Why speed has so many units
Speed is distance divided by time, so it inherits a unit from each. Every combination that anyone found convenient has survived somewhere: road transport in miles or kilometres per hour, physics in metres per second, ballistics and short-distance kinematics in feet per second, and marine and aviation navigation in knots. They all describe the same quantity, and converting between them is one multiplication.
The factors are exact because the underlying lengths are defined rather than measured. The 1959 International Yard and Pound Agreement fixed the yard at 0.9144 m, and a mile is 1,760 yards, so a mile is exactly 1,609.344 m. Divide by 3,600 seconds in an hour and one mile per hour is exactly 0.44704 m/s. The kilometre per hour is even simpler: 1,000 m over 3,600 s, so km/h ÷ 3.6 gives m/s.
The knot is the outlier, and it is the one with the best reason to exist. A nautical mile was originally one minute of arc of latitude, which makes it a natural unit for navigation: a degree of latitude is 60 nautical miles anywhere on the globe. Since the Earth is not a perfect sphere, that definition varied slightly with latitude, so it was standardised at exactly 1,852 m. A knot is one nautical mile per hour, or 1.852 km/h, and it remains the working unit at sea and in the air precisely because it maps directly onto a chart.
The factors, and the ones worth memorising
Working through metres per second as a pivot keeps the set small. The full list:
- mph to m/s: × 0.44704. That is 1,609.344 ÷ 3,600.
- km/h to m/s: ÷ 3.6. Exactly, since 1,000 ÷ 3,600 = 1/3.6.
- ft/s to m/s: × 0.3048. The foot definition itself.
- knots to m/s: × 0.5144444... That is 1,852 ÷ 3,600.
- mph to km/h: × 1.609344, and back by ÷ 1.609344, which is the same as × 0.62137119.
Three approximations are worth carrying in your head. First, mph × 1.6 gets you within 0.6% of km/h, which is fine for reading a foreign speed limit. Second, km/h × 0.62 goes the other way — 100 km/h is about 62 mph, the everyday case; the cruder × 0.6 gives 60 mph and errs on the safe side of a limit. Third, and most useful in a vehicle, mph × 1.47 gives feet per second: 60 mph is 88 ft/s exactly, and that identity is the basis of every reaction-distance rule of thumb, since a one-second reaction at 60 mph covers 88 feet.
Running pace is the reciprocal of speed, not a scaled version of it, which is why it behaves differently. Minutes per mile is 60 divided by mph, so a 10 mph runner holds a 6:00 mile, and an 8 mph runner holds 7:30. Because it is a reciprocal, equal changes in pace are not equal changes in speed: going from 10 mph to 11 mph saves 33 seconds a mile, while 5 mph to 6 mph saves two full minutes.
Worked example: a 100 km/h motorway limit in mph
You are driving abroad and the sign reads 100 km/h. Your speedometer is graduated in mph.
- Convert to metres per second. 100 ÷ 3.6 = 27.778 m/s.
- Convert to mph. 27.778 ÷ 0.44704 = 62.137 mph. Equivalently, 100 ÷ 1.609344 = 62.137.
- What to hold. Sixty-two mph. The rough rule — multiply km/h by 0.6 — gives 60 mph, which is 96.6 km/h and leaves 3.4 km/h in hand.
- In feet per second. 27.778 ÷ 0.3048 = 91.13 ft/s, so a one-second lapse of attention covers 91 feet, roughly six car lengths.
- In knots. 27.778 ÷ 0.5144444 = 53.996 kn, which is the figure a marine or aviation instrument would show for the same speed over the ground.
Reverse the problem and the arithmetic is identical. A US 70 mph limit is 70 × 1.609344 = 112.65 km/h, which is why most European motorway limits of 110–130 km/h feel familiar to an American driver: 110 km/h is 68.4 mph and 130 km/h is 80.8 mph.
Reading a converted speed in context
Round to the precision the situation has. A speed limit is a legal threshold, so convert it and round down to stay inside it: 100 km/h is 62.14 mph, and holding 62 mph keeps you legal while 63 does not. A speedometer, by contrast, is not a precision instrument — UNECE Regulation 39, which governs speedometers for most of the world, requires that the indicated speed never be lower than the true speed and sets an upper bound on how much higher it may read. That is why a car's speedometer typically reads a few per cent optimistic and a GPS-derived speed reads lower.
For physics and engineering, work in metres per second and convert only for presentation. Kinetic energy goes with the square of speed and drag with roughly the square as well, so a speed carried in mixed units through a chain of formulas produces errors that are hard to trace. The braking and stopping distance calculator shows why: doubling speed roughly quadruples the braking distance, so a unit slip of 1.6 becomes a factor of 2.6 in the answer.
At sea and in the air, keep knots. Charts, air traffic control, wind reports and vessel speed logs are all in knots, and converting to km/h to do a calculation and back again invites transcription errors. The one figure worth knowing is that a knot is 1.15 mph and 1.85 km/h — see the knots to mph calculator for the marine and aviation cases.
Speed limits and common speeds in four units
| Miles per hour | Kilometers per hour | Meters per second | Feet per second |
|---|---|---|---|
| 20 | 32.187 | 8.941 | 29.333 |
| 25 | 40.234 | 11.176 | 36.667 |
| 30 | 48.280 | 13.411 | 44.000 |
| 35 | 56.327 | 15.646 | 51.333 |
| 40 | 64.374 | 17.882 | 58.667 |
| 45 | 72.420 | 20.117 | 66.000 |
| 50 | 80.467 | 22.352 | 73.333 |
| 55 | 88.514 | 24.587 | 80.667 |
| 60 | 96.561 | 26.822 | 88.000 |
| 65 | 104.607 | 29.058 | 96.333 |
| 70 | 112.654 | 31.293 | 103.333 |
| 75 | 120.701 | 33.528 | 110.000 |
The feet-per-second column is mph times exactly 22/15, which is why 60 mph is exactly 88 ft/s and 30 mph is exactly 44 ft/s.
Speed conversion traps
- Treating a knot as a mile per hour. A knot is 15.1% faster than a mile per hour, because a nautical mile is 1,852 m against the statute mile's 1,609.344 m. Writing “knots per hour” compounds the error: a knot already contains the hour.
- Dividing km/h by 1.6 and calling it exact. Dividing by 1.6 is the same as multiplying by 0.625, against the true 0.621371, so it overstates mph by 0.58%. At 130 km/h that is 81.25 mph against the true 80.78 — nearly half a mile per hour on the wrong side of a legal limit.
- Rounding a speed limit upward. Convert and round toward the slower speed. 50 km/h is 31.07 mph, so 31 mph is inside the limit and 32 is not.
- Trusting the speedometer as ground truth. Regulations such as UNECE R39 require speedometers to read at or above true speed, never below, so an indicated speed is generally a little optimistic. Tyre size and wear shift it further — see the tire size to inches diameter calculator.
- Confusing speed with pace. Pace is the reciprocal of speed, so it does not scale linearly. Averaging two paces is not the same as averaging two speeds, and for a run split into equal distances the correct average speed is the harmonic mean of the segment speeds.
- Carrying mixed units into a squared term. Kinetic energy and drag both scale with the square of speed, so a unit error of 1.609 becomes 2.59 in the result. Convert to metres per second before any physics.
Related speed, distance and pace tools
Speed conversions usually sit next to a distance conversion. The miles to kilometers calculator handles the length side with the same exact 1.609344 factor, and the meters to feet calculator covers the metric-imperial length pair generally.
For runners and cyclists, pace is the working unit rather than speed, and the useful question is usually what a given pace implies over a race distance — the race time prediction calculator takes that on. For drivers, the practical consequence of a speed is a distance: reaction distance is linear in speed while braking distance goes with its square, which the braking and stopping distance calculator works through.
One conversion this page deliberately leaves out is Mach number. Mach is a ratio of true airspeed to the local speed of sound, and the speed of sound depends on air temperature — roughly 340 m/s at 15 °C at sea level, and slower at altitude where the air is colder. Because there is no fixed number of metres per second in a Mach, it is not a unit conversion but a calculation requiring the atmospheric conditions.