Solution Dilution Calculator

In short Every dilution rests on one fact: the amount of solute does not change, only the volume around it. That gives C₁V₁ = C₂V₂, and it is the most useful equation in a wet lab. Taking a 10 M stock down to 1 M in a final volume of 500 mL needs 50 mL of stock and 450 mL of diluent, because 10 × 50 and 1 × 500 are both 500. The units only have to match each other — molar with molar, millilitres with millilitres — and then they cancel, which is why the same equation works for percentages, mg/mL or anything else. Two practical points the equation does not tell you. The first is that volumes are not always additive: mixing 50 mL of ethanol with 50 mL of water gives about 96 mL, not 100, because the molecules pack differently together than apart. That is why every real protocol says "make up to the mark" rather than "add this much diluent". For dilute aqueous solutions the difference is negligible and the diluent figure is reliable. The second is that a large dilution should not be done in one step. A 10,000-fold dilution into 1 mL calls for 0.1 µL of stock, which no ordinary pipette measures accurately, so the error in that one tiny volume becomes the error in the whole result. Four 10-fold steps reach the same endpoint with far less uncertainty, which is why serial dilution exists. Note finally that 1:100 has two readings — one part in a hundred of finished solution, which is what chemistry means, or one part to a hundred parts of diluent, which is what horticulture and cleaning usually mean. Both are shown here.