The units that are two different units with one name

Convert in CONVERT, which lists every shared name twice with its system attached and names the one it used beside the answer. Factors are exact where an exact definition exists, and the handful that are approximations say so. Nothing is uploaded.

The gallon

The imperial gallon is exactly 4.54609 litres. The US liquid gallon is exactly 3.785411784 litres. The imperial one is about twenty per cent larger, both are called a gallon, and nothing in the word distinguishes them.

In 1983 an Air Canada 767 ran out of fuel at forty-one thousand feet and glided to a landing at a former air force base at Gimli. The aircraft was among the first Canadian ones specified in metric, the refuelling calculation was done with a conversion factor in pounds per litre rather than kilograms per litre, and the aircraft left with roughly half the fuel everybody believed was aboard. Nobody was killed, which is entirely to the credit of the crew rather than the process.

The lesson is not that people should be more careful. It is that a quantity written down without its unit system is an accident waiting for a coincidence.

The fluid ounce, which goes the other way

This one catches people who think they have learned the rule. The imperial gallon is larger than the US gallon, so it is natural to assume the imperial fluid ounce is larger too.

It is smaller. 28.41 millilitres against 29.57.

The reason is that the two systems divide differently: an imperial pint is twenty imperial fluid ounces, a US pint is sixteen US fluid ounces. So the imperial pint is larger than the US pint and the imperial fluid ounce is smaller. Both facts are true simultaneously and neither can be derived from the other.

Three tons

The long ton is 2,240 pounds, about 1,016 kg. The short ton is 2,000 pounds, about 907 kg. The metric tonne is exactly 1,000 kg. They differ by up to twelve per cent, they are all called a ton in speech, and the metric one is distinguished in writing only by a spelling that half of everybody treats as optional.

Shipping, freight and structural work all use tons routinely, and the difference between 907 and 1,016 kilograms per unit is the sort of error that accumulates invisibly across a manifest.

Two miles

The statute mile is 1,609.344 metres. The nautical mile is exactly 1,852 metres, defined as one minute of latitude, which is why it is used at sea and in the air — a nautical mile is a distance you can read off a chart with dividers.

They differ by fifteen per cent. A speed in knots is nautical miles per hour and a speed in miles per hour is not, so a vessel doing twenty knots is doing twenty-three miles an hour, and confusing the two produces an estimated time of arrival that is wrong by an hour and a half a day.

Two mils

An angular mil is a thousandth of a radian, approximately — and the approximations differ. The NATO mil divides a circle into 6,400; the Soviet and Warsaw Pact mil divides it into 6,000. Both are called a mil and both are used for the same job, which is adjusting indirect fire.

The difference is about six and a half per cent. At four kilometres that is a lateral error of over two hundred metres, which is not a rounding.

To confuse matters further, “mil” in an engineering context usually means a thousandth of an inch, which is a length rather than an angle. Three unrelated quantities, one syllable.

Two calories

The calorie a physicist means is the energy to raise a gram of water by one degree: 4.184 joules. The Calorie on a food label is a kilocalorie, a thousand of those, and is sometimes written with a capital C and very often not.

So a food label reading “250 calories” means 250,000 calories in the scientific sense. This causes no practical harm in nutrition, where everybody means the same thing, and considerable confusion the moment a nutrition figure meets an engineering one.

The kilobyte, which is about the missing space on your drive

A kilobyte is 1,000 bytes. A kibibyte is 1,024. The prefixes kilo, mega, giga and tera mean powers of a thousand; the binary prefixes kibi, mebi, gibi and tebi mean powers of 1,024.

Storage is sold in powers of a thousand and most operating systems report in powers of 1,024 while labelling the result “GB”. The gap compounds: about 2.4% at kilobytes, 7.4% at gigabytes, and 10% at terabytes. That is the entire explanation for a 1 TB drive showing as 931 GB, and it is not the manufacturer shortchanging anybody.

Fuel economy, which is not a factor at all

Miles per gallon and litres per hundred kilometres measure the same thing in opposite directions: one is distance per volume, the other volume per distance. Converting between them is a reciprocal, not a multiplication, which means you cannot average them, you cannot interpolate them linearly, and improving from 30 to 40 mpg is a bigger saving than improving from 40 to 50.

And there are two gallons, so there are two mpg figures for the same car, differing by twenty per cent. A US figure of 25 mpg is 30 mpg imperial.

The rule that prevents all of it

Never write a quantity without the system when the unit has two meanings. “4,500 gallons” is not a quantity. “4,500 imperial gallons” is.

And software should never resolve the ambiguity for you. A converter that offers a single “gallon” has made a guess about the most important thing in the conversion and has not told you which way it guessed.