Friday, February 17, 2012

Comparing Pet Foods: The Math is Simple, But The Thought Process is Complex: Many Ways Exists to Solve the Problem

Written by Marion (Meg) Smart DVM PhD

An Example

A canned cat food: Without doing math you will find it difficult to compare diets based on the label information.  You must bring all the nutrient values down to a common denominator:
• % DM (dry matter)
• gram/ 1000 Kcal
• gram of nutrient/day as fed

Information available from the label:

1. Guaranteed Analysis Min  and/or Nutrient % as Fed
** On the rarer label or website you may get a typical or actual nutrient % as fed

• Example: Fuzzy Warm Cat Food
• Protein min %     10
• Fat min %       9
• Fibre max %     0.8
• Ash max %     1.5
• Ca min %     0.8 (or 800mg/100g)
• P min %     0.7 (or 700mg/100g)
• Moisture Max     78%
2. Ingredient List

3. Suggested Feeding Recommendations

Without some magical math transformations this information is of little value:

First convert all % to a dry matter (DM) basis:
• % DM = 100 - moisture %
= 100 - 78 % = 22%

Take the % DM and convert the rest of the Guaranteed Analysis Min
• Example: Protein % = 10g/22g  = Xg/100g
= 10 * 100/22 = 45g/100g of DM or 45%

Next determine the Carbohydrate % as fed
• CHO % = 100 - (Protein % + Fat % + Fibre % + Ash % + Moisture %)
= 100 - (10 + 9 + 0.8 + 1.5 + 78) = 0.7 % or 3 % DM

If the caloric density of the diet is not on the label you must calculate it
• Kcal/100g = (Protein % x 3.5) + (CHO % x 3.5) + (Fat % x 8.5)
= (30) + (2.5) + (76.5)
= 109 Kcal/100g or 495 Kcal/100g/DM

Now we can determine how many grams of nutrients there is in 1 Kcal (1000 cal)

• We know 10g protein/100g of the diet, we also know there are 109 Kcal in 100g of diet.
• Therefore, there are 10g protein/109Kcal or 0.09g protein per Kcal or 90g/1000cal
• For fat = 9/109 = 0.8g per Kcal or 80g/1000cal
• For fibre = 0.8/109 = 0.0073g/Kcal or 7.3g/1000cal
• For Ca = 0.8/109 = 0.0073g/Kcal or 7.3g/1000cal
• For P = 0.7/109 = 0.0064g/Kcal or 6.4/1000cal

We can use the suggested feeding guide on the label to determine:

• what the manufacturer is recommending
• 1 can for 2.5 kg body weight and a can weighs 170g
• 109Kcal in 100g therefore one can has (109/100) x 170 = 185 Kcal
• A cat requires about 50-60 Kcal/kg of body weight, therefore a 2.5kg cat requires
• 2.5 x 55 = 137.5 Kcal or Approximately 74% of one can

We can even go one more step and calculate the grams of protein, fat etc. our 2.5kg cat is getting in one day:
• using the caloric requirements:
• Protein = gram of protein x Kcal required = 0.09 x 137.5 Kcal = 12.4g/day
• Fat = .08 x 135.7 = 10.8g/day
• continue with other nutrients

• Using the % nutrients as fed:
• 1 can = 170g
• to meet the cat's requirements you must feed 74% of a can or 125g/day
• On an as fed basis the protein is 10%g of protein/day
• = 0.1 x 127.5 = 12.5
• Fat is = 0.09 x 125 = 11.2 g/day

What if the only information you have is that:

• 30.5% of the calories come from protein
• 67.5% of the calories come from fat
• 2.0% of the calories come from carbohydrates
• 109Kcal/100g of diet as fed

To calculate g of protein/day the cat's energy requirements are 137.5
• therefore it requires 137.5/1.09 = 126g of food/day
• Protein g/d = 0.10 x 126 = 12.6
• Fat g/d = 0.09 x 126 = 11.3

As you can see there are many ways to come up with the same answer, it all depends on how the data is presented to you.
The bottom line is to compare data.
In order to do this, the data must all be brought to a common denominator: %DM, g/100Kcal or g/day.