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.