Chemistry
Alligation Calculator
Work out how much of a weak and a strong solution to mix to reach a target strength.
Your inputs
Change any value to update the result instantly.
Weaker solution needed
266.667 mL
Stronger solution needed
233.333 mL
Mixing ratio (weak : strong)
8 : 7
Total prepared
500 mL
Strength check
12 %
What this calculator does
Splits a required quantity between a weaker and a stronger solution so the blend reaches a target strength.
What your result means
The two quantities that, mixed together, give exactly the target strength; the parts follow the alligation cross.
Formula and working
Q_low = Q(C₂ − C_t) ÷ (C₂ − C₁) ; Q_high = Q(C_t − C₁) ÷ (C₂ − C₁)
- 1
Collect the inputs
Strength of the weaker solution (C₁) = 5 %; Strength of the stronger solution (C₂) = 20 %; Target strength (C_t) = 12 %; Total quantity needed (Q) = 500 mL
- 2
Apply the formula
Q_low = Q(C₂ − C_t) ÷ (C₂ − C₁) ; Q_high = Q(C_t − C₁) ÷ (C₂ − C₁)
- 3
Result
Weaker solution needed = 266.667 mL
Frequently asked questions
Symbols and assumptions
- C1
- Strength of the weaker solution
- C2
- Strength of the stronger solution
- Ct
- Target strength
- Q
- Total quantity required
- • The strengths are on the same basis.
- • Quantities add without volume contraction.
Sources and review
Reviewed 2026-09-22 · Next review 2027-09-22
- • The target must lie between the two strengths. Mixing alcohol and water contracts in volume, so use mass for those blends.
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
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