How can 128 ounces = 133.5 ounces?

According to Google Search and Wolfram and other online conversion programs, 3.785411784 liters = 128 fluid ounces. Please feel free to check for yourself.

So I would think that if you switch from liters (volume) to grams (a mass equivalent to a 1,000th of a liter) and divide by 1,000, the result should still be 128 ounces.

But in fact according to Google Search and Wolfram and other online conversion programs (again, please check me), 3,785.411784 grams = 133.526471232309 ounces, which is more than 4% higher than 128. I have not found even one conversion utility that says 3,785.411784 grams = 128 ounces.

I have been unable to find an explanation for the contradiction, which makes a difference to a spreadsheet I’m writing that purports to perform this very sort of conversion for purchasers of a cookbook I’m editing.

If you understand what’s going on, please let me know.

There’s a difference between fluid ounces, which measure volume, and weight ounces, which measure weight (not mass, although we can treat it as mass).

If a fluid ounce of water weighed an ounce, like a milliliter of water masses one gram, then you could convert easily. But it doesn’t, so you can’t.

1 L of water = 1 kg.

Furthermore, 128 US ounces = 133.228 Imperial ounces.

Or 128 US weight ounces = 116.667 Troy ounces.

One fluid ounce of water does weigh one ounce here in the US. As noted above it’s a difference in the units of measurements.

Wikipedia is your friend, here:

That 4% difference is suspiciously familiar…

Lemur866, you say, “There’s a difference between fluid ounces . . . and weight ounces.” Now my question is What is that difference?

You say, “If a fluid ounce of water weighed an ounce, like a milliliter of water masses one gram, then you could convert easily. But it doesn’t, so you can’t.” Now my question is how the figure of 133.5 came about. It seems like someone is doing some sort of division problem or something somewhere.

thelurkinghorror, you say, “1 L of water = 1 kg.” Now my question is What difference does that make?

You say, “Furthermore, 128 US ounces = 133.228 Imperial ounces.” Now my question is Where did that figure come from, especially since it’s so close to 133.526?

You say, “Or 128 US weight ounces = 116.667 Troy ounces.” Now my question is What difference does that make?

No it doesn’t, at least not exactly.

A US fluid ounce = 30 ml
An ounce = 28.349523125 g

The difference the OP is noting is simply because A US fluid ounce and an ounce do not have the same relationship to each other that litres and kilograms do.

TriPolar, you say, “One fluid ounce of water does weigh one ounce here in the US. As noted above it’s a difference in the units of measurements.” Now my question is What is that difference in the units of measurement? I wish to use US units.

Quercus, you say as follows:

"Wikipedia is your friend, here, https://en.wikipedia.org/wiki/Fluid_ounce

…making the imperial fluid ounce exactly 28.4130625 ml… With the adoption of the international inch the US fluid ounce became 29.5735295625 ml exactly, or about 4% larger than the imperial unit.

That 4% difference is suspiciously familiar…"

First, thanks for the link. I read the article three times and paid special attention to your quote therefrom. Now my question is What difference does it make how many mL are in a US fluid ounce? I mean, how does that resolve the contradiction?

Thanks to everyone who’s trying to help.

Yeah, I’m seeing that now. I missed that little detail somewhere along the line, I’ve been believing there was an equivalence intended at some specific temperature for a long time.

All this does go to show that the metric system does have at least the benefit of consistency.

The error that the OP just made is of the same nature that plunged the Mars Climate Orbiter to it’s mechanical death. Non-SI units was literally the death of the poor thing.

A pint’s a pound, the world 'round is close enough for most things, but it’ll bite you sometimes.

Sure it does. You can convert between one and the other using the density of water.

The problem is that the density of water varies widely with temperature. Any kind of fixed conversion like “1 kg = 1 l” or “1 fl-oz = 1 oz” can only possibly work at a single temperature. These temperatures happen to be different between metric and US customary, but in both cases there’s only a single one that works.

This chart explains all. You can see that 1 fl-oz of water weighs 1 oz at just a little under 212 degrees F (this is the same as 8 lb/gal). At 32 F up to room temperature, there is roughly a 4% difference.

There is no contradiction. Although fluid ounces and ounces both share a word, they are not the same thing and don’t convert to metric units in the same way.

Do you understand that different liquids weigh different amounts? A litre of water weighs a kilogram, but a litre of milk doesn’t, not quite. So while the metric system has some convenient equivalences such as a litre of water weighing a kilogram, the US system does not have the same equivalences. A fluid ounce of water does not weigh an ounce. Therefore when you convert metric units of volume and weight to US units of volume and weight you do not get the same answers.

In short, the answer is effectively in your question.

3.785411784 litres = 128 fluid ounces because that’s the conversion between those units.
3.785411784 kg = 133.526 ounces because that is the conversion between those units.

The numbers are different because a fluid ounce is not equivalent to an ounce.

128 fluid ounces of water = 133.526 ounces.

The thing is, fluid ounces are probably near enough to ounces that people can safely consider them to be equivalent for most purposes around the home. You may then get the impression that the equivalence is exact when it is not.

I take your point, however no, they don’t have the same relationship to each other. The temperature of the fluid is part of the relationship. Whatever temperature of water you pick, the relationship between litres and kilograms is not the same as that between fluid ounces and ounces.

Richard Pearse, you say as follows:

“A US fluid ounce = 30 ml.”

Now my question is Where did you learn that “A US fluid ounce” = 30 ml? According to Wolfram, “1 us fluid oz in ml” is 29.57 mL, not 30. According to plain old Google, “1 us fluid oz in ml” is equal to 29.5735 mL.

You say, “An ounce = 28.349523125 g.” Now my question is Why did you tell me that? FWIW, my spreadsheet agrees with you, so I’m not sure how this helps resolve the contradiction.

You say, “The difference the OP is noting is simply because A US fluid ounce and an ounce do not have the same relationship to each other that litres and kilograms do.”

Now my question is In what way do a US fluid ounce and an ounce not have the same relationship to each other that litres and kilograms have? More specifically, how do a US fluid ounce and an ounce differ?

Sure, the temperature for the “easy conversion” crossover is different between the two–in metric, it is 4 C, or just above freezing (and the maximum liquid density); while in US customary it is at the boiling point, or the minimum liquid density. Both temperatures are totally arbitrary, and chosen for practical purposes, so one can’t say that one is somehow better or fundamentally different than the other.

According to the US Bureau of Weights and Measures (http://www.nist.gov/pml/wmd/pubs/upload/hb44-2016-final2.pdf Appendix C) the proper conversion is 29.57353 mL for 1 fluid oz.

It’s 31.1034768 g for 1 Avoirdupois or Troy oz.

I suspect in common usage rounding is done in many ways.

One is not better than the other but they are fundamentally different. There is no temperature of water where the ratio of kg to lt is the same as the ratio of oz to fl oz, therefore, the fl oz/oz relationship is not the same as the kg/lt relationship.

Further more, the temperature of 212ºF for water wasn’t chosen at all, the fluid ounce and ounce relationship was not chosen with reference to water. The fluid ounce is based on the US gallon and the ounce is currently defined as 28.349523125g. Any relationship between the two is accidental.

The lt and kg on the other hand were originally defined with reference to each other. That original definition has been changed very slightly but their relationship is no accident.

I was referencing Wikipedia and the relationship was given as “approximately 30 ml”, 29.5735 ml is obviously more precise but it doesn’t change my point.

Because the ounce is not the same number in grams as the fluid ounce is in litres. That is why you have a difference in your numbers. As I said earlier, there is no contradiction, your numbers are all correct.

1 litre of water = 1 kilogram.
1 fluid ounce of water does not equal 1 ounce.

That is how they differ. Therefore when you convert litres to fluid ounces you get a different number than if you convert kilograms to ounces.

In order to get 3.785411784 litres = 128 ounces in a conversion calculator, an ounce would have to equal 29.5735g, but it doesn’t.

It might help if you explain why you think your two conversions should result in the same number.

I think that should be “Apothecaries or Troy oz”, the Avoirdupois is the one used in the US and is 28.349523125g by definition.