Convert km to mi

Kilometres are the road distance nearly everywhere outside the United States and the United Kingdom, which is why converting them is usually about reading a map or a race entry.

A mile is 1,760 yards — a number that comes from a Roman thousand paces, adjusted by an Elizabethan statute to fit the furlong. It is exactly 1,609.344 metres.

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.

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.

The mile 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 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.

Multiplying by 0.6 is the one everybody knows and the worst of the three. The true factor is 0.621371, so 0.6 is 3.4 per cent low: fine for 5 km, where it costs a tenth of a mile, and not fine for a 300 km drive, where it hides ten miles. The error is proportional, which means it grows exactly where you stop being able to check it.

Halving and adding an eighth is better and no harder. Half of a kilometre figure plus an eighth of it is 0.625 of it, which is 0.58 per cent high — an error of about six miles in a thousand. For 80 km that is 40 plus 10, giving 50 miles against a true 49.71. Over any distance a person drives in a day the shortcut and the calculator agree to the nearest mile.

Consecutive Fibonacci numbers convert between the two units. 5 km is about 3 miles, 8 km about 5, 13 km about 8, 21 km about 13, 34 km about 21. This is not a mnemonic somebody invented; it falls out of the ratio between successive terms converging on 0.6180, which happens to sit half a per cent below the real 0.6214.

That half per cent is the accuracy ceiling, and the sequence reaches it quickly: 8 km is 4.97 miles against the 5 you would say, 13 km is 8.08 against 8, 21 km is 13.05 against 13, 34 km is 21.13 against 21. The single weak step is the first, where 5 km is really 3.107 miles and calling it 3 is 3.4 per cent low. Start at 8 and the trick is better than most people need.

The mile is not a measured quantity. It has been exactly 1,609.344 metres since the international yard and pound agreement of 1959, when the United States, the United Kingdom, Canada, Australia, New Zealand and South Africa agreed on a yard of exactly 0.9144 m and let the mile, foot and inch follow from it. Before that a US mile and a UK mile differed in the seventh decimal place, which mattered to surveyors and to nobody else.

So the conversion from kilometres has no measurement error in it at all. One kilometre is exactly 1,000 divided by 1,609.344 miles, a decimal that does not terminate, and every discrepancy between two converters is a rounding choice made on the way to the screen. If two answers disagree in the fourth decimal, one of them truncated a factor before multiplying rather than after.

The distances on a European sign are whole kilometres, which means their mile equivalents never are. 50 km/h in a town is 31 mph, 80 km/h on a rural road is 50 mph, 100 km/h is 62 mph and the French and German 130 km/h is 81 mph. The one pairing worth memorising is 80 km/h and 50 mph, because they are close enough that a driver used to a 50 mph limit can treat the two as the same rule.

Distance signs are easier because precision does not matter: a sign reading 240 km to the next city is 149 miles, and knowing it is "about 150" is the whole of what the sign was for. The place drivers go wrong is fuel and range, where the units are compounded — litres per 100 km against miles per gallon inverts the fraction as well as converting it, and the two numbers move in opposite directions.

Road racing is metric almost everywhere and the mile figures are all untidy. A 5K is 3.107 miles, a 10K is 6.214, a half marathon at 21.0975 km is 13.109, and the marathon at 42.195 km is 26.219 — the 26.2 that appears on every bumper sticker. Only the 5K and 10K are round in the system they were set in, and none of them is round in miles.

The marathon is the interesting case because the metric number is the translation, not the original. The distance was fixed by the international federation in 1921 at 26 miles 385 yards, which is 42,194.988 metres exactly; 42.195 km is that figure rounded up by twelve millimetres. An awkward number in both systems, and awkward because it was inherited from a particular course rather than chosen.

A used car advertised at 148,000 km is a 91,963-mile car, and the psychological difference between those two numbers is most of why the conversion gets searched. Round figures cross badly in both directions: 100,000 km is 62,137 miles and 100,000 miles is 160,934 km, so neither system's milestone means anything in the other, and a car a shade under 100,000 in one is unremarkable in the other.

Service intervals carry the same problem with a sharper edge. A schedule written as every 15,000 km is every 9,321 miles, and an owner who rounds that to 10,000 miles is running 7 per cent past the interval every time. Round service distances down when converting, not to the nearest convenient number — the interval was a limit, not an estimate.

At sea and in the air a mile is a different unit. The nautical mile is exactly 1,852 metres, about 15 per cent longer than the statute mile on a road sign, and it exists because it is one minute of latitude — which makes a distance on a chart directly readable off the chart's own edge. A speed of one nautical mile per hour is a knot, so knots and miles per hour are not interchangeable either.

Nothing on this page is about that unit, and the reason to mention it is that "mile" alone is ambiguous in exactly one context: anything involving a boat, an aircraft or a coastline. A marine forecast quoting visibility in miles means nautical miles. A road sign never does. If the source is a chart or a flight plan, 1.609 is the wrong factor and 1.852 is the right one.

Litres per 100 km and miles per gallon are not the same quantity in different units — one is volume over distance and the other is distance over volume, so the conversion is a division rather than a multiplication and the two numbers move in opposite directions. A good figure is a low one in metric and a high one in imperial. Divide 235.2 by the litres per 100 km to get US miles per gallon: 7 l/100 km is 33.6 mpg, and 5 l/100 km is 47.0.

The divisor changes with the gallon, which is where this goes wrong. A US gallon is 3.785 litres and an imperial gallon 4.546, so the imperial constant is 282.5 rather than 235.2 — 7 l/100 km is 40.4 imperial mpg against 33.6 US. Twenty per cent apart, same word, and a car described as doing 40 to the gallon is a different car depending on which side of the Atlantic the review was written.