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PEARSON’S SQUARE INTRODUCTION
Pearson’s Square is a simple, quick
way to Calculate the amounts of
feed necessary to meet a nutrient
requirement of poultry and other
animals.
This method is most effective when
only two feeds are being used.
TO USE PEARSON’S SQUARE
1. Calculate the absolute diagonal difference of the
nutrient concentration of two feed stuff from the
nutrient requirement
2. The answers on the right side of the square are
the parts of each feed to include in the ration
3. Sum the parts of the two feeds to get the total
4. Then, divide each part by the sum of the parts to
calculate the percent of each feed in the ration.
SIMPLE RATION FORMULATIONS
Soybean
Meal 45%
C.P
Corn 10%
C.P
15%
C.P
5 parts of
soybean
meal
30 parts
of maize
Total parts
(30+5=35)
PEARSON’S SQUARE CALCULATION1.Subtract across the diagonal:
a. 15% - 10% = 5 parts Soybean meal
b. 15% - 45% = 30 parts Corn
2. Sum the parts:a. 5 parts soybean meal + 30 parts corn = 35 total
parts
3. Divide each part by the total to calculate the percent
of each feed to include:a.5 ÷ 35 =0.143 x 100 = 14.3% Soybean meal
b.30 ÷35= 0.857 x 100 = 83.6% Maize
IMPORTANT THINGS TO REMEMBER
1. This method is only efficient when two
ingredients are being used.
2. The animal nutrient requirement (number
in center of the square) must fall between
the nutrient concentrations in both feeds.
3. Disregard any negative numbers calculated
on the right side of the square. Treat them
as positive numbers.
USING PEARSON’S SQUARE TO FORMULATE
USING MORE THAN TWO INGREDIENT
a. It is possible to use Pearson's square to
balance more than two ingredients. Though
not always recommended,
b. For example, thought of two separate
mixed grain (A and B), each made up of
two ingredients, making it a total of four
feedstuffs.
Example.
FEED Maize Fish
meal
Sunflower
seed cake
Barley
C.P (%) 9 45 26 11.5
1. Grain mixture A is 50% maize and 50% sunflower
meal (SFM)
2. Grain mixture B is 70% barley and 30% fish meal
(FM).
Note: The protein requirement being balanced for is 18% Crude protein.
Mixing of grain mixes.
Treat grain mixture A and B as the two
feeds to use in the Pearson’s Square.
Calculate the amount of crude protein
available in each mixture.
These are the steps:
Grain mix A
a. 50% Maize at 9% C.P, so 9% x (50 ÷ 100)
=4.5 CP parts in 50 parts Maize
b. 50% SFM at 26% C.P, so 26% x (50 ÷ 100)
=13 CP parts in 50 parts SFM
c. 4.5 + 13 = 17.5 CP parts in 100 parts grain mix
A
2. Grain mix B
a. 70% Barley at 11.5% C.P, so 11.5% x (70
÷100) = 8.05 CP parts in 70 parts of barley
b. 30% FM at 45% C.P, so 45% x (30 ÷ 100)
= 13.5 CP parts in 30 parts of FM
c. Total crude protein 8.05+ 13.5 = 21.55 CP parts in 100 parts grain mix B
Make sure the crude protein requirement (18%
C.P) falls within the range of the protein content of
each grain mix (17.5 to 21.55 C.P); otherwise, the
pearson’s Square method will not work.
Formulating using two ingredients.
Grain mix
A 17.5 C.P
Grain mix B
21.55 C.P
3.55 parts
grain mix A
0.5 parts grain mix B
4.05 Total parts
Pearson’s square calculation
1. Subtract across the diagonal:
a. 18% – 17.5 = 0.5 parts grain mix A
b. 18% - 21.55 = 3.55 parts grain mix B
2. Sum the parts:
a. 0.5 parts grain mix A + 3.55 parts grain mix B
= 4.05 total parts
3. Divide each part by the total to calculate the percent of each feed to include. This step varies from the first example, because more than two ingredients are being used. Before dividing, multiply the parts of each grain mix by the proportions of each ingredient in the mix
CONTINUATION
The total ration will be 87.6% grain mix A
(50% maize and 50% SFM) and 12.4% grain
mix B (70% Barley and 30% FM):
i.e.
3.55 x (50 ÷ 100) = 1.78 parts Maize
3.55 x (50 ÷ 100) = 1.78 parts SFM
0.5 x (70 ÷ 100) = 0.35 parts Barley
0.5 x (30 ÷ 100) = 0.15 parts FM
For grain mix A:
1.78 parts maize ÷ 4.05 total parts = 0.44
1.78 parts SFM ÷ 4.05 total parts = 0.44
For Grain mix B:
0.35 parts Barley ÷ 4.05 total parts = 0.086
0.15 parts FM ÷ 4.05 total parts = 0.037
Finally, go back and check the math
as follows:
0.44 Maize x 9% C.P = 3.96
0.44 SFM x 26% C.P = 11.4
0.086 Barley x 11.5% C.P= 1
0.037 FM x 45% C.P= 1.67
3.96 + 11.4 + 1 + 1.67 = 18.03 % C.P
SIMPLE COSTING.Cost of formulating a 100kg bag.
1.78/4.05 parts of maize x100kgs =43.8kgs x
sh.35/kg=Ksh.1,533
1.78/4.05 parts of SFM x100kgs =sh.43.8kgs x
sh.30/kg=Ksh.1,314
0.35/4.05 parts of Barley x 100kgs =8.7kgs x
Ksh.35/kg=Ksh.305
0.15/4.05 parts of FM x 100kgs =3.7kgs x
Ksh.100/kg=Ksh.370
Total estimated cost 1,533+1,314+305+305=sh.3522
per 100kg bag of feed.