The Relationship
Speed, distance and time form one of the simplest and most useful relationships in physics. Know any two and the third follows.
Speed = Distance ÷ Time
Distance = Speed × Time
Time = Distance ÷ Speed
The only trap is units. Mixing miles with hours and metres with seconds in the same calculation produces nonsense, so this calculator converts everything internally to metres and seconds before doing the arithmetic.
Speed Unit Conversions
| Unit | m/s | km/h | mph | knots |
|---|---|---|---|---|
| 1 m/s | 1 | 3.600 | 2.237 | 1.944 |
| 1 km/h | 0.278 | 1 | 0.621 | 0.540 |
| 1 mph | 0.447 | 1.609 | 1 | 0.869 |
| 1 knot | 0.514 | 1.852 | 1.151 | 1 |
| 1 ft/s | 0.305 | 1.097 | 0.682 | 0.592 |
A knot is one nautical mile per hour, and a nautical mile is one minute of latitude — 1,852 metres. That is why ships and aircraft use it: a degree of latitude is exactly 60 nautical miles, which makes chart navigation straightforward.
Quick Mental Conversions
- mph to km/h: add 60%. 60 mph ≈ 96 km/h.
- km/h to mph: multiply by 0.6, or use Fibonacci — 50 km/h ≈ 30 mph, 80 ≈ 50, 130 ≈ 80.
- m/s to km/h: multiply by 3.6.
- km/h to m/s: divide by 3.6.
- Knots to mph: add about 15%.
Familiar Speeds
| Thing | m/s | km/h | mph |
|---|---|---|---|
| Walking | 1.4 | 5.0 | 3.1 |
| Jogging | 2.7 | 9.7 | 6.0 |
| Cycling, casual | 5.6 | 20 | 12.4 |
| Usain Bolt, peak | 12.4 | 44.7 | 27.8 |
| City driving | 13.4 | 48 | 30 |
| Motorway driving | 31.3 | 113 | 70 |
| High-speed train | 89 | 320 | 199 |
| Airliner cruise | 250 | 900 | 559 |
| Speed of sound (sea level) | 343 | 1,235 | 767 |
| Speed of light | 299,792,458 | 1.08 billion | 671 million |
Average Speed Is Not the Average of Speeds
This trips up almost everyone. If you drive 60 miles at 60 mph and the return 60 miles at 30 mph, your average speed is not 45 mph.
| Leg | Distance | Speed | Time |
|---|---|---|---|
| Out | 60 mi | 60 mph | 1.0 h |
| Back | 60 mi | 30 mph | 2.0 h |
| Total | 120 mi | 40 mph | 3.0 h |
The correct answer is 40 mph, because you spend twice as long at the slower speed. Average speed is always total distance divided by total time — the harmonic mean, not the arithmetic one. The slower leg dominates.
Why Speeding Saves So Little Time
Time saved falls off sharply as speed rises, because time is inversely proportional to speed. Over a 100-mile journey:
| Speed | Time | Saved vs. 60 mph |
|---|---|---|
| 60 mph | 1 h 40 min | — |
| 65 mph | 1 h 32 min | 8 min |
| 70 mph | 1 h 26 min | 14 min |
| 80 mph | 1 h 15 min | 25 min |
| 90 mph | 1 h 7 min | 33 min |
On a typical 20-mile commute, driving at 80 instead of 70 saves under two minutes — while fuel consumption rises roughly 10–15% and stopping distance grows with the square of speed.
Speed and Velocity
In everyday use the words are interchangeable; in physics they are not. Speed is a scalar — a magnitude only. Velocity is a vector, with both magnitude and direction. A car going round a roundabout at a constant 20 mph has constant speed but continuously changing velocity, and therefore an acceleration, which is exactly why you feel pushed sideways.
Frequently Asked Questions
How long will a 240-mile trip take at 65 mph?
240 ÷ 65 = 3.69 hours, or 3 hours 41 minutes — before stops, traffic and slower sections.
How do I convert mph to km/h?
Multiply by 1.609. Mentally, add 60%: 70 mph is about 112 km/h.
Why is my journey slower than the calculation?
Because the figure assumes constant speed. Junctions, traffic, roadworks and stops all reduce the real average, which is typically 10–25% below the cruising speed on a long drive.
What is a knot?
One nautical mile per hour, equal to 1.852 km/h or 1.151 mph. The name comes from the knotted rope once used to measure a ship's speed.