What formula switches from pints to milliliters?

Factual Questions
1

February 26, 2015

Hello, all,

I’m writing a calculator for a digital cookbook, and I can’t figure out the exact conversion rate from the American system of teaspoons and pints and gallons to the metric system of milliliters and deciliters and liters.

Distance is covered by the formula 1 inch = 25.4 millimeters exactly. If you know that you can convert completely from the American method of measuring distance to the metric method and vice versa.

But what is the formula for measures of volume? Has someone officially declared a conversion formula that lets us travel freely from the antiquated Imperial system of tablespoons to the obviously better metric system of mls?

Research has shown that supposedly there are 236.5882365 milliliters in 1 cup, and if that’s the exact number, with no more significant decimal places, then I still want to see some official declaration of that fact. And even if it’s not the exact number, it seems likely that, with so many decimal places, it is the result of the division of some number by another, in which case what is that formula?

And then there’s the problem of converting from units such as tablespoons, which measure volume, to units such as ounces, which measure weight.

FWIW, I do tell the readers of the cookbook that the conversions I offer work perfectly only when the substance being measured is water, as opposed to, say, flour, which is less dense, and plutonium, which is more dense than water. While many recipes in the book call for various amounts of flour, so far none of them calls for even the tiniest smidgen of plutonium, but you get my point.

Is there a conversion factor or formula that converts from volume to weight, whether in the Imperial system or the metric?

I know this is a lot of questions, and I think I’ve confused myself a little in composing them for you, so I will appreciate ANY answers you can offer.

And please tell Unca I can’t go skating next weekend after all.

2

Google to the rescue

It’s the result of dividing 236.5882365 ml by 1 cup.

The relevant formula is mass = volume * density. This formula, like all physics formulas, applies in every system of units, though use of peculiar units on your inputs will result in peculiar units for your output. Density is different for every substance, and must be determined by measurement. For irregular materials like flour, it may even vary considerably depending on various conditions.

3

For future reference, convert.exe is an extremely handy program to have around.

4

Yes the “Customary” cup is defined as 236.5882365 milliliters. This is exact based on the definitional relations between an inch and a centimeter, a milliliter and a cubic centimeter, and a cup and a cubic inch.

However, the “legal” cup for nutritional labeling purposes is 240 mL.

Ain’t the U.S. system wonderful (don’t ask about the “Survey” mile.)

5

The OP asked about the imperial system as well. Imperial cups are larger than US cups, so one imperial cup
Is approximately 250 ml.

6

You should also know that, in the U.S. system, the words “pint,” “quart” and “gallon” mean different things depending on whether you’re measuring liquids or solids. A dry measure pint is about 16.4% bigger than a liquid pint (the same ratio holds when comparing dry and liquid quarts and gallons). This isn’t true for cups, though - a dry and liquid cup are the same volume.

Conversion factors between volume measures and weight measures depend on the density of what’s being measured. There are plenty of web sites that will tell you, for example, how much a cup of sugar weighs. One complication is that some ingredients (notably flour) don’t have a fixed density - they can be compressed significantly. Other ingredients come in different forms that have different densities (e.g. table salt is denser than kosher salt).

Most recipes don’t require extreme accuracy of measurement. There isn’t much point in going beyond two or three significant digits in most cases.

7

1 pint is half a liter. This works for anything besides laboratory work (where everything should be expressed in ml anyway, even in distant heathen America.)

If I go into a bar and order a pint, it will be a 500ml glass. If a cake recipe calls for a pint of milk, I will use 500ml and it will not flop.

I grew up after Imperial was droppped in south Africa, but I still grew up with pints of milk being dropped off by the float - only, they were 500ml pints.

450ml pints are just … unnecessary. 480ml ones are just showing off :slight_smile:

8

In my English kitchen I use both imperial and metric, and I have a set of weights for both. Recipes have one or sometimes both measurements but it actually doesn’t matter because it’s not the actual weight or volume that matters but the ratio of the component parts.

The recipe for a Victoria sponge calls for: *
8oz Stork
8oz caster Sugar
8 oz self raising flour
4 medium eggs
1 teaspoon vanilla essence
Jam for filling
*

As you can easily see, the margarine, sugar and flour are all equal, so it does not matter what units are used. Ounces are used for simplicity but what actually matters is that the weights of the components are roughly equal. The number of eggs is only a guide really as eggs can vary quite a lot anyway.

There are so many variables when cooking a recipe, it rarely works first time. Ovens in particular vary a lot and cooking instructions on ready meals often have a get-out clause allowing for that. My oven is set in degrees Celsius, so I do have a conversion chart in the kitchen.

With reference to Mr Dibble’s post above - The UK decided that milk, beer and miles would not be metricated, so I still buy my milk in 4 pint containers, my beer in pints and measure long distances in miles.

9

You’re making a big mistake here. There are several different kinds of ounces, and it is important to understand the differences.

There is indeed a unit of weight (or mass, for the pedants) called the avoirdupois ounce. But there is also a unit of volume called the fluid ounce, which measures exactly two tablespoons.

Would you like to learn about the troy ounce? It is a unit of weight, and there are twelve of them in a pound of gold.

10

This seems pretty irrelevant for a digital cookbook

11

If you’re talking about the gold and troy ounces, yes you’re correct, but it was only a side point.

The ambiguity of “5 ounces of shortening” probably won’t make much of a difference in most cases, but it could be significant sometimes.

12

it is a mistake and only confusing to convert volumes to a mass unless the person does their own density determination.

13

February 27, 2015

Chronos, you say 236.5882365 is “. . . the result of dividing 236.5882365 ml by 1 cup,” but I want to know where that number came from. Was it declared by some official organization such as NIST?

Machine Elf, convert.exe is useful, and I thank you for bring it to my attention, but it doesn’t provide the formulas that inform its conversions.

OldGuy, you say “Yes the “Customary” cup is defined as 236.5882365 milliliters.” Where did you learn that that is the definition? This is exactly what I’m looking for.

You go on to say, “This is exact based on the definitional relations between an inch and a centimeter, a milliliter and a cubic centimeter, and a cup and a cubic inch.” What do you mean by that? because that is even more exactly what I’m looking for. I want to know the math that gets us from cups to milliliters or vice versa. I like my spreadsheets to be as precise as possible, and I like to show the entirety of the formulas, both for the readers’ edification and my own.

Jeff Lichtman, you’re right, I need to more fully consider the difference between fluid and dry measures. You say pints, quarts and gallons vary whether it’s a fluid or a solid, but you don’t mention teaspoons and tablespoons. Where did you get your information? so I can follow up.

Thanks to everyone who’s responded so far.

14

1 gallon = 16 cups
1 US gallon = 231 cubic inches
1 inch = 2.54 cm (by definition in the US)
1 cubic cm=1 ml.

so, 1 cup = 231/16 cubic inches, or (213/16)*2.54^3 ml

Multiply it out and get 236.5882365ml.

15

1 US gallon is exactly 231 cubic inches. With your 1 inch = 2.54 cm conversion, you should have everything set.

16

ThisOneGuy, you pulled it all together for me. Now I know why 236.5882365 is officially the number of mls in 1 cup, at least for my purposes as editor of a U.S. cookbook.

Thank you and thanks to all the other contributors who helped me to understand this problem better. More people in the world should know about SD’s message boards as a source of free expertise.

17

This thread just begs for puns on different cup sizes.

18

I wish people would put a note somewhere stating whether they’re using US units or Imperial units when doing non-metric things. This is an issue for us in Canada as many of our cookbooks are from the US, but old family ones, at least in my case, are from England, and we need to know exactly which set of units we are using.

The same applies to car commercials, which even now in Canada often reference “miles per gallon”, but don’t say which gallon they are using.

At least the miles are the same. I think.

19

I realize this thread died half a year ago, but I want to follow up now that I’ve been forced to by the aforementioned cookbook, where I explain the math for converting cups to milliliters. The paragraphs are below. Have I made any mistakes? What can be improved? Thanks.

START START START

. . . Here’s how it works.

(The letters mL mean milliliters, i.e., one thousandth of a liter. The letters cm mean centimeters, i.e., a hundredth of a meter. All the numbers below are exact to the very last last decimal place except the very last number, which is precise to only 16 decimal places.)

1 US liquid gallon = 231 cubic inches (given, per NIST)
1 US liquid gallon = 16 cups (by definition)

Therefore 1 cup of water = 14.4375 cubic inches (from 231 cubic inches per gallon / 16 cups per gallon).

At this point we have 1 cup of water converted to 14.4375 cubic inches, and now it’s time to convert from inches to metric.

1 inch = 2.54 cm (given, per NIST)

Therefore 1 cubic inch = 16.387064 cubic cm (from 2.54 cm/inch of height * 2.54 cm/inch of width * 2.54 cm/inch of depth).

If there are 14.4375 cubic inches per cup and each cubic inch is 16.387064 cubic cm, then the product of those two numbers is the answer we’re seeking, the number of cubic cm of water in 1 cup, which because 1 cubic cm is equal to 1 mL means the magic number is 236.5882365 mL in one cup. The formula for your calculator or spreadsheet is (231 / 16) * (2.54 ^ 3).

(The reciprocal, if you need to convert from mL to cups, which is 236.5882365 raised to the power of -1, is pretty close to 0.00422675283773037 if I typed it right, in case you care.)

END END END

20

You’ve got a typo there. It’s ml, not mL. Everyone else in the world uses a lower case letter L there, don’t confuse your readers by being the only one who doesn’t.

Or…

One cup = 14.4 cubic inches, which varies from your 6-digit figure by 2/10ths of one percent.

One cubic inch = 16.4 cc, which varies from you 8-digit figure by 1/10th of one percent.

One cup = 237 ml (not mL), which varies from your 10-digit figure by 2/10ths of one percent.

I don’t know why you seem to be focused so intently on precision to the umpteenth decimal place in your book. It won’t have any practical value for your readers – they can’t measure such tiny differences and even if they could it wouldn’t matter in the results of their cooking. In my opinion all it accomplishes is boring people to tears with tedious arithmetic. And it is simple arithmetic, not only is it immaterial to cooks, it holds no interest for mathematicians or engineers either. Three significant digits should be more than adequate for nearly anything.