Convert km/h to mph

Kilometres per hour is the speed limit almost everywhere in the world. Dividing by 3.6 gives metres per second, because there are 3,600 seconds in an hour and 1,000 metres in a kilometre.

Miles per hour is the road speed of the United States and the United Kingdom, which is a rare pairing — the UK uses miles for road speed and metric for nearly everything else.

The factor is 0.621371, and almost nobody carries that around. Rounded to 0.62 it is off by 0.22 % — which stays invisible on small numbers and turns into a whole unit somewhere around 1,000 km/h.

That is the number worth knowing before you round: not the error itself, but where it stops being ignorable. Below that point the shorter factor is the sensible one; above it, use the field above, which never rounds until it prints.

A speed is a distance over a time, and these two are counted over the same time. The hour on each side cancels, which leaves 0.621371 — the plain km-to-mi factor, with nothing added for the clock.

That makes this the one speed conversion you already know the number for: whatever you use to turn a road distance in km into mi works unchanged on a road speed, because the time unit never enters the arithmetic at all.

The mile per hour has been defined in metric terms since the international yard and pound agreement of 1959, and in this page's units that comes out at 1.609344 km/h to one. The definition is exact by stipulation — it was not measured, and it cannot be refined by measuring it better. The decimal above is the whole of it, with nothing rounded away at the end.

Before that agreement the US and the British versions differed slightly, and old survey figures still carry the older definition. For anything outside land surveying the difference is far below the precision anybody is working to.

Five numbers cover most of continental Europe. 50 km/h is the default in built-up areas and comes out at 31 mph; 80 or 90 km/h on an ordinary rural road is 50 or 56 mph; 110 or 120 km/h on a dual carriageway is 68 or 75 mph; and 130 km/h, the motorway figure in France, Italy and much of eastern Europe, is 81 mph. None of those is far from a limit a British or American driver already knows, which is why the unit change is a smaller adjustment than it looks.

The one that catches people is the low end. A 30 km/h zone — increasingly the default in city centres — is 19 mph, not 30, and reading it as a familiar number puts you at roughly half again the posted speed. The same trap sits at 20 km/h in a residential or shared-space zone, which is 12 mph and slower than most people cycle.

A limit that is a round number in one unit is almost never round in the other, and that asymmetry is a useful reading aid. Continental limits are round in kilometres per hour and untidy in miles: 50, 80, 120 and 130 become 31.07, 49.71, 74.56 and 80.78. British limits are round the other way: 30, 60 and 70 mph are 48.28, 96.56 and 112.65 km/h.

So when a converted figure lands on something like 62 or 81, the number was set in metric and you are the one doing the translating. When a metric figure lands on something ugly like 48 or 113, the limit was set in miles and somebody has already converted it for you — which happens on hire-car documentation, on some border signage and in the small print of European car reviews written for a British audience.

The exact factor is 0.621371, and five eighths — 0.625 — is close enough to run the whole trip on. Halve the number, then add a quarter of that half: 120 becomes 60 plus 15, so 75 mph against a true 74.6. At 130 it gives 65 plus 16 to make 81, and the exact answer is 80.8.

The error is 0.6 per cent high and it always points the same way, which is the useful part: the shortcut never tells you a limit is lower than it is. If you would rather work from the other end, the Fibonacci pairs are exact enough to be eerie — 8 km/h is 5 mph, 13 is 8, 21 is 13, 55 is 34, 89 is 55. Each of those is right to within a third of a mile an hour.

A speedometer in a European-market car is built to a rule that is deliberately one-sided: the indicated speed may never be lower than the true speed, and may exceed it by at most ten per cent plus 4 km/h. There is no tolerance in the other direction at all. A car showing 120 km/h is therefore doing somewhere between about 105 and 120, and converting the dial reading gives you the pessimistic end of that band rather than your actual speed.

This matters more than the arithmetic on any single conversion. If you convert 120 km/h to 75 mph and then compare it against a satellite-derived figure on your phone, the two will disagree by more than the rounding in the factor, and the phone is usually the honest one. Tyre wear and a change of tyre size move the dial too, always in the direction of reading high as the tyre wears down.

Cars sold in the United Kingdom and Ireland almost always carry both scales, with one printed large and the other in a smaller inner ring. Which is which depends on the market the car was built for, and on a hire car collected in another country the ring you want may be the one you cannot read at a glance in the dark. A digital display usually has a unit toggle buried in the instrument settings, and finding it before you leave the car park is worth more than any mental shortcut.

Ireland is the case that surprises people, because the language on the signs is familiar and the unit is not. Irish speed limit signs changed from miles to kilometres per hour on 20 January 2005 and distances went metric with them, while Northern Ireland kept miles — so a single day's driving on the island crosses the unit boundary twice.

The dangerous direction is metric to imperial in a low-speed zone, because the numbers are close enough to look like each other. Thirty is thirty on both signs and means 19 mph on one of them. A residential 30 km/h street driven at 30 mph is 48 km/h, which is over the general urban limit as well as the local one.

At the top end the error runs the other way and is mostly harmless: a driver who reads 130 as a mile-per-hour figure will drive far too slowly for a motorway and be a nuisance rather than a hazard. The asymmetry is worth remembering when you are tired — the mistake that matters is always the one in town.

Converting the speed solves one number and leaves the others. Distances on the same signs are in kilometres, so an exit at 45 km is 28 miles, and the fuel that gets you there is sold in litres. A driver who converts only the speed ends up doing the journey planning in one system and the driving in another, which is more mental arithmetic than doing the whole trip in metric would have been.

The useful pairing is that 100 km/h covers 100 km in an hour and 62 miles in the same hour, so a journey of 300 km at motorway speed is three hours and 186 miles. Once the distance and the speed are in the same system the time falls out without any conversion at all, which is the argument for converting at the planning stage and then leaving the unit alone until you are back home.

The mile-per-hour figure is always the smaller of the two, by a bit more than a third. If your answer is larger than the number you started with, the conversion went the wrong way, and no amount of decimal places will rescue it.

Beyond that, the arithmetic here does not need policing. The factor between the two units is fixed by definition and the field above carries it to more digits than any road sign deserves, so the only real sources of error are direction and the speedometer itself.