Alligation & Reconstitution
Mix two solutions of known strength to land on a target concentration — the alligation method — or work out how much diluent to add to a powder to reach a target concentration. Both are everyday pharmacy and lab tasks.
How to use this tool
The Alligation tab blends a stronger and a weaker stock to a target in between. The Reconstitution tab tells you how much diluent to add to a dry drug to reach a target concentration.
What to enter
- Alligation: the two stock concentrations, the target (which must sit between them), and the total volume you want. Use any consistent unit (%, mg/mL, M).
- Reconstitution: the amount of drug in the vial, the target concentration, and (optional) the powder's displacement volume.
Reading the result
Alligation returns the volume of each stock and the mixing ratio; a quick check confirms the blended concentration equals your target. Reconstitution returns the diluent to add and the final volume.
Worked example
To make 100 mL of 40% from 70% and 20% stocks: mix 40 mL of 70% with 60 mL of 20% (ratio 2 : 3).
Result
Alligation balances how far the target sits from each stock: the closer a stock is to the target, the more of it you use.
Methodology
Alligation
To make volume V at target Ct from stocks C₁ and C₂, the volume of the first stock is V₁ = V·(Ct − C₂)/(C₁ − C₂) and the rest is C₂. Equivalently, the parts are taken from the alligation cross: each stock's parts equal the absolute difference between the other stock and the target. The target must lie between the two stock concentrations.
Reconstitution
To reach concentration Ct from a mass m of drug, the final volume is V = m / Ct. If the dry powder occupies a known displacement volume d, add V − d of diluent so the final volume (and hence concentration) is correct.
Sources
- Standard pharmaceutical calculations (alligation alternate / medial).
- USP / manufacturer reconstitution and displacement-volume data.
Known limits
- Assumes ideal mixing (volumes additive); for non-ideal mixtures verify the final concentration.
- Concentrations must share a unit; the target must be between the two stocks (you cannot mix outside their range).