Solution Mixing Calculator – Combine Solutions or Hit a Target Strength
Mixing two solutions that both contain solute is one of the most common jobs at the bench, in the pharmacy and in the kitchen. This solution mixing calculator answers both directions of the problem. Give it the solutions you combined and it returns the final concentration of the mix. Give it two stocks and a target and it uses alligation to tell you how much of each to measure out.
Mixing is a weighted average
When you pour solutions together, nothing is created or destroyed: the moles (or grams, or equivalents) of solute from each portion simply add up, and so do the portions themselves. That makes the concentration of the mix a weighted average of the inputs, weighted by how much of each you used:
C_final = Σ(Cᵢ × Vᵢ) / ΣVᵢ (by volume)
w_final = Σ(wᵢ × mᵢ) / Σmᵢ (by mass)Mixing 100 mL of 0.5 M NaCl with 300 mL of 0.1 M NaCl gives (0.05 + 0.03) mol ÷ 0.400 L = 0.200 M. Because it is an average, the result always lands between the weakest and strongest input, pulled toward whichever portion is larger. The balance beam in the tool draws exactly this: each solution is a weight sitting at its concentration, sized by its amount, and the mix balances at the fulcrum. The beam also shows why the larger portion pulls harder: 100 × (0.5 − 0.2) = 300 × (0.2 − 0.1).
Only quantities in the same family can be averaged. 1 M and 0.25 mM combine directly, but 1 M and 50 g/L do not, because turning grams into moles needs a molar mass. Convert first with the Solution Concentration Converter. The same maths in a general setting is the Weighted Average Calculator.
Alligation by hand: the Pearson square
Pharmacists and lab technicians often work the other way round: they have a strong stock and a weak stock and need something in between. Alligation solves it without algebra. Write the stocks on the left, the target in the middle, and subtract along each diagonal:
70 % w/w 15 parts of 70 % (25 − 10)
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25 %
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10 % w/w 45 parts of 10 % (70 − 25)
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60 parts total → 1 : 3So 500 g of 25 % w/w needs 500 × 15/60 = 125 g of the 70 % stock and 375 g of the 10 % stock. The amounts are inversely proportional to each stock's distance from the target: the stock closer to the target is the one you need more of. The calculator also handles the two common variants: you already have a fixed amount of the weak solution and need to know how much strong stock to add (fortifying), or you will use a fixed amount of the strong stock.
Why volumes don't always add up
By volume, the tool assumes the final volume is the sum of the portions, which is very close for dilute aqueous solutions. Concentrated solutions break the rule. 50 mL of 95 % ethanol plus 50 mL of water gives only about 97 mL, because the molecules pack more tightly together. Strong acids behave similarly. If you measured the mixed volume, enter it and the calculator recomputes the concentration on the real volume.
Working by mass is always exact, because masses are conserved. For concentrated reagents use % w/w and weigh the portions; if you only know a volume, enter it with the density and the tool converts it with m = V × ρ.
“Make up to volume” versus “add X mL of water”
When one of the two stocks is pure solvent, alligation becomes a plain dilution, and the right lab instruction is to measure the stock and add solvent up to the final volume in a volumetric flask. That is exact even if the mix shrinks, because all the solute comes from the stock. Adding a calculated 263 mL of water to 737 mL of 95 % ethanol would land slightly off 70 % for the same shrinkage reason. For simple one-stock dilutions and serial dilutions, the Dilution Calculator is a quicker fit.
Mixing several solutes
Add columns to track up to five solutes at once, for example a NaCl stock and a KCl stock combined with water. Each solute is averaged independently. The tool only does bookkeeping: it does not model reactions, so an acid mixed with a base, or two salts that precipitate, will not contain what the totals suggest.