Pearson Square Calculator

Use the Pearson Square Calculator to determine the proportions of two ingredients needed to achieve a desired nutrient level in a final mixture.

Mixture Proportions

Table showing the parts and percentage of each ingredient in the mix.

Ingredient	Parts	Percentage (%)
Ingredient 1	–	–
Ingredient 2	–	–
Total	–	100.00

What is a Pearson Square Calculator?

A Pearson Square Calculator is a tool used to determine the correct proportions of two ingredients needed to achieve a specific nutrient concentration in a final mixture. It’s most commonly used in animal nutrition to formulate feed rations, ensuring livestock receive the desired amount of a particular nutrient, like protein or energy, by mixing two feedstuffs with different concentrations of that nutrient.

The method is a simple graphical way to solve simultaneous equations. You place the desired nutrient level in the center of a square, the nutrient levels of the two ingredients at the two left corners, and then calculate the differences diagonally to find the parts of each ingredient needed. The Pearson Square Calculator automates this process.

Who should use it?

• Farmers and livestock producers mixing their own feeds.
• Animal nutritionists formulating rations.
• Students learning about animal nutrition and feed formulation.
• Feed mill operators.

Common misconceptions

• It only works for protein: While commonly used for protein, the Pearson Square method can be used for any nutrient (energy, calcium, phosphorus, etc.) as long as you have two ingredients with different levels of that nutrient and a target level in between.
• It’s overly complicated: The manual method looks like a diagram, but the underlying math is simple subtraction and ratio calculation, which the Pearson Square Calculator handles easily.
• It balances the entire diet: The Pearson Square only balances ONE nutrient using TWO ingredients. A complete diet formulation requires balancing multiple nutrients and often uses more complex methods or software, but the Pearson Square is a fundamental tool for simple mixtures.

Pearson Square Calculator Formula and Mathematical Explanation

The Pearson Square is a visual method for solving a simple mixing problem. Let’s say:

• D = Desired nutrient level in the final mix (%)
• H = Nutrient level in the higher-nutrient ingredient (%)
• L = Nutrient level in the lower-nutrient ingredient (%)

The desired level (D) must be between L and H.

The steps are:

1. Write the desired nutrient level (D) in the center of the square.
2. Write the nutrient levels of the two ingredients (H and L) at the left corners.
3. Subtract diagonally across the square, taking the absolute difference:
   • Parts of Higher Ingredient = |D – L|
   • Parts of Lower Ingredient = |H – D|
4. The sum of these parts (|D – L| + |H – D|) gives the total parts in the mixture.
5. To get the percentage of each ingredient:
   • % of Higher Ingredient = (|D – L| / Total Parts) * 100
   • % of Lower Ingredient = (|H – D| / Total Parts) * 100

Variables Table

Variable	Meaning	Unit	Typical Range
D	Desired Nutrient Level	%	0-100 (must be between L and H)
H	Nutrient in High Ingredient	%	0-100
L	Nutrient in Low Ingredient	%	0-100
Parts H	Parts of High Ingredient	Parts	0+
Parts L	Parts of Low Ingredient	Parts	0+
Total Parts	Total Parts in Mixture	Parts	0+

Practical Examples (Real-World Use Cases)

Example 1: Mixing Broiler Feed for Protein

A farmer wants to create a broiler starter feed with 22% crude protein. They have corn with 8% protein and soybean meal with 45% protein.

• Desired Nutrient (D) = 22%
• Ingredient 1 (Corn – L) = 8%
• Ingredient 2 (Soybean Meal – H) = 45%

Using the Pearson Square Calculator:

• Parts of Soybean Meal (H) = |22 – 8| = 14 parts
• Parts of Corn (L) = |45 – 22| = 23 parts
• Total Parts = 14 + 23 = 37 parts
• % Soybean Meal = (14 / 37) * 100 = 37.84%
• % Corn = (23 / 37) * 100 = 62.16%

The farmer needs to mix 37.84 kg of soybean meal with 62.16 kg of corn to get 100 kg of feed with 22% protein.

Example 2: Adjusting Energy Content

An animal nutritionist needs to create a mix with 13 MJ/kg of digestible energy (DE). They are using barley (11.5 MJ/kg DE) and a fat source (36 MJ/kg DE).

• Desired Nutrient (D) = 13 MJ/kg
• Ingredient 1 (Barley – L) = 11.5 MJ/kg
• Ingredient 2 (Fat – H) = 36 MJ/kg

Using the Pearson Square Calculator:

• Parts of Fat (H) = |13 – 11.5| = 1.5 parts
• Parts of Barley (L) = |36 – 13| = 23 parts
• Total Parts = 1.5 + 23 = 24.5 parts
• % Fat = (1.5 / 24.5) * 100 = 6.12%
• % Barley = (23 / 24.5) * 100 = 93.88%

The mix should contain 6.12% fat and 93.88% barley to achieve 13 MJ/kg DE.

How to Use This Pearson Square Calculator

1. Enter Desired Nutrient Level: Input the target percentage or concentration of the nutrient (e.g., protein, energy) you want in your final mix in the “Desired Nutrient Level” field.
2. Enter Ingredient 1 Nutrient Level: Input the nutrient level of your first ingredient in the “Nutrient Level in Ingredient 1” field.
3. Enter Ingredient 2 Nutrient Level: Input the nutrient level of your second ingredient in the “Nutrient Level in Ingredient 2” field. Ensure the desired level falls between the levels of ingredient 1 and 2.
4. Calculate: Click the “Calculate” button or simply change any input value. The results will update automatically.
5. Read Results: The “Results” section will show the parts and percentages of each ingredient needed. The table and chart will also update to reflect these proportions.
6. Reset (Optional): Click “Reset” to return to default values.
7. Copy Results (Optional): Click “Copy Results” to copy the main findings to your clipboard.

The Pearson Square Calculator provides the proportions on an “as-is” or “as-fed” basis if your input nutrient levels are on that basis. If you input on a “dry matter” basis, the results will be on a dry matter basis.

Key Factors That Affect Pearson Square Results

1. Desired Nutrient Level: The target concentration directly influences the ratio. A target closer to one ingredient’s level will require more of that ingredient.
2. Nutrient Levels of Ingredients: The difference between the nutrient levels of the two ingredients and the desired level dictates the proportions. The wider the difference, the smaller the amount of the high-nutrient ingredient might be needed if the desired is close to the low.
3. Accuracy of Nutrient Data: The results are only as accurate as the input values for the ingredients. Using outdated or incorrect nutrient composition data for feedstuffs will lead to an incorrectly balanced mix. Regular feed analysis is recommended for precision. We have more on our feed ingredient database.
4. Ingredient Availability and Cost: While the Pearson Square Calculator gives proportions, the practical choice of ingredients and their use will depend on what’s available and their relative costs.
5. Mixing Efficiency: The calculated proportions assume perfect mixing. In practice, ensure your mixing equipment can homogenously blend the ingredients in the calculated ratios.
6. Other Nutrients: The Pearson Square balances only one nutrient. You must consider the impact of the mix on other essential nutrients in the diet. A livestock ration balancer might be needed.
7. Dry Matter vs. As-Fed Basis: Ensure you are consistent. If you use nutrient values on a dry matter basis, your proportions are for dry matter, and you’ll need to adjust for moisture content when actually mixing. For a guide, see animal nutrition basics.

Frequently Asked Questions (FAQ)

What is the Pearson Square used for?

It’s primarily used in animal nutrition to calculate the proportions of two feed ingredients needed to achieve a desired concentration of a single nutrient (like protein or energy) in a mixture.

Can the Pearson Square Calculator balance more than one nutrient?

No, the basic Pearson Square method and this Pearson Square Calculator are designed to balance only one nutrient at a time using two ingredients. For multiple nutrients, more advanced techniques or software are needed, although you can use it sequentially with pre-mixes.

What if my desired nutrient level is outside the range of my two ingredients?

The Pearson Square method only works if the desired nutrient level is between the nutrient levels of the two ingredients you are mixing. If it’s outside, you cannot achieve it by simply mixing these two ingredients; you’d need at least one ingredient with a level on the other side of your target.

Can I use the Pearson Square Calculator for liquids?

Yes, as long as you express the concentration of the “nutrient” (e.g., alcohol content, sugar content) consistently (e.g., as percentages by weight or volume) for both ingredients and the desired mix.

How accurate is the Pearson Square method?

The mathematical method is accurate. The accuracy of the final mix depends entirely on the accuracy of the nutrient values you use for your ingredients and how well you mix them. See our feed formulation guide for more.

What are “parts” in the Pearson Square results?

“Parts” represent relative amounts (by weight or volume, depending on how your nutrient levels are expressed). If you get 5 parts of A and 10 parts of B, it means for every 5 kg of A, you need 10 kg of B (or 5 lbs of A and 10 lbs of B, etc.).

Can I use more than two ingredients with the Pearson Square?

You can, but indirectly. You could first mix two ingredients to create a “pre-mix” with a new average nutrient level, and then use that pre-mix as one of your “ingredients” in a second Pearson Square calculation with a third ingredient.

Is the Pearson Square Calculator free to use?

Yes, this online Pearson Square Calculator is free for you to use for your feed formulation needs.