About the Pearson Square Calculator
This Pearson square calculator works out how much of two ingredients with different concentrations to blend to reach a target concentration. It is the classic method dairy technicians use to standardise milk and cream to a fat percentage, and it works equally well for sugar (Brix) in juices and syrups, protein in feed or flour blends, or any other property that mixes in proportion to amount. It is also used for fortifying wine with spirit, where ABV blends approximately by volume (real mixtures shrink slightly, so the result lands a touch low).
Enter the concentration of the first ingredient, the concentration of the second, the target and the total amount you want to end up with. The calculator gives the weight of each ingredient, the parts ratio and the percentage of the batch each one makes up. For example, whole milk at 3.25% fat and heavy cream at 36% blend into 12% half-and-half at roughly 2.7 parts milk to 1 part cream.
The target must lie between the two concentrations — you cannot make 40% cream from 3% milk and 36% cream. Percentages should be by weight (as fat and Brix normally are) and amounts should be weighed; mixing by volume introduces small errors because ingredients have different densities.
With the default inputs, the amount of ingredient a is 732.82. Change any value above to recalculate instantly.
How to use the pearson square calculator
- 1Enter the concentration of each ingredient (fat %, Brix, protein %…).
- 2Enter the concentration you want to reach.
- 3Enter the total batch size and unit.
- 4Weigh out the amounts of A and B shown and mix thoroughly.
Formula and method
Draw a square with the two ingredient concentrations on the left corners and the target in the middle. Subtracting diagonally across the square — ignoring signs — gives the parts of each ingredient: the parts of A equal the distance between B and the target, and the parts of B equal the distance between A and the target. The ingredient closer to the target gets more parts.
It is a shortcut for the mass balance A·x + B·(1 − x) = T, solved for the fraction x of ingredient A. It only works when the property blends linearly by weight (fat, solids, sugar, protein) and when the target lies between the two concentrations.
- A, B
- Concentrations of the two ingredients (%)
- T
- Target concentration (%)
- Total
- Total blend amount wanted
Worked examples
Half-and-half from whole milk and heavy cream
Parts of milk = 36 − 12 = 24; parts of cream = 12 − 3.25 = 8.75, for 32.75 parts in all. For 1,000 g, use 1,000 × 24 ÷ 32.75 ≈ 733 g of milk and 267 g of cream.
Sweetening juice to 20 °Brix with syrup
Juice at 12 °Brix gets 65 − 20 = 45 parts; syrup at 65 °Brix gets 20 − 12 = 8 parts. For 10 kg, that is 8.49 kg of juice and 1.51 kg of syrup.
2% milk from skim and whole milk
Skim (0.1%) gets 3.25 − 2 = 1.25 parts and whole milk gets 2 − 0.1 = 1.9 parts. For 4 kg of 2% milk, mix about 1,587 g skim with 2,413 g whole milk.
Frequently asked questions
How does the Pearson square work?+
Write the two concentrations on the left corners of a square and the target in the center. Subtract diagonally, ignoring negative signs, to get the parts of each ingredient. The parts tell you the ratio to blend them in.
How do I make half-and-half from milk and cream?+
Half-and-half is about 10.5–18% fat. Using whole milk (3.25%) and heavy cream (36%), a 12% blend takes roughly 2.7 parts milk to 1 part cream by weight — about 733 g milk and 267 g cream per kilogram.
Can I use the Pearson square with volumes?+
Only approximately. The method assumes percentages and amounts are on the same basis, usually weight. Milk and cream have similar densities, so volume works well enough at home, but syrups and alcohol need weighing.
Why does the calculator say my target is impossible?+
A blend of two ingredients always ends up between their concentrations. If the target is higher than both or lower than both, you need a stronger or weaker ingredient, or a third ingredient.
What else is the Pearson square used for?+
It is used in animal-feed formulation to balance protein, in winemaking to fortify with spirit or blend acid levels, in ice-cream mix standardisation and in chemistry to dilute solutions.