How this calculation works
The Pearson square solves one blend target using two ingredients that bracket it. Its fractions must be calculated on a shared basis. This page uses dry-basis protein and only afterward converts the dry ingredient masses to as-fed weights.
Low dry share = (high protein − target)/(high protein − low protein); wet ingredient mass = assigned dry mass/ingredient DM fractionA worked example
A twenty-percent target between ten and forty percent protein needs two-thirds of its dry matter from the low ingredient and one-third from the high ingredient. For 100 dry kilograms, that is 66.667 and 33.333 kg. At ninety and fifty percent DM, the corresponding as-fed masses are about 74.074 and 66.667 kg. Their wet weights differ from the dry shares, which is why moisture conversion follows the protein balance.
Good to know
Two ingredients, one nutrient and supplied target only; no full ration, price optimization, digestibility or feeding prescription. Additional ingredients or simultaneous nutrient constraints require a broader formulation method. Do not interpret this single-target solution as nutritional adequacy.
Reference: Oregon State University — Pearson square (opens in a new tab) ↗
What the model answers
The Pearson square solves one blend target using two ingredients that bracket it. Its fractions must be calculated on a shared basis. This page uses dry-basis protein and only afterward converts the dry ingredient masses to as-fed weights.
That separation matters when the two ingredients have different moisture levels. Equal dry shares do not necessarily mean equal weights on a feed scale. The table retains both dry and as-fed quantities.
The Feed ration dry matter and protein calculator can audit the resulting ingredient masses alongside additional feeds. It totals composition without assuming that this two-ingredient target supplies every nutritional need.
Measure and enter consistently
Low protein must be strictly less than high protein, and the target must lie between them. An endpoint target is allowed and uses only its corresponding ingredient. Identical analyses cannot determine a unique mixture.
Enter dry-matter percentages separately for the two ingredients and use prices per as-fed kilogram. The target and ingredient suitability must be supplied externally; no species or life-stage requirement is generated here.
Interpret the result
Protein kilograms from the two dry shares should sum to target percentage times total dry mass. This conservation check is more informative than relying only on the final wet weights.
The formula balances only one nutrient. It neither minimizes cost nor enforces maximum inclusion levels or other nutrient requirements. A cheap computed blend is not automatically a usable complete ration.
Work through the numbers
A twenty-percent target between ten and forty percent protein needs two-thirds of its dry matter from the low ingredient and one-third from the high ingredient. For 100 dry kilograms, that is 66.667 and 33.333 kg.
At ninety and fifty percent DM, the corresponding as-fed masses are about 74.074 and 66.667 kg. Their wet weights differ from the dry shares, which is why moisture conversion follows the protein balance.
Where this model stops
Two ingredients, one nutrient and supplied target only; no full ration, price optimization, digestibility or feeding prescription.
Additional ingredients or simultaneous nutrient constraints require a broader formulation method. Do not interpret this single-target solution as nutritional adequacy.
A few questions, answered
Why must the target be bracketed?
A weighted mixture cannot have a protein fraction outside both ingredient fractions without adding a different component.
Can I solve directly using wet weights?
Only after converting analyses to a shared basis. This page solves dry shares and then derives wet weights separately.