Diluting 50% dextrose with 5% dextrose to make 1000 mL of 10%
Parts are 5 (strong) to 40 (weak), so about 111 mL of the 50% solution and 889 mL of the 5% solution.
Alligation dilution calculator
For healthcare professional reference only. This performs the alligation arithmetic on the values entered — it does not verify chemical compatibility, stability or the clinical appropriateness of the mixture. Compounding should follow institutional protocol and pharmacist verification, never this page alone.
Result
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How it works
The alligation rule finds a mixing ratio by comparing how far the target sits from each of the two source concentrations: the "distance" from the target to the low concentration sets the parts of the high-concentration solution needed, and the distance from the target to the high concentration sets the parts of the low-concentration solution — the further the target is from one side, the more of the other side is needed to pull the mixture toward it.
This is the same arithmetic taught as the "alligation cross" in pharmacy compounding: it is a shortcut for solving the mass-balance equation that says the total amount of active ingredient before mixing must equal the amount after mixing.
Formulas used
Alligation ratio
Parts of strong = target − weak; Parts of weak = strong − target
Volume of each solution
Volume of strong = total volume × (parts of strong / total parts); Volume of weak = total volume × (parts of weak / total parts)
Worked examples
A 70% stock alcohol diluted with water (0%) to 40%, 500 mL total
Parts are 40 (strong) to 30 (weak), giving about 286 mL of the 70% stock and 214 mL of water.
Assumptions and limits
- Volumes are assumed simply additive when mixed — accurate for dilute aqueous solutions, less so for some concentrated or non-aqueous mixtures where mixing can change total volume.
- This does not check chemical compatibility, stability, or whether mixing the two specific products is appropriate — that judgement belongs to a pharmacist.
Frequently asked questions
What if I want to dilute with plain water or a diluent with no active ingredient?
Set the lower concentration to 0 — the alligation method works the same way, and it reduces exactly to the simpler C1V1 = C2V2 dilution case when one of the two starting concentrations is zero.
Why does the calculator reject a target outside the two concentrations?
Mixing two solutions can only ever produce a concentration between the two you started with — you cannot mix a 5% and a 50% solution and end up with 60% or with 2%, since neither operation adds or removes active ingredient beyond what the two source solutions already contain.
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