Dilution is one of the most common jobs in a laboratory, a classroom, and even a kitchen. You have a strong solution, and you need a weaker one. The rule that makes it simple is C1V1 = C2V2. Here C1 is the starting concentration, V1 is the volume of strong solution you take, C2 is the final concentration you want, and V2 is the final volume after you add solvent. The idea behind the rule is plain: the amount of solute does not change when you add solvent, so concentration times volume stays the same on both sides.
This calculator solves for any one of the four values. Enter the three values you know, and leave the fourth blank. For example, suppose you have a 10 mol/L stock solution and you need 100 mL of a 2 mol/L solution. Leave V2 blank, and the tool returns 500 mL. That means you take 100 mL of stock and add solvent up to 500 mL in total. The same tool works in reverse: if you know the final volume and both concentrations, it tells you how much stock to measure out first.
Here is a worked example with different numbers. A teacher has a 5% salt solution and needs 250 mL of a 1% solution for a class. The missing value is V1, the volume of stock to use. The formula gives V1 = C2 times V2 divided by C1, which is 1 times 250 divided by 5, or 50 mL. So the teacher measures 50 mL of the 5% solution and adds water up to 250 mL. The dilution factor is 5, because the stock is five times stronger than the final solution.
Units matter more than the maths itself, and they cause most mistakes. C1 and C2 must use the same unit, whether that is mol/L, percent, or milligrams per millilitre. V1 and V2 must also match each other, so do not mix millilitres with litres in one calculation. If your stock is in mol/L and your target is in percent, convert one of them first, because the formula cannot fix a unit mismatch. Always write the units next to your numbers before you start.
The dilution factor is a handy second result. It is simply C1 divided by C2, and it tells you how many times weaker the final solution is. A factor of 10 means a 1-in-10 dilution: one part stock plus nine parts solvent. Serial dilutions use this idea step by step. To make a 1-in-1000 dilution, for example, you might do three 1-in-10 steps in a row, because each step is easier to measure accurately than one tiny volume. Errors shrink when every step uses a comfortable volume.
There are limits to what C1V1 = C2V2 can tell you. It assumes the solute stays dissolved and does not react with the solvent, and it assumes volumes add up neatly. In real life, mixing some liquids, such as ethanol and water, gives a slightly smaller total volume than the sum of the parts. The formula also says nothing about safety: a diluted acid is still an acid, and a diluted poison may still be dangerous. Always check the safety sheet for your chemical, whatever the concentration.
Students meet this formula in chemistry class, but the same maths shows up elsewhere. A cook diluting cordial, a gardener mixing plant food, and a photographer mixing developer all use the same idea. The key question is always the same: how much of the strong liquid do I need, and how much solvent brings it to the final volume? Once you can answer that with C1V1 = C2V2, you can scale any recipe or preparation up or down without guessing.
To use this tool well, follow a simple routine. First, write down the concentration you have and the concentration you want. Second, decide the final volume you need, and leave that blank only if it is the unknown. Third, check that your units match in pairs. Fourth, read the answer and ask whether it makes sense: the final volume must be larger than the stock volume, and the stock volume must be smaller than the final volume. If either check fails, a number was entered wrong.