# Everything you know is wrong

I had always assumed, given the name, that a fluid ounce was the volume occupied by an ounce of water. I had also assumed, since I had always been told it was true, that a liter of water weighed exactly a kilogram. So imagine my surprise when I discovered that while a fluid ounce is 29.6 mL, an ounce is 28.3 g.

A fluid ounce is exactly one eighth of a cup, aka one sixteenth of a pint, aka one thirty-second of a quart, aka one one-hundred-and-twenty-eighth of a gallon, which was originally defined as the volume of eight pounds of wheat (at least, if you trust Wikipedia) or possible eight pounds of wine (also according to Wikipedia). Eight pounds is, in fact, 128 oz, but not only do densities of different substances vary, today’s (U.S.) gallon is defined in terms of cubic inches (exactly 231), which bear no relation to weight or mass.

The metric version does better; these days, the liter (aka the cubic decimeter) is defined in terms of the speed of the light, and the while the kilogram is no longer defined as the mass of a liter of water at a specific temperature and pressure, it’s still pretty darned close (to within a tenth of a percent, anyway).

As an aside, the modern British imperial fluid ounce does a lot better: it is 28.4 mL, extremely close to the ounce’s 28.3 grams. While these days defined in terms of liters, the original 1824 definition apparently (that’s me trusting Wikipedia again) defined an imperial gallon as ten pounds of water at 62° F. Perhaps the error is due to the difference in temperature; the kilogram was originally defined by water at 3.98° C, or about 40° F.

## 2 thoughts on “Everything you know is wrong”

1. I finally got around to looking up the numbers and figuring out the temperature effects. The difference in temperature isn’t quite enough to explain the difference — the difference in density is about 0.115%, while the difference between 28.4 and 28.3 is about 0.35%.

On the other hand, that sounds like it could be just the rounding error. So: more precisely, an avdp. oz. is 28.349g, and a British fluid oz. is 28.412g. Which reduces it to 0.22% difference, but that’s still twice too high.

Incidentally, the reason for picking 3.98°C for the (original) definition of a kilogram is that that’s the point at which water reaches its maximum density. It’s still equal to a exactly one litre of water to at least five decimal places.

2. Er, the British fluid oz. is 28.412 mL, not 28.412 g, obviously.