 9.8 m/s²). This comes up in US or older physics textbooks.
mph vs knots — the nautical difference
Both mph and knots look like "miles per hour", but they use different miles.
| Unit | Speed in km/h | Speed in m/s | Mile definition |
|---|---|---|---|
| 1 mph (statute) | 1.609344 | 0.44704 | 1609.344 m (statute mile) |
| 1 knot (nautical) | 1.852 | 0.514444 | 1852 m exactly (nautical mile) |
The nautical mile is about 15% longer than the statute mile, so 1 knot is about 15% faster than 1 mph. Aviation and marine navigation use knots because a nautical mile is defined as one minute of latitude on the Earth's surface — so if you know your position in degrees and minutes, distance in nautical miles is straightforward to read off a chart. A typical airliner cruises at about 480 knots (≈ 900 km/h), and fast patrol boats often top out around 40 knots (≈ 74 km/h).
Real-world speed reference
These everyday speeds help you sanity-check any conversion.
| Object / motion | km/h | m/s | Notes |
|---|---|---|---|
| Walking | 5 | 1.4 | Typical adult pace |
| Jogging | 10 | 2.8 | Recreational pace |
| Sprinting (top athlete) | 43 | 12 | Usain Bolt range |
| City traffic (Karachi, Lahore) | 40–60 | 11–17 | Varies heavily with congestion |
| Pakistani motorway limit (cars) | 120 | 33.3 | M-2 Lahore–Islamabad |
| Pakistani motorway limit (heavy vehicles) | 100 | 27.8 | Buses and trucks |
| Passenger train (Pakistan Railways) | 60–120 | 17–33 | Varies by route and train type |
| Speedboat | 55 | 15.3 | 30 knots |
| PIA jet cruise (typical airliner) | 850–920 | 236–256 | About Mach 0.85 |
| Speed of sound (20 °C, sea level) | 1234.8 | 343 | Mach 1 |
| Speed of light | 1.08e9 | 3e8 | Fundamental constant c |
A useful rule of thumb: walking is about 1.4 m/s, city driving is about 14 m/s, and motorway driving is about 33 m/s. Having these anchors in mind lets you quickly check whether a computed speed is plausible.
Full reference table
Exact or standard equivalences for every unit in the converter.
| Unit | In m/s | In km/h | In mph |
|---|---|---|---|
| 1 m/s | 1 | 3.6 | 2.23694 |
| 1 km/h | 0.27778 | 1 | 0.621371 |
| 1 mph | 0.44704 | 1.609344 | 1 |
| 1 knot | 0.514444 | 1.852 | 1.15078 |
| 1 ft/s | 0.3048 | 1.09728 | 0.681818 |
The 5/18 and 3.6 factors in the top two rows are the most frequently used — worth memorising in both directions. The remaining rows appear less often but are still useful for imported problems or technical specifications.
Common mistakes to avoid
- Multiplying by 5/18 when you should divide (or vice versa). km/h → m/s uses × 5/18. m/s → km/h uses × 3.6. Reversing these gives an answer that is off by a factor of 12.96. Remember: m/s is the bigger number for the same physical speed (since 1 m/s = 3.6 km/h).
- Using 1 m/s = 3.6 km/h but writing it as 1 m/s = 36 km/h. A factor-of-10 slip. 1 m/s is 3.6 km/h, not 36.
- Confusing mph with knots. mph uses the statute mile (1609.344 m); knots use the nautical mile (1852 m exactly). The difference is about 15%. Aviation and marine navigation use knots; road speeds in the US and UK use mph.
- Assuming a "mile" in an old textbook is the modern statute mile. Some pre-1959 British textbooks use a slightly different mile. Modern school problems always use the international statute mile = 1609.344 m.
- Forgetting that ft/s appears in older imperial problems. Gravity in imperial units is 32 ft/s². This comes up in American or older physics texts. Convert to m/s by multiplying by 0.3048.
- Treating speed and velocity as interchangeable. Speed is a scalar (magnitude only); velocity is a vector (magnitude + direction). This converter handles magnitudes only — it cannot convert negative speeds or directional changes.
- Mixing km/h with seconds in a distance problem. If speed is in km/h and time in seconds, you must convert one to match the other before multiplying for distance. s = d/t works only when the units are consistent.
FAQ
How do I convert km/h to m/s?
Multiply km/h by 5/18, which is the same as dividing by 3.6. For example, 72 km/h = 72 × 5/18 = 20 m/s. The factor comes from 1000 m per km divided by 3600 s per hour. This is the single most used conversion in BISE physics.
How do I convert m/s to km/h?
Multiply m/s by 3.6. For example, 20 m/s = 20 × 3.6 = 72 km/h. This is the inverse of the km/h to m/s conversion and is the more common direction in exam questions because answers to physics problems are often in m/s but road speeds are quoted in km/h.
What is the difference between mph and knots?
mph means miles per hour, using the statute mile (1609.344 m). Knots mean nautical miles per hour, using the nautical mile (exactly 1852 m). One knot = 1.852 km/h = 1.15078 mph. Aviation and marine navigation use knots because a nautical mile corresponds to one minute of latitude, simplifying position calculations on charts.
What is a typical Pakistani motorway speed?
Pakistani motorways (like the M-2 Lahore–Islamabad) have a speed limit of 120 km/h for cars and 100 km/h for heavy vehicles. Typical cruising speed is 100–120 km/h. City driving in Karachi or Lahore is usually 30–60 km/h with heavy traffic reducing it further.
What is the speed of sound?
The speed of sound in dry air at 20 °C is about 343 m/s, which is 1234.8 km/h or about 667 knots. At higher altitudes (where air is colder and thinner), it is slower — around 295 m/s at 11 km altitude. Objects faster than this are supersonic; the speed of sound is also called Mach 1.
Why is 1 m/s equal to 3.6 km/h?
In one hour there are 3600 seconds, and in one kilometre there are 1000 metres. So 1 m/s means 1 metre every second, which is 3600 metres every hour, which is 3.6 kilometres every hour. So 1 m/s = 3.6 km/h, and 1 km/h = 5/18 m/s ≈ 0.2778 m/s.
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