Mix by weight
97.3%Hay
- 2.7%Supplement
- 97.3lbkg Hay
- 2.7lbkg Supplement
- Mix 97.3% Hay and 2.7% Supplement to get 9.8% crude protein.
- That is 30.2 parts Hay to 0.85 parts Supplement.
- For 100 lb of mix: 97.3 lb Hay and 2.74 lb Supplement.
- The answer is on the same basis as your numbers. Extension guides work in dry matter.
- This balances crude protein only. Check the other nutrients too.
How the Pearson square works
- Write the target in the middle of a square.
- Write each feed and its % on the two left corners.
- Subtract along each line, corner to corner: the small number from the big one. Drop any minus sign.
- Write each answer on the right corner where the line ends. That is the parts of the feed on the same row.
- Add the parts. Divide each feed’s parts by the total, then times 100. That is its % of the mix.
- Check it. In 100 lb of mix, each feed’s pounds times its %, added up, should equal the target.
The steps are from Montana State, Kentucky, New Mexico State and NC State. The calculator does the same math.
A worked example
NC State’s example: a farmer feeds a 20% protein feed. The goal is 28%. A second feed has 31%.
- Feed 1: 31 − 28 = 3 parts.
- Feed 2: 28 − 20 = 8 parts.
- In all: 3 + 8 = 11 parts.
- Feed 1: 3 ÷ 11 = 27.3%. Feed 2: 8 ÷ 11 = 72.7%.
- In 100 lb of mix: 27.3 lb of Feed 1 and 72.7 lb of Feed 2.
- Check: Feed 1 gives 5.46 lb of protein, and Feed 2 gives 22.54 lb. That is 28 lb in 100 lb: 28%.
| Source and target | Feeds | Mix |
|---|---|---|
| Montana State11% protein | Chopped hay 12.25% Corn silage 10.8% | 13.8% 86.2% |
| Montana State9.8% protein | Hay 8.95% Supplement 40% | 97.3% 2.7% |
| NC State28% protein | Feed 1 20% Feed 2 31% | 27.3% 72.7% |
| Kentucky67.5% TDN | Fescue hay 48% Shelled corn 90% | 54% 46% |
| Arkansas68% TDN | Fescue hay 52% Shelled corn 90% | 58% 42% |
| New Mexico State76.8% TDN | Wheat hay 53% Corn 88% | 32% 68% |
Our calculator gives the same answers, rounded the way each source rounds. All are on a dry matter basis.
Dry matter or as fed?
The Extension guides work on a dry matter basis (NC State, Kentucky). That means the feed with the water taken out. Animal needs are listed that way too.
But you weigh feed with its water in: as fed. New Mexico State changes each feed back: divide its dry matter pounds by its dry matter. 5.16 lb of hay at 84% dry matter is 6.14 lb as fed.
Type both dry matters in step 3 and the calculator does this for you. If you leave them blank, the answer is on the same basis as your numbers.
What the square can’t do
- One nutrient at a time. Any one works: protein, TDN, or another (New Mexico State).
- Two feeds. Each can be a mix of feeds (New Mexico State). It works best with two (NC State). With many feeds, it is not always simple or exact (Arkansas).
- The target must be between the two feeds (Montana State, New Mexico State).
- Check the rest. Kentucky, Arkansas and New Mexico balance TDN first. Then they check protein, and run a second square with soybean or cottonseed meal.
- It does not know your animal. For how much an animal needs, ask your county Extension office. If an animal is sick or off feed, ask your vet.
Questions
What is the Pearson square method?
It is a quick way to mix two feeds to hit one nutrient, like crude protein or TDN. You draw a square, subtract across it, and get the parts of each feed. Extension guides from Montana, Kentucky, Arkansas, New Mexico and NC State all teach it.
How do you do a Pearson square?
Put the target in the middle. Put each feed and its % on the left corners. Subtract across each corner to corner line, and drop any minus sign. The numbers on the right are the parts of each feed. Divide each by the total parts, then times 100, for the % of the mix.
What if my target is not between the two feeds?
Then the square does not work. The target must be between the two feeds, say Montana State and New Mexico State. Swap one feed for one with more (or less) of the nutrient.
Can I use the Pearson square for three feeds?
Only two at a time. But each one can be a mix of feeds, says New Mexico State. Kentucky and Arkansas mix hay and corn first, then run a second square with soybean meal. Arkansas says that with many feeds it is not always simple or exact.
Does the Pearson square work for TDN?
Yes. Any one nutrient works, says New Mexico State. Kentucky, Arkansas and New Mexico balance TDN first, then check the protein.
Should I use dry matter or as fed?
Extension guides work on dry matter. To weigh feed out, change each feed back to as fed: divide its dry matter pounds by its dry matter. New Mexico shows 5.16 lb of hay at 84% dry matter is 6.14 lb as fed.
Sources
- Montana State University Extension, Pearson Square ExamplesundatedThe rule (target between the two feeds) and two worked examples
- NC State Extension, Craven County, The Pearson SquareNov 2023The five steps on a dry matter basis; 20% and 31% feeds mixed to 28%
- University of Kentucky Extension ASC-12, Balancing Rationsrevised June 1991Fescue and corn to 67.5% TDN, then soybean meal to 11.4% protein
- University of Arkansas Extension FSA3080, Formulating RationsundatedFescue and corn to 68% TDN, then soybean meal to 12.9% protein
- New Mexico State University Extension B-125, Ration Balancing on the RanchundatedLimits of the square; dry matter to as-fed pounds