Short answer: The Pearson Square is a pencil method that finds the ratio of two ingredients needed to hit one target, usually crude protein. For maize at 8.5 per cent protein and soya at 44 per cent, a 20 per cent target needs about 68 parts maize to 32 parts soya. The method cannot see energy, amino acids or calcium on its own, so treat it as a first pass, not a finished ration.
Key takeaways
- The Pearson Square balances two ingredients against one nutrient at a time, usually crude protein.
- Subtract across the diagonal, and the differences are parts of each ingredient, not percentages.
- Divide each set of parts by the total to get the share of each ingredient in the mix.
- Non-protein ingredients such as limestone dilute the target, so adjust it before you square.
- The square reports protein only. It says nothing about energy, lysine or calcium.
- Use the square as a first pass, then check the full ration before you buy the sacks.
Two ingredients, one target, and a square on the back of a receipt
Draw a square on the back of a feed receipt and you can work out a grower mash in about five minutes. That is the Pearson Square. It is an old, plain method, and it survives because the arithmetic is simple enough to do without a computer, a calculator or a nutritionist sitting next to you.
The method answers one narrow question. If I have a low-protein feed and a high-protein feed, how much of each do I need to hit a protein target in the middle? The square gives you the ratio. It does not give you a ration, and it is important to be clear about that from the start.
This article shows the square with real numbers, explains what it can and cannot tell you, and sets out the traps that catch people who use it on a live farm.
What the square actually does
Put the low-protein ingredient at the bottom left of a square, the high-protein ingredient at the top left, and the target in the centre. Then subtract across the diagonals. The high figure minus the target gives the parts of the low ingredient. The target minus the low figure gives the parts of the high ingredient. Those two numbers are a ratio, and the ratio is the answer.
- Write the low ingredient bottom left, the high ingredient top left, and the target in the centre.
- Subtract diagonally: high minus target goes to the bottom right, target minus low goes to the top right.
- Read the right-hand figures as parts. Add them to get the total parts.
- Divide each part count by the total to get each ingredient's share of the mix.
There are two limits built into the method. It handles only two ingredients, and it handles only one nutrient. Crude protein is the usual choice because it is the figure on the bag, but the same square works for any single figure that mixes in a straight line, such as fat or fibre.
Ingredient values you can square with
Protein figures move between lots, mills and samples, and a figure from a general table is only a starting point. Use the analysis on the bag, or a laboratory result if the ration matters. The table gives the working values we use when we walk a farmer through the sum. Farmers who mix their own feed will find the batch steps in our guide to mixing your own poultry feed useful once the numbers are settled.
| Ingredient | Working crude protein (%) | What to watch |
|---|---|---|
| Ground maize | 8.5 | Energy source with almost no protein to speak of |
| Soya bean meal 44% | 44 | The usual high-protein partner, and worth checking for heat damage |
| Groundnut cake | 45 | Strong protein, but test for aflatoxin before use |
| Wheat bran | 15 | Cheap and bulky, with moderate protein |
| Fishmeal 60% | 60 | Very rich, and the quality varies from lot to lot |
For a fuller look at the protein sources themselves, our article on protein sources for poultry feed in Ghana compares them by cost per kilo of usable protein.
Worked example: 20 per cent protein from maize and soya
Say the grower mash needs 20 per cent crude protein, and the only two ingredients you are balancing are ground maize and soya meal. Here is the square worked through, one line at a time.
- Low ingredient is maize at 8.5. High ingredient is soya at 44. Target is 20.
- Maize parts: 44 − 20 = 24.
- Soya parts: 20 − 8.5 = 11.5.
- Total parts: 24 + 11.5 = 35.5.
- Maize share: 24 ÷ 35.5 = 67.6 per cent. Soya share: 11.5 ÷ 35.5 = 32.4 per cent.
In a 100 kg batch, that is 67.6 kg of maize and 32.4 kg of soya. The table shows where the protein comes from.
| Ingredient | Parts | Share (%) | Protein contributed (%) |
|---|---|---|---|
| Ground maize | 24 | 67.6 | 5.75 |
| Soya 44% | 11.5 | 32.4 | 14.26 |
| Total | 35.5 | 100 | 20.0 |
Notice what the square did and did not do. It hit the protein figure and nothing else. There is no fat, lysine, calcium or energy figure in that answer, so the mash still needs its minerals, premix and any amino acid correction added in the proper way.
Multiply back before you trust the answer
Every square should be checked the same way. Multiply each share by its protein figure, add the results, and see whether you land back on the target. For the maize and soya mash, that is 0.676 × 8.5 plus 0.324 × 44, which comes to about 20.0. Small differences come from rounding the shares.
If the multiplication misses the target by a lot, the usual cause is a swap. Someone subtracts the low figure from the target when they should subtract the target from the high figure, and the parts come out negative or lopsided. A negative part is always a sign to stop and redo the diagonals.
Keep the working on the receipt. The next time the bag changes, you want to redo the sum in two minutes, not reconstruct it from memory.
The dilution trap: limestone and premix change the target
This is the mistake we see most often. Suppose you want 20 per cent protein in the finished mash, but 3 kg of every 100 kg is limestone, salt and premix, which carry no protein. Those 3 kg are dead weight as far as protein goes. The 97 kg that carry protein must now deliver the full 20 per cent of the batch, which means they must average a little more than 20.
The fix is to adjust the target before you square. Divide 20 by 0.97 to get 20.62, and square the maize and soya against that figure. The sum then gives 63.9 kg of maize and 33.1 kg of soya in the 97 kg, and the protein comes out at 20.0 for the whole batch.
| Approach | Maize (kg) | Soya (kg) | Limestone and premix (kg) | Protein delivered (%) |
|---|---|---|---|---|
| Square against 20 without adjusting | 65.6 | 31.4 | 3.0 | 19.4 |
| Square against 20.62, adjusted | 63.9 | 33.1 | 3.0 | 20.0 |
The unadjusted mash looks right on the sum and still falls short by 0.6 points of protein. Over a whole batch, that gap is the difference between a ration that meets its target and one that does not.
When the target sits close to one ingredient
The square can produce an answer that is arithmetically correct and practically useless. Take a layer target of 16 per cent protein, with wheat bran at 15 per cent and soya at 44 per cent. Set the bran as the low ingredient and the soya as the high one, and the parts come out at 28 for the bran and 1 for the soya.
That is 96.6 per cent bran and 3.4 per cent soya. The protein adds up, so the square says the job is done. But a mash of nearly all bran is bulky, low in energy and far from what a laying hen needs. The protein target was met by the wrong ingredient.
When the square gives you a share that looks lopsided, do not argue with the sum. Go back to the energy and the other nutrients, and choose ingredients that can carry them.
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What the square cannot see
The square is blind to everything except the one figure you give it. A mash can hit 20 per cent protein and still be short of energy, lysine, methionine, calcium and available phosphorus. Two ingredients that give the same protein can differ a great deal in energy, and maize against soya is a good example, since the soya brings protein but much less energy per kilo than the maize.
There is also the question of quality within the protein. Soya that has been overheated, or groundnut cake that carries a toxin, can have the same protein figure on paper and a very different value to the bird. The square cannot tell the difference.
For a full multi-ingredient ration, you need a method that balances several nutrients at once. Our article on least-cost poultry feed formulation in Ghana shows how that works, and the broader feed formulation basics guide explains which nutrients to check first.
Three ingredients: fix one share, then square the rest
The square handles only two ingredients, but you can bring in a third by fixing its share first. Suppose you want 4 kg of fishmeal at 60 per cent protein in every 100 kg, and you want maize and soya to do the rest of the work. The fishmeal supplies 2.4 kg of protein, so the remaining 96 kg must supply 17.6 kg, which is 18.33 per cent.
Square maize against soya at 18.33. The maize parts are 44 − 18.33 = 25.67, and the soya parts are 18.33 − 8.5 = 9.83. The total is 35.5 parts. Maize is 72.3 per cent of the 96 kg, which is 69.4 kg, and soya is 27.7 per cent, which is 26.6 kg. Add the 4 kg of fishmeal and the batch delivers 20.0 per cent protein.
The method works, but it gets fiddly fast. Each extra ingredient means another fixed share and another adjusted target. Once you have four or five ingredients to balance, a spreadsheet or a least-cost calculation is the safer tool.
Pitfalls on a live farm in Ghana
Most of the pitfalls come from the ingredients, not the arithmetic. Maize moisture changes with the season, so the energy and protein you square against in the dry harmattan months can be a little off by the rains. Soya lots vary, and a bag that says 44 may test lower. Groundnut cake can carry aflatoxin, which the square will never show you, so it needs a test before it goes in the mix.
The other pitfall is the scale. Parts that come out to 1.4 or 0.7 are hard to weigh out on a farm scale that reads in whole kilos. Scale the batch first, then convert the parts to grams or kilos for the weighing. In a 250 kg batch, each one per cent of the mix is 2.5 kg, so the rounding error is small in relative terms but real in absolute ones. Our note on storing feed to stop aflatoxin covers how to keep the groundnut cake and maize sound once you have bought it.
Our note on soya and groundnut cake processing covers how to check those two ingredients before they reach the trough.
A checklist for a five-minute square
- Write down the protein of each ingredient from the bag analysis or a recent test.
- Write the target protein for your birds and their stage, from your breeder guide or nutritionist.
- Subtract diagonally, high minus target and target minus low, and write the parts.
- Add the parts and divide each by the total to get the shares.
- Adjust the target for any ingredient that carries no protein, such as limestone or premix.
- Multiply each share by its protein and confirm the answer returns the target.
- Check energy, lysine, methionine and calcium in a full formula before you buy the sacks.
If you want help turning the square into a full ration, our common questions page is a good starting point, and WhatsApp +233 24 915 1503 reaches us directly with questions about the chicks you are feeding. If you are starting a new flock, our breeds section and layer day-old chicks page list the lines we hatch and import.
Questions farmers ask
What is the Pearson Square used for?
It is used to find the ratio of two ingredients that will hit one target figure, usually crude protein. A farmer can use it to decide how much maize and how much soya to put in a mash for a given protein level. It does not balance energy, amino acids or minerals, so it is a first step, and the result still needs checking against the full formula before any sacks are bought.
Can the Pearson Square handle more than two ingredients?
Not directly. You can handle a third ingredient by fixing its share first, then squaring the remaining two against an adjusted target. Beyond three or four ingredients, a least-cost calculation or a spreadsheet solver is much more reliable, because it checks several nutrients at once instead of one.
Which protein figure should I use for soya?
Use the analysis on the bag or a recent laboratory result for your own lot. A soya bean meal sold as 44 per cent protein may test a little higher or lower, and the square is only as good as the number you feed it. Keep the figure and the batch date on the working sheet.
Why do my parts not add up to 100?
The parts are ratios, not percentages. They add up to a total number of parts, such as 35.5, and you divide each by that total to get the percentage share. If you divide the wrong way, the shares will not add up to 100, so check the division first.
Does the Pearson Square tell me about energy?
No. It only sees the one nutrient you give it. Two ingredients can match on protein and differ a lot in energy, so a protein-balanced mash can still be short of energy. Check the energy figure separately, and compare the result with your target for the stage of the birds.
Can I use the Pearson Square for layers?
Yes, for the protein part of a layer ration. Layer rations also need calcium, phosphorus and amino acids, and those are not covered by the square. Use the square to set the grain share, then check the calcium separately, because many layer mashes fail on calcium rather than protein.
Is the Pearson Square accurate enough for a commercial mix?
It is accurate enough for a first pass and for understanding why a ration behaves as it does. A commercial mix needs a full formula that balances several nutrients, uses laboratory values and includes safety margins. Treat the square as the sketch, not the drawing.
