Solution Dilution Calculator

It is the fundamental dilution equation. C1 and V1 are the concentration and volume of the concentrate, while C2 and V2 are the concentration and volume of the diluted solution. The product of concentration and volume (the amount of dissolved substance) stays constant, so any missing quantity can be derived from the equation.

The volume of concentrate is V1 = C2 x V2 / C1. To make 1000 ml of a 5% solution from a 30% concentrate you need 5 x 1000 / 30 = 166.67 ml of concentrate, with the rest made up with water.

The volume of water is the difference between the final volume and the volume of concentrate: V water = V2 - V1. The calculator works this out automatically. For precise laboratory work it is recommended to top up to the mark in a volumetric flask.

The dilution factor is the ratio of the initial concentration to the target concentration (C1 / C2). A value of 10 means a ten-fold dilution. The factor helps you quickly judge how strongly a preparation must be diluted.

The C1V1 = C2V2 equation works for any concentration measure (percent, mol/l, g/l) as long as you use the same unit on both sides. This calculator assumes percentage concentrations, but the maths is identical for molar concentrations.

Dilution lowers concentration by adding solvent, so the final solution always has a concentration lower than or equal to the starting one. To obtain a more concentrated solution you would have to concentrate it or add pure substance. That is why the calculator reports an error when C2 is greater than C1.

Approximately yes, so the volume of water equals the final volume minus the volume of concentrate. In reality, mixing some liquids (e.g. ethanol with water) causes volume contraction. For most practical uses the difference is negligible.

The rule is: always add acid to water, never the other way round. Adding water to concentrated acid can release heat violently and cause splashing. Always wear goggles and gloves, work under a fume hood and add the acid slowly while stirring.

The calculator is educational and helps you understand the principle of dilution. For preparing pharmaceutical or medical solutions of critical importance you should follow proper procedures and specialist supervision.