Pearson Square Calculator (Mixing Two Strengths)
How much of a strong and a weak ingredient to mix to reach a target strength: the parts of each, and the amounts for a total quantity.
Results
What this tool does
The Pearson square is the quick way to blend two things of different strength into a target between them, long used for animal feed and equally good for dilutions. Put the target in the middle: the parts of the strong ingredient are the target minus the weak one, and the parts of the weak one are the strong minus the target. For 70 % and 20 % to make 40 %, that is 20 parts and 30 parts, so 40 % and 60 % of the batch. It assumes the strengths mix linearly, which holds for percentages by weight; for alcohol by volume the mixed volume is a little less than the sum of the parts.
Formula
parts of A = C − B · parts of B = A − C · amount of A = total × (C − B) ÷ (A − B)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
a | Strength of the stronger ingredient (A) | % |
b | Strength of the weaker ingredient (B) | % |
c | Strength you want (C) | % |
t | Total amount to make | — |
QA | Amount of A | — |
QB | Amount of B | — |
PA | Parts of A | — |
PB | Parts of B | — |
ST | Can the mix reach it? | — |
Worked example
- Strength of the stronger ingredient (A)70 %
- Strength of the weaker ingredient (B)20 %
- Strength you want (C)40 %
- Total amount to make100
- Amount of A40.00
- Amount of B60.00
- Parts of A20.00
- Parts of B30.00
- Can the mix reach it?Yes: C lies between B and A
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.