Pearson square calculator

Mix two ingredients to reach a target percentage: milk fat, feed protein, meat fat, syrup °Brix and more. You get the amounts, the ratio, the square itself and the full working, so you can check every step.

Ingredients and target

Examples

Crude protein on the same moisture basis (as-fed or dry matter) for both feeds.

Concentrations are measured by

Exact when you weigh the ingredients (fat %, protein %, °Brix, % lean).

Ingredient A
Ingredient B

Must lie between the two ingredient concentrations.

Blend

Corn
885.71 kg
88.571% of the blend
Soybean meal
114.29 kg
11.429% of the blend
Ratio Corn : Soybean meal
7.75 : 1
31 : 4 parts
Blend
1000 kg
at 14%
Pearson squareCorn 10% top left, Soybean meal 45% bottom left, target 14% in the centre. Differences across the diagonals give 31 parts of Corn and 4 parts of Soybean meal.14%target10%Corn45%Soybean meal31parts Corn4parts Soybean meal

Worked calculation

  1. Write Corn (10%) and Soybean meal (45%) on the left corners and the target (14%) in the centre.
  2. Subtract across each diagonal and ignore the sign: |14 − 45| = 31 parts of Corn; |10 − 14| = 4 parts of Soybean meal.
  3. Total parts = 31 + 4 = 35. So Corn is 31 ÷ 35 = 88.571% of the blend and Soybean meal is 11.429%.
  4. For 1000 kg: Corn = 1000 × 88.571% = 885.71 kg; Soybean meal = 1000 × 11.429% = 114.29 kg.
  5. Check: 885.71 × 10% + 114.29 × 45% = 140 kg, which is 14% of 1000 kg.

How to use it

  1. Pick an example, or enter your two ingredients and their concentrations.
  2. Say whether the percentages are by mass or by volume (see below; most food and feed percentages are by mass).
  3. Enter the target concentration. It must lie between the two ingredients.
  4. Enter the batch size to get amounts, and optionally the cost per unit of each ingredient to get the batch cost.

How the Pearson square works

Put ingredient A's concentration in the top-left corner, ingredient B's in the bottom-left, and the target in the middle. Subtract across each diagonal, ignoring the sign. The number in the top-right is the parts of A you need; the number in the bottom-right is the parts of B.

parts of A = |target − B| parts of B = |A − target| share of A = parts of A ÷ (parts of A + parts of B)

It works because it is a mass balance. The amount of the measured substance (fat, protein, sugar) in the blend equals the sum of the amounts brought in by each ingredient. The calculator shows this check under every result.

Example (feed): corn at 10% crude protein and soybean meal at 45%, mixed to 14%: 45 − 14 = 31 parts corn and 14 − 10 = 4 parts soybean meal. Corn is 31 ÷ 35 = 88.57% of the mix and soybean meal 11.43%. For 1,000 kg that is 885.7 kg of corn and 114.3 kg of soybean meal. This matches the worked example published by Cornell Cooperative Extension.

Example (milk): standardising to 3.25% fat with 38% cream and 0.05% skim milk: 3.2 parts cream to 34.75 parts skim, so 100 kg of milk needs 8.43 kg of cream and 91.57 kg of skim.

Mass or volume?

The square is exact when the concentrations are mass percentages and you weigh the ingredients. Fat in milk, protein in feed, lean or fat in meat, and °Brix (sugar by mass) are all mass percentages. If you measure the ingredients by volume, convert with their densities first.

For volume percentages such as % alcohol by volume, the method assumes the volumes simply add up. Alcohol and water shrink slightly when mixed, so the result is approximate; check the finished blend with a hydrometer or alcoholmeter.

Limitations

Frequently asked questions

Why does it say my target cannot be reached?
A blend always lies between its ingredients. To reach 14% you need one ingredient above 14% and one below it.
What if the target equals one ingredient?
Then you only need that ingredient. The calculator shows 100% of it.
Can I use it for three ingredients?
Not yet. With three ingredients there are many possible blends for a single target, so you would need to fix one amount or add another target.

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