C1V1 Dilution Calculator

Every dilution question reduces to the same statement: the amount of solute does not change when you add solvent. Concentration is only a way of reporting that amount against a volume, so as the volume grows the concentration must fall by exactly the same proportion. Write the amount on both sides of the equality and you have C1V1 = C2V2, and any of the four terms can be isolated by dividing through by the other three.

That is the whole reason a single calculator can solve for a starting concentration, a starting volume, a target concentration or a total volume without knowing in advance which one you are after. The algebra is identical in all four directions. What changes between them is not the mathematics but which of the four numbers you actually hold, and which one you are inferring.

The practical consequence is that a dilution is fully described by any three of the four values, and the fourth is redundant rather than unknown. That redundancy is why this page can also work as a consistency check: give it all four and it is telling you whether your arithmetic survived the round trip, which is a cheap way to catch a unit slip or a transcription error before it becomes a prepared solution.

The single most consequential detail on this page is that V2 is the total volume of the finished solution, not the volume of solvent you add. The two differ by exactly V1, and the difference is small enough to be easy to overlook whenever the stock volume is small relative to the total.

Consider a dilution of 1 mL of stock up to 10 mL. The final concentration is one tenth of the stock, which is a factor of ten. If instead you treated the 10 mL as the volume of diluent, you would have made 11 mL in total and the factor would be eleven. The arithmetic looks entirely reasonable in both cases, which is what makes this the most common way a dilution goes quietly wrong.

If you are working backwards from a desired concentration and a final volume, the two-step version is usually clearer than the single formula. Find the total volume first, then subtract the stock volume to get the diluent. The stock solution calculator does exactly that decomposition, and the working solution calculator extends it to the case where you are preparing a working solution from a weighed mass rather than from a stock.

The equation is unit agnostic, which is exactly why it is dangerous. C1V1 in milligrams per millilitre and C2V2 in moles per litre still balances dimensionally, because the units cancel within each product, so a mismatch between the two terms is arithmetically invisible. It produces a number, and the number is wrong by the conversion factor.

The practical habit is to pick one volume unit and one concentration unit and stay in them for the whole problem. Most peptide work lives naturally in milligrams per millilitre, and the concentration unit converter exists for the moments when a protocol, a label or an instrument reports something else. Converting both sides to a single frame before computing is slower than typing carefully and faster than debugging a factor of one thousand.

Ratio notation needs particular care. A written dilution of 1:100 means one part of stock in one hundred parts of finished solution, which is one percent of the stock concentration. But 1:10 is frequently used loosely to mean ten times weaker, and some suppliers use ratio notation that refers to a volume of diluent rather than a total. When the source of a ratio is ambiguous, convert it to an explicit starting concentration and a total volume and use those, which removes the ambiguity entirely. The dilution factor calculator handles the ratio itself once it has been pinned down.

C1V1 = C2V2 assumes that volumes are additive. Adding 5 mL of one solution to 45 mL of another gives exactly 50 mL only if the volumes are genuinely additive, which is a good approximation for dilute aqueous solutions and a poor one for concentrated ones, for mixtures of different densities, and for anything involving a non aqueous solvent. The error is small, but it is systematic rather than random, so it does not cancel.

It also says nothing about whether the solute is still dissolved. A dilution arithmetic result describes what the numbers would be if everything had dissolved evenly, and it cannot detect precipitation, aggregation, or a solute that has bound to the vessel wall. If the visible result does not match the calculated result, the discrepancy is in the physical system and not in the equation.

None of this makes the equation wrong. It makes it a statement about concentration rather than about behaviour, and knowing which of those two a number is describing is most of what there is to know about it. For the arithmetic of getting from one concentration to another, nothing on this page is going to be more reliable than this, and for anything beyond that arithmetic the right move is to reach for one of the more specific tools on the site rather than to push this one further.