The Fresh Loaf

News & Information for Amateur Bakers and Artisan Bread Enthusiasts

Measuring Cup Percentage Accuracy

doughooker's picture
doughooker

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?

doughooker's picture
doughooker

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 accurate 236.6 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

mwilson's picture
mwilson

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%

dabrownman's picture
dabrownman

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.  

mwilson's picture
mwilson

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.

doughooker's picture
doughooker

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%

doughooker's picture
doughooker

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.

balmagowry's picture
balmagowry

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.

doughooker's picture
doughooker

Positive and negative percentages are ubiquitous in finance.

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

balmagowry's picture
balmagowry

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

Guess I'd use a yardstick for that.

;-P

doughooker's picture
doughooker

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

yy's picture
yy

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. 

doughooker's picture
doughooker

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