BackTwo-Component Mixture Solver (Target % by Mass)
Enter two component mass percentages (% w/w) and a target mass percent. Optionally, provide a total mixture mass. The calculator returns the required mass ratio (A : B) and, if total is given, the actual grams of each component. Uses the classic alligation method.
Background
For components with compositions \(C_A\%\) and \(C_B\%\) mixed to reach a target \(C_T\%\), the ratio of masses depends on the differences from the target: if \(C_H=\max(C_A,C_B)\) and \(C_L=\min(C_A,C_B)\), then parts of the lower composition = \(C_H-C_T\) and parts of the higher composition = \(C_T-C_L\). Map these parts back onto A and B to get the required mass ratio.
How to use this two-component mixture solver
1) Enter % for Component A and B (w/w).
2) Enter the desired target % (must lie between A and B, inclusive).
3) (Optional) Enter total mass to get grams of A and B.
4) Click Calculate Mixture to see the required mass ratio and step-by-step alligation.
Key Points
- All percentages are mass percent (w/w).
- If target equals A or B, the mixture uses only that component.
- If A = B = target, any ratio works (we display 1:1 canonically).
Formula & Equation Used
Let \(C_A\), \(C_B\) be component mass percentages; \(C_T\) is the target. With \(C_H=\max(C_A,C_B)\) and \(C_L=\min(C_A,C_B)\):
Map parts_high to the higher-% component and parts_low to the lower-% component to get the mass ratio \(m_A:m_B\). If total mass \(M\) is provided:
Example Problem & Step-by-Step Solution
Example
Mix a 10% w/w solution (A) with a 40% w/w solution (B) to obtain a 25% w/w mixture. If you want 500 g total, how many grams of A and B are required?
- \(C_A=10\), \(C_B=40\); target \(C_T=25\). So \(C_H=40\), \(C_L=10\).
- parts_low \(= C_H−C_T = 40−25 = 15\); parts_high \(= C_T−C_L = 25−10 = 15\).
- A is the lower component, B is higher → \(A:B = 15:15 = 1:1\).
- With \(M=500\) g → \(m_A=250\) g, \(m_B=250\) g.
Frequently Asked Questions
Q: What if the target is outside the range of A and B?
Then the mixture is impossible with just these two components. Target must be between A and B (inclusive).
Q: Do I need total mass?
No. Without total mass, the calculator still gives the correct mass ratio A:B.
Q: What if A = B but not equal to target?
You cannot reach a different target using identical components.
