US and imperial units that share a name but are not the same

Most unit confusion announces itself. Nobody mistakes a kilometer for a mile. The dangerous kind is quieter: two units that share a name, are written down identically, and are not the same size. There are three of these in everyday use, and the gaps between them run from a few percent to about a fifth.

First, the mass units that are exact

Everyday mass rests on a handful of definitions that are exact rather than measured, which is a nicer position than most conversions start from. Since 1959 the international avoirdupois pound has been defined as exactly 0.45359237 kg — not approximately, exactly. Everything else in the imperial and US mass family follows from it by whole-number division:

• 1 pound = 453.59237 g exactly.
• 1 ounce = 1 pound / 16 = 28.349523125 g exactly.
• 1 stone = 14 pounds = 6350.29318 g exactly.
• 1 metric ton = 1000 kg exactly, by definition.

Going the other way is where the exactness stops. One kilogram is 1 / 0.45359237 pounds, which does not terminate: about 2.2046 pounds. Same relationship, but write that one as an approximation, because it is one.

The free Weight Converter handles grams, kilograms, milligrams, pounds, ounces, stone and metric tons, all from those exact factors. Notice what is not on that list — there is one kind of ton on it, and the reason is the rest of this piece.

Trap one: three different ounces

The ounce is the worst offender because there are three of them in circulation.

The ounce of mass is the one above, exactly 28.349523125 g. The US fluid ounce is a volume: a US gallon is exactly 3.785411784 L and there are 128 fluid ounces in it, giving exactly 29.5735295625 ml. The imperial fluid ounce is a different volume again: the imperial gallon is exactly 4.54609 L and holds 160 fluid ounces, giving exactly 28.4130625 ml.

So a US fluid ounce is larger than an imperial one by 29.5735295625 / 28.4130625 ≈ 1.0408, about four percent. Four percent is small enough to pass unnoticed in one measurement and large enough to be visible once it has been multiplied through a whole recipe.

The near-coincidence in those numbers is not an accident and is the origin of the whole mess: an imperial fluid ounce of water weighs very close to one ounce of mass. That is where the shared name came from, and it holds only for water. For anything else the two ounces have nothing to do with each other, and a converter cannot tell which one a recipe meant.

Trap two: the pint

Same story, bigger gap. A US pint is 16 US fluid ounces, so 473.176473 ml exactly. An imperial pint is 20 imperial fluid ounces, so 568.26125 ml exactly. The imperial pint is larger by about 20.1 percent.

A fifth is not a rounding error. If a recipe written in one convention is read in the other, the liquid is out by a fifth in one direction or the other, and nothing in the text gives you a clue. The tell is usually the rest of the document: a recipe that also uses cups and quarts is almost certainly US, and one that uses stone and imperial gallons is almost certainly not.

Trap three: the ton

Three units, one word, and the differences here are the ones that reach real money.

• The metric ton is 1000 kg exactly.
• The US ton, or short ton, is 2000 pounds, which works out at 907.18474 kg exactly — about nine percent lighter than a metric ton.
• The long ton, the imperial one, is 2240 pounds, or 1016.0469088 kg exactly — a little over one and a half percent heavier than a metric ton.

The long ton is exactly 2240 / 2000 = 1.12 short tons, so the two customary tons differ by twelve percent while sitting either side of the metric one. A figure quoted in "tons" with no further qualification is genuinely ambiguous, and the honest move is to find out which before converting anything. That is also why the converter offers only the metric ton: a menu entry labelled "tons" would be a guess about the reader's document dressed up as a unit.

The one that trips people up domestically

Stone is straightforward as a factor — exactly 14 pounds — but it is written in a way that invites arithmetic errors. A body weight given as eleven stone four is eleven stone plus four pounds, which is 11 × 14 + 4 = 158 pounds. It is not 11.4 stone, and reading it that way overstates the weight by about a pound and a half. Convert the whole thing to pounds first, then to whatever you actually want.

How to avoid all of it

Two habits cover almost every case. Write down which system a figure came from at the moment you write the figure, because that context is never recoverable from the number later. And when a document crosses a border or an ocean, convert to metric once, at the boundary, and work in metric from there. A gram and a milliliter mean the same thing everywhere, which is the entire reason they exist.