## Measuring Cup Percentage Accuracy

I don't want this to turn into a debate about volume vs. weight measurements, thank you. It is strictly a math problem.

I have a measuring cup which is marked "240 ml". We know that 1 ml of water weighs 1 gram. I have a Jennings CJ4000 scale which I like. We also know that 1 U.S. nickel weighs 5 grams. On my scale, 20 U.S. nickels weigh 100 grams, so I'm satisfied that my scale is accurate.

I take my 240 ml measuring cup and fill it with water. I weigh it on the scale and it weighs 232 grams. My question is, how to state the error as a percentage?

Do I use the actual measurement as the numerator or the denominator of a fraction, i.e. 232 / 240 (the actual weight over the weight it is supposed to be), or should it be 240 / 232, with the measured weight as the denominator?

232 / 240 gives 0.9666666666666667. I subtract this number from 1 and get 0.0333333333333333. Multiplying this number by 100 gives me 3.333333333333333, so I have a 3.33% error.

240 / 232 gives 1.03448275862069. I subtract 1 and multiply by 100, for 3.448275862068966, or a 3.44% error.

My question is, which is the correct way to do this? Do I have a 3.33% error or a 3.44% error?

Now suppose the measuring cup held 120 grams of water. 120/240 gives 0.5. 1 minus 0.5 gives 0.5. Multiplying by 100 gives a 50% error.

240/120 = 2. Subtract 1 and multiply by 100 and we have a 100% error, which can't be right.

So it seems the correct way to do this is: actual measurement over the "supposed to be" measurement. What do we think?

Apart from the above question, I have a set of Trudeau plastic measuring cups: http://www.amazon.com/Trudeau-5-Piece-Measuring-Cup-Set/dp/B000RT85JW/ref=sr_1_1?s=home-garden&ie=UTF8&qid=1417294501&sr=1-1&keywords=trudeau+measurin...

I measured the 250 ml cup and it is spot-on! I'm happy that the actual weight is the same as the marked weight. I love these cups, but 250 ml equal 1 Australian/New Zealand cup.

There are at least three kinds of cup:

1 U.S. "customary" cup = 236.5882365 ml

1 U.S. "legal" cup = 240 ml

1 Australian/New Zealand cup = 250 ml

As happy as I am with the Trudeau cups, I was hoping to find something which is either an

accurate236.6 ml or 240 ml.I use the Trudeau cups to measure flour and have found the measurements to be more than consistent enough for bread baking. When first testing a recipe I may adjust the water quantity up or down, but once adjusted, the results are plenty consistent. OTOH, I measure wet ingredients by weight. I measure salt using measuring spoons and they work just fine.

http://en.wikipedia.org/wiki/Cup_%28unit%29

240 (the desired). Error percentage would be a fraction of that.

232 (actual) - 240 = 8 (measure of error)

8/240 = .333333333333, 3.3%

3.33%

wouldn't the error be -3.33% showing the error was light instead of heavy by 3.33%? I have to admit i have no idea about this and it is only a hunch. Another reason to use scales and toss the cups away at least when baking .

I use the 1/3 C to feed Lucy twice a day, the 1 C to make rice, the 1/4 C to make coffee and my wife uses the 1/2 C for her morning oatmeal or something since I can never find it except in the oatmeal box :-)

Guess we will have to keep them around for other stuff after all.

Well not really. A percentage by definition is a fraction of 100 parts. We know from the described situation we are dealing with a loss. 3.33% is the percentage of that loss. A margin of error can go either way.

Usually whenever I see a post where someone has mentioned cups, I stop reading. Over here in the UK, pretty much nobody uses cups.

8 / 240 = 0.0333333333333333

One could use the error * 100 as the numerator:

800 / 240 = 3.33%

or give it a sign: -800 / 240 = 3.33%

I have one recipe which I make all the time. It has been tailored to my measuring cups so that the flour measurement is in even cups or fractional cups, e.g. 1 1/2 cups. This makes it easy to measure the flour. Salt is measured in teaspoons. If I were making a different recipe and the dry ingredients didn't work out to even cups or fractional cups, then it would be scale all the way.

I had laid in a supply of these in various sizes for the dye studio, and I kept back a few of each because I had a hunch they'd be useful in the kitchen... sure enough, they've become my go-to for water measurements. My only problem with them is that as my eyes get older I find the graduation marks a little harder to read, but We Have The Technology for that. I do still check most things on the scale as well because I don't quite trust myself to fill to precisely the right point. Nevertheless - good tool for the job.

Positive and negative percentages are ubiquitous in finance.

Graduated beakers aren't what you want for dry measuring.

Did I miss something? Were we talking about dry-measuring water?

Guess I'd use a yardstick for that.

;-P

Flour, salt, sugar, baking soda, baking powder, corn starch, corn meal, etc. are dry ingredients, not water.

I wouldn't read too much into the results of this experiment. I don't think the error you encountered indicates that your measuring cup is off.

When it comes to dry ingredients like flour, you can fill the measuring cup and then "sweep" with a palette knife so that you get the prescribed volume. However, water has surface tension, so you're unlikely ever to get exactly the interior volume of the cup. You'll either get a bit under, with the edges of the meniscus flush with the lip of the cup, or you'll get a bit over, with the mass of water "bubbling" over the lip a bit.

Long story short, don't normalize all your formulas to this -3.33% error.

As I have said, the Trudeau cups are spot on, for Australian cup measurements.