P2632 Simple Ration Formulation: Pearson's Square

1 pearson s Square is a Simple , quick way tocalculate the amounts of feed necessary tomeet a nutrient requirement of livestockand other animals. This method is mosteffective when only two feeds are beingused. For example, when two grains aremixed for part of a total mixed Ration (TMR) or as a supplement to pasture feed-ing, pearson s Square can be used to deter-mine what quantity of each grain wouldbe needed to achieve a specific nutrientlevel in the mixture. The basic structure of a pearson sSquare can be seen in Figure 1. In thisexample, soybean meal and corn are beingused to meet the crude protein (CP)requirement of a lactating dairy cow.

2 Thenutrient requirement, in this case CP,could also be energy, total digestible nutri-ents (TDN), fat, and so on, depending onthe information needed by the user. The number in the center of the squareor box is the animal s nutrient require-ment. This number is usually determinedfrom the National Research Council publi-cation for a specific livestock species orfrom producer experience. It is based onanimal class and production stage andlevel. The two feeds being considered arelisted at the top and bottom left-hand cor-ners of the Square . The nutrient concentra-tion of each feed is listed as use pearson s Square :1.

3 Subtract the nutrient requirement(middle of Square ) from the nutrientconcentration (on left of Square ) in thefeed across the diagonal (top left middle = bottom right; bottom left middle = top right). Repeat this forboth feeds. Make any negative num-bers on the right side of the squarepositive. The answers on the right sideof the Square are the parts of each feedto include in the Ration . 2. After subtracting across the diagonal,sum the parts of the two feeds to getthe total. 3. Then, divide each part by the sum ofthe parts to calculate the percent ofeach feed in the Ration .

4 Simple Ration Formulation: pearson s Square15% CPCorn, 10% CPSoybean meal, 45% CPFigure 1. Using pearson s Square to calculate amounts of corn and soybean meal needed to meet crudeprotein (CP) requirement. 30 parts (15% - 45%) corn35 total parts5 parts (15% CP - 10% CP) soybean mealPearson s Square calculations: 1. Subtract across the diagonal: a. 15% - 10% = 5 parts soybean mealb. 15% - 45% = 30 parts corn2. Sum the parts:a. 5 parts soybean meal + 30 parts corn = 35 totalparts3. Divide each part by the total to calculate the per-cent of each feed to include:a.

5 5 parts soybean meal 35 total parts = *100 = soybean mealb. 30 parts corn 35 total parts = * 100 = cornSo, in a half-ton (1,000-pound) batch of this cornand soybean meal mix, 143 pounds of soybean mealand 857 pounds of corn are needed to achieve 15% CPin the mix (calculations shown below). Soybean meal: 1,000 lb * ( 100) = 143 lb SBMCorn: 1,000 lb * ( 100) = 857 lb cornThere are a few important things to rememberabout using pearson s Square for formulations:1. This method is only efficient when no more thantwo ingredients are being used. 2. The animal requirement (number in center of thesquare) must fall between the nutrient concentra-tions in both feeds.

6 For example, if the requirementis 60% TDN, then one feed must be greater than60% TDN and one must be less than 60% TDN. 3. Disregard any negative numbers calculated on theright side of the Square . Treat them as Nutrient concentrations of the feeds and therequirement must be expressed on the same basis(for example, dry matter or as-fed ). 5. Always CHECK THE MATH for check for the example above:143 lb soybean meal * 45% CP = lb CP857 lb corn * 10% CP = lb CPCow s requirement = 1,000 lb * 15% CP = 150 lb CPCheck: lb CP + lb CP = 150 lb CPUsing pearson s Square withSupplement MixesThough not always recommended, it is possible to usePearson s Square to balance more than two ingredi-ents.

7 For example, with two separate grain mixes (Aand B), each made up of two ingredients, for a total offour feedstuffs, pearson s Square method can be usedto calculate the amount of grain mixes A and B neededto meet the requirements. Energy (Mcal/d) is therequired nutrient in the following example. Grain mix A is 40% corn and 60% soybean hulls(SBH), whereas grain mix B is 50% dried distillersgrains (DDG) and 50% cottonseed hulls (CSH). Theenergy requirement being balanced for is energy contents of the feeds are listed in Table 1. Energy concentrations (mcal/kg) ofvarious feedstuffs (NRC, 2001).

8 FeedEnergy (Mcal/kg) distillers , treat grain mixes A and B as the two feeds touse in the pearson s Square . This means you must cal-culate the amount of energy (Mcal/kg) available ineach mix. These are the steps:1. Grain mix Aa. 40% corn at Mcal/kg, so * (40 100) = Mcal/kgb. 60% SBH at Mcal/kg, so * (60 100) = + = Mcal/kg2. Grain mix Ba. 50% DDG at Mcal/kg, so * (50 100)= 50% CSH at Mcal/kg, so * (50 100)= + = Mcal/kgSecond, make sure the energy requirement ( ) falls within the range of the energy content ofeach grain mix ( to Mcal/kg); otherwise, thePearson s Square method will not , set up the pearson s Square as in Figure s Square calculations: 1.

9 Subtract across the diagonal: a. = parts grain mix Ab. - = parts grain mix B2. Sum the parts:a. parts grain mix A + parts grain mix B= total parts3. Divide each part by the total to calculate the per-cent of each feed to include. This step varies fromthe first example, because more than two ingredi-ents are being used. Before dividing, multiply theparts of each grain mix by the proportions of eachingredient in the mix (this should sum to the totalparts). The total Ration will be 55% grain mix A(40% corn and 60% SBH) and 45% grain mix B(50% DDG and 50% CSH).

10 :a. * (40 100) = parts cornb. * (60 100) = parts SBHc. * (50 100) = parts DDGd. * (50 100) = parts CSHFor grain mix parts corn total parts = parts SBH total parts = grain mix parts DDG total parts = parts CSH total parts = , go back and check the math as follows: corn * Mcal/kg = SBH * Mcal/kg = DDG * Mcal/kg = CSH * Mcal/kg = Mcal/d + + + = Mcal/d = Orig. req. Now, calculate how much of each feed ingredientto use in a 1,000-pound batch. Because the energy con-centration is in Mcal/kg, first convert 1,000 pounds tokilograms (see conversion section below for directions).