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Serving Size, Calories, Daily Values, and Food Labels

Date: 05/26/2005 at 15:35:52
From: joe
Subject: how to determine the serving size and % DV

I'm trying to figure out the equations used for values that are 
displayed on a food label.  I can't figure how they determine the
serving size and the grams involved.  For example:

serving size 1 cup (228g)
calories 250             %DV
Total Fat 12g             18%
Saturated Fat 3g          15%

I can't come up with an equation nor the possible variables that might 
be used to determine these results.



Date: 05/27/2005 at 09:48:12
From: Doctor Wilko
Subject: Re: how to determine the serving size and % DV

Hi Joe,

Thanks for writing to Dr. Math!

Good question.  I'd say you'd probably get more insight into food 
labels and nutrition by going to the Internet and searching for some 
good websites that discuss "nutrition" or "nutrition labels".  One
good starting point might be the FDA's site:

  http://www.fda.gov

As I saw your question come through, I was sitting here eating a bag 
of Famous Amos Chocolate Chip Cookies and thought, "Perfect, let's try 
it!"

The label looks as follows:

  -----------------------------------------------
  Serving Size 1 package, 1 serving per container
  Calories 280, Calories from Fat 120
  -----------------------------------------------
  Total Fat     13g    20%DV
  Sat Fat      4.5g    23%DV
  Total Carbs   38g    13%DV
  Fiber          1g     4%DV
  Protein        3g      --
  ------------------------------------------------

If you notice, the labels will usually say, "Percent Daily Values are 
based on a 2,000-calorie diet."  Then the legend below will be listed.  
This legend is how you calculate the %DV:

  ------------------------------------------------
  For a 2,000-Calorie Diet:

  Total Fat should be less than       65g
  Saturated Fat should be less than   20g
  Total Carbs should be less than    300g
  Dietary Fiber should be             25g
  ------------------------------------------------

Let's calculate the %DVs and see if we are close to the label.

The way we do this is just make a ratio of the amount of nutrient in 
one serving size over the recommended daily amount (based on a 2000-
calorie diet).

  Total Fat:    13g/65g = 0.20    = 20%   DV
  Sat Fat:     4.5g/20g = 0.225   = 22.5% DV (Label rounded to 23%)
  Total Carbs: 38g/300g = 0.126.. = 12.7% DV (Label rounded to 13%)
  Dietary Fiber: 1g/25g = 0.04    =  4%   DV

Our calculations look good.  Remember the %DVs are not recommended 
intakes, but just reference points to help people gauge what their 
overall dietary needs should be.  Again, most labels calculate the 
%DV from a 2,000-calorie diet.  If you calculated these values from a 
2,500-calorie diet, the %DV would be different from what's listed on 
the package.

The only other math I can think of from the label is to see how they 
calculate the "Total Calories" and the "Calories from Fat" at the top 
of the label.

You do need some additional information that is not on the label to 
do this.  You need to know:

  1g Fat     = 9 calories

  1g Protein = 4 calories

  1g Carb    = 4 calories

From here we can calculate the calories from fat.  From the label, we 
were given the following:

  Total Fat 13g

Since 1g fat = 9 calories, then 13 * 9 = 117 calories from fat.  The
label said 120 calories were from fat, so there may be some rounding 
going on here, but we're still close.  

Let's calculate the calories from protein and carbs to find the total
calories:

  Total Carbs 38g

Since 1g Carb = 4 calories, then 38 * 4 = 152 calories from carbs.

  Protein 3g

Since 1g Protein = 4 calories, then 3 * 4 = 12 calories from protein.

If we add these calories, we get:

  117 calories from fat
  152 calories from carbs
   12 calories from protein
+ --------------------------
  281 calories total  (Label said 280 calories total)

This should give you some good insight into understanding nutrition 
labels.  Now the challenge is for you to take something from your
fridge and see if you can calculate the values like we've done above!

Does this help?  Please write back if you have further questions.

- Doctor Wilko, The Math Forum
  http://mathforum.org/dr.math/ 



Date: 06/06/2005 at 14:26:09
From: joe
Subject: Thank you (how to determine the serving size and % DV)

I want to thank you for this very helpful response.  A million thanks!
Associated Topics:
Middle School Fractions
Middle School Measurement

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