The units of speed
Speed is distance divided by time, so every conversion is really two conversions at once. The SI unit is the metre per second, which is what every physics formula expects; kilometres per hour and miles per hour are the everyday units, and knots survive in aviation and at sea because a nautical mile is one minute of latitude.
| Unit | Symbol | Equals |
|---|---|---|
| Metres per second | m/s | 1 m/s |
| Kilometres per hour | km/h | 0.27777778 m/s |
| Miles per hour | mph | 0.44704 m/s |
| Knots | kn | 0.51444444 m/s |
| Feet per second | ft/s | 0.3048 m/s |
How to convert by hand
Every speed conversion follows the same procedure: take the amount to the base unit, then from there to the target unit. In practice it is a single multiplication, because the two steps combine into one factor.
Convert to metres per second first, then out to the target. The three factors worth memorising: divide km/h by 3.6 for m/s, multiply mph by 1.609 for km/h, and multiply knots by 1.852 for km/h.
The equivalents people look up most
| Conversion | Result |
|---|---|
| A walking pace | 5 km/h · 3.1 mph · 1.4 m/s |
| An urban speed limit | 50 km/h · 31 mph · 13.9 m/s |
| A motorway limit | 120 km/h · 74.6 mph · 33.3 m/s |
| A cruising airliner | 889 km/h · 480 kn |
| Usain Bolt at peak | 44.7 km/h · 12.4 m/s |
Common mistakes
- Putting km/h into a formula that expects m/s. Every kinematics equation assumes SI units, and the answer comes out 3.6 times wrong.
- Saying knots per hour. A knot is already a speed.
- Assuming 60 mph is 100 km/h. It is 96.6, so 0-60 and 0-100 acceleration figures are not comparable.
- Converting an average speed by averaging two speeds. Average speed is total distance over total time, not the mean of the two figures.