Feeding Sheep

Author: Steven H. Umberger, Extension Animal Scientist, Virginia Tech

Publication Number 410-853, June 1996

Pearson Square

Protein is often the major limiting nutrient in a sheep diet. The Pearson Square is used to formulate simple diets on the basis of protein.

Problem: Using Table 1, assume a 155 lb ewe needs .92 lb crude protein per day to meet her nutrient requirements in early lactation. Four pounds of mixed grass-clover hay (13% crude protein) will be fed per day along with 2 lb of a mixture of barley and soybean meal. What proportion of barley and soybean meal should be used in the mix?


  1. Determine the percentage of crude protein (CP) contributed by the hay.
    1. 4 lb x .88% Dry Matter = 3.52 lb Dry Matter
    2. 3.52 lb Dry Matter x 13% CP = .46 lb CP

  2. Determine the amount of additional CP needed from the barley and soybean meal mix.
    1. .92 lb CP Required - .46 lb CP from the Hay = .46 lb additional CP needed

  3. Determine the percentage of crude protein needed in the barley and soybean meal mix.
    1. 2 lb x .90% Dry Matter = 1.8 lb Dry Matter
    2. .46 lb additional CP needed — 1.8 lb Dry Matter = 25.5% CP in the grain mix

  4. Use a Pearson Square to determine the proportion of barley and soybean meal in the mix.
    1. Subtract diagonally across the square, the smaller number from the larger number without regard to the sign and record the difference at the right corners.
    2. The parts of each feed can be expressed as a percentage of the total.
      • 18.5 — 33.0 (100) = 56% Barley
      • 14.5 — 33.0 (100) = 44% Soybean Meal
    3. Check the math to make sure that .46 lb CP is coming from the barley and soybean meal mix.
      • 1.8 lb Dry Matter from Grain Mix x 56% Barley x 11% CP = .11 lb CP
      • 1.8 lb Dry Matter from Grain Mix x 44% Soybean Meal x 44% CP = .35 lb CP
      • .11 lb CP from Barley + .35 lb CP from Soybean Meal = .46 lb CP from the 2 lb Grain Mix

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