Convert st to oz

A stone is fourteen pounds, and it is used for body weight in Britain and Ireland and essentially nowhere else — which is why an American reading a British weight usually needs this conversion.

An ounce is a sixteenth of a pound. It is not the fluid ounce, which measures volume, and the two are only loosely related — a fluid ounce of water weighs about an ounce, which is where the name came from and where the confusion starts.

Going this way is a multiplication, and by a whole number: one stone is 224 ounces, exactly, and 224 is the definition rather than a measurement that came close.

That makes it one of the few conversions worth doing in your head, and it makes the answer checkable: divide back and you must land on the number you started with, exactly, with no remainder to explain away.

The ounce 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 0.00446428571 st 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 not the whole of it, though: this page stops at nine significant digits and the ratio carries on past them.

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.

The avoirdupois system counts upward in a fixed sequence: sixteen drams to the ounce, sixteen ounces to the pound, fourteen pounds to the stone, two stone to the quarter, four quarters to the hundredweight, twenty hundredweight to the ton. The stone and the ounce sit three steps apart, and the 224 between them is the product of the two steps in the middle.

None of the multipliers is ten and none was chosen to make arithmetic easy. They were chosen to make division easy, in a trade where a quantity had to be split among buyers without a calculator: sixteen halves four times, fourteen splits into halves and sevenths, a hundredweight of 112 lb divides into quarters, stone, half-stone and pounds without a fraction anywhere.

Above the stone the ladder keeps going, and it keeps going in stone. A quarter is two stone, 28 lb, 448 oz. A hundredweight is eight stone, 112 lb, 1,792 oz. Those are the units sacks, bales and loads were sold in, and the stone survives in Britain today as the last living rung of a sequence whose upper half has gone entirely.

That is why the stone looks like an oddity now and was not one then. It was the unit between the pound you could hold and the hundredweight you could not, and it sat exactly one halving away from the quarter above it. A modern reader meets it only as a body weight, which is the one use that never involved dividing a load among anybody.

The long ton is the number that makes no sense until the ladder is laid out. It is twenty hundredweight; the hundredweight is eight stone; the stone is fourteen pounds. Multiply those and 2,240 appears, along with 35,840 ounces. Nothing in it was chosen directly — every one of its digits is inherited from the rungs below.

It is also why the two tons differ by exactly the ratio the two hundredweights do. The American short ton is twenty American hundredweights of 100 lb, which gives 2,000, and 2,240 over 2,000 is 1.12 — the same 112 to 100 as the hundredweights. One decision about a single rung propagated all the way to the top of the system, and it is still visible in freight quotes.

The rung under the ounce is the dram, a sixteenth of one, 1.772 g. It disappeared from commerce with the rest of the small customary weights, and the one place a modern reader still meets the word is on a box of shotgun shells: the "dram equivalent" figure is a reference to the black-powder charge that would have given the same performance, and there is no black powder in the cartridge and no drams in anything.

That is a fair picture of what happened to the whole lower ladder. Where a unit still describes something people buy — the ounce, the pound — it survived; where it described a quantity that has since been replaced by a measurement, it became a label without a referent. The stone is a third case again: it survived by attaching itself to bodies, which are the one thing that never had to be metricated for trade.

Multiplying by 224 is one of the few conversions on this site where no digit is ever lost. Both steps are whole-number definitions, so a stone figure with a decimal in it converts to an ounce figure with the same information and no more: 12.5 stone is 2,800 oz, 11.75 stone is 2,632.

The check is the same in reverse. Divide any ounce answer by 224 and the original number has to come back exactly, with no drift in the last place. That is not true of any conversion crossing into metric, where the pound's definition puts an eight-digit factor into the arithmetic — which is worth remembering when an ounce figure and a gram figure for the same weight disagree in the fourth decimal and neither is wrong.

Three cases account for most of them. Old records — agricultural returns, shipping manifests, trade ledgers — are written in stone, quarters and hundredweights, and reducing them to a single unit is how they get into a spreadsheet. Rations and feed are worked per animal per day in ounces, against a total held in stone. And a scale that reads only in pounds and ounces has to be met in its own units.

For all three the pound is the unit to stop at first. 224 is a large enough multiplier that a slip of a factor of sixteen or fourteen produces a plausible-looking answer, and going through pounds makes both steps checkable: stone times fourteen, then pounds times sixteen, with a recognisable number in the middle.

Old commercial records are laid out in columns, one per rung, and the abbreviations are terse: cwt for hundredweight, qr for quarter, st for stone, lb and oz below them. A line reading "3 2 1 7" is three hundredweight, two quarters, one stone and seven pounds, and the columns are positional in the same way a date is — nothing in the row states its own unit.

Reducing such a row to a single figure means multiplying each column by its own factor and adding: 3 × 112, plus 2 × 28, plus 14, plus 7, giving 413 lb, or 6,608 oz. The check that the transcription is right is that no column except the first may exceed its own limit — a quarter figure of 4 or more, or a stone figure of 2 or more, means the row has been misread or the clerk carried something incorrectly.

Ounces are the right destination when the answer is going onto a scale or into a document that is itself in customary units. They are the wrong one when the figure is going into a spreadsheet, a database or any analysis, because everything it will be compared against will be metric and a second conversion will happen later, less carefully.

For that case the direct route is grams: a stone is 6,350.29318 g, exactly 224 times 28.349523125. Storing the metric value and displaying whatever the reader wants is the arrangement that survives, and it puts the one lossy step — choosing how many digits to show — at the end of the pipeline rather than in the middle of it.