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Solution Mixing Calculator

Computes the concentration obtained by combining two solutions of the same solute from their volumes and concentrations, C = (C1·V1 + C2·V2) / (V1 + V2), or, given a target concentration, the volumes and mixing ratio of the two stocks by the alligation method.

When to use

You combine two solutions of known concentration and need the resulting concentration, or you must blend a stronger and a weaker stock (or a stock and pure solvent) to reach a target concentration.

Do not use when: You dilute one stock with pure solvent and want the C1V1 = C2V2 form (use dilution), or the two solutions contain different solutes or react with each other.

Formula

Mixing: final_concentration = (C1·V1 + C2·V2) / (V1 + V2). Alligation: parts_1 = |target − C2|, parts_2 = |C1 − target|, V1 = total_volume × parts_1 / (parts_1 + parts_2), V2 = total_volume − V1

Assumes the solute amount is conserved and volumes are additive (no volume contraction), which holds for dilute aqueous solutions; for % w/w blends enter masses instead of volumes and the same arithmetic applies.

Inputs

ParameterTypeUnitRequiredDescription
concentration_1numberyesConcentration of the first solution in any unit shared by all concentrations (mol/L, %, mg/mL, ppm). Use 0 for pure solvent. Range: ≥ 0
concentration_2numberyesConcentration of the second solution, same unit as concentration_1. Range: ≥ 0
volume_1numbernoVolume of the first solution in any unit shared with volume_2 (mL, L). Required unless target_concentration is given. Range: > 0
volume_2numbernoVolume of the second solution, same unit as volume_1. Required unless target_concentration is given. Range: > 0
target_concentrationnumbernoDesired concentration of the mixture; when given, the calculator solves the volumes of solutions 1 and 2 (alligation) instead of the final concentration. Must lie between the two stock concentrations. Range: ≥ 0
total_volumenumbernoTotal mixture volume in alligation mode (any unit); when omitted only the ratio and percentages are reported. Range: > 0

Outputs

OutputTypeUnitDescription
final_concentrationnumberConcentration of the mixture (unit of the concentration inputs).
volume_1numberVolume of solution 1 used or required.
volume_2numberVolume of solution 2 used or required.
total_volumenumberV1 + V2 (volumes assumed additive).
total_solute_amountnumberC1·V1 + C2·V2 in concentration × volume units (e.g. mmol for mol/L and mL).
ratio_1_to_2numberVolume of solution 1 per unit volume of solution 2.
fraction_1_percentnumber%100 × V1 / (V1 + V2).
fraction_2_percentnumber%100 × V2 / (V1 + V2).
parts_1number|target − C2|: relative parts of solution 1 (alligation mode only).
parts_2number|C1 − target|: relative parts of solution 2 (alligation mode only).
solved_forstringfinal_concentration (mixing) or volumes (alligation).

Example

100 mL of 0.5 M plus 300 mL of 0.1 M: {"concentration_1":0.5,"volume_1":100,"concentration_2":0.1,"volume_2":300} → {"final_concentration":0.2,"total_volume":400,"total_solute_amount":80,"ratio_1_to_2":0.333333,"fraction_1_percent":25,"solved_for":"final_concentration"}

500 mL of 40 % from 70 % and 20 % stocks: {"concentration_1":70,"concentration_2":20,"target_concentration":40,"total_volume":500} → {"parts_1":20,"parts_2":30,"ratio_1_to_2":0.666667,"volume_1":200,"volume_2":300,"fraction_1_percent":40,"final_concentration":40,"solved_for":"volumes"}

GET https://tttkmbb.com/api/v1/calculate/mixing-solutions?concentration_1=0.5&volume_1=100&concentration_2=0.1&volume_2=300

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Sources

FAQ

Which units can I use?

Any, as long as both concentrations share one unit and both volumes share one unit; a 0 concentration represents pure solvent, so the calculator also covers dilution with water.

What is alligation?

A cross-multiplication shortcut for mixtures: the parts of each stock are the absolute differences between the target and the other stock's concentration, which is exactly the solution of C1·V1 + C2·V2 = C·(V1 + V2).

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