The Dilution Calculator:
C1V1 = C2V2
The Equation You Use Every Day
If you work at a bench, you have used this equation. Possibly without thinking about it, possibly while scribbling on a glove. C1V1 = C2V2 is the conservation of solute principle reduced to its simplest form: the amount of stuff you start with equals the amount of stuff you end with, because dilution does not create or destroy molecules, it just spreads them out.
C1 is your starting concentration, V1 is the volume you take from that stock, C2 is the concentration you want, and V2 is the total volume you are making. You know three of these, and the equation gives you the fourth. It is, at its core, a statement about conservation of mass in solution, and it applies to anything from diluting a 10x PBS stock to preparing working concentrations of antibiotics.
When C1V1 = C2V2 Is Not Enough
The simple dilution equation assumes a single step: take some stock, add diluent, done. But if your target concentration is orders of magnitude below your stock (which happens routinely with drugs, signalling molecules, and standard curves), a single dilution can require pipetting volumes so small that the error exceeds the measurement. This is where serial dilutions come in.
A serial dilution is a chain of stepwise dilutions, where each step takes the output of the previous step as its input. By dividing a large dilution factor into smaller, more manageable steps, you keep pipetting volumes within the accurate range of your equipment. The maths is straightforward, the pipetting volumes per step are consistent, and the error per step is controlled. But planning the steps, especially when you need specific final concentrations at each point (as with a dose-response curve), requires more thought than the simple equation.
Common Mistakes
The most frequent error I see is confusing "volume to add" with "total volume". If you calculate V2 = 10 mL, that is the total volume of the final solution, not the amount of diluent you add. The diluent volume is V2 minus V1. This seems obvious written down, but mid-experiment, with three other things going on, it catches people out more than it should.
The second is unit mismatches. If C1 is in mg/mL and C2 is in ug/mL, the equation still works, but only if you are careful with the conversion. Mixing units without noticing is the kind of mistake that wastes an afternoon.
The third, and perhaps most insidious, is not accounting for the volume contribution of the solute itself when working with viscous or concentrated solutions. At high concentrations, the solute displaces a non-trivial volume of solvent. C1V1 = C2V2 assumes ideal dilution behaviour, which is fine for most bench work, but worth being aware of when precision matters.
What BenchCalc Does
BenchCalc includes a dilution calculator for simple C1V1 = C2V2 problems, a serial dilution planner that works out the step-by-step pipetting volumes for you, a molarity calculator for solution preparation, a percent solution calculator for w/v, v/v, and w/w, and a normality calculator with N1V1 = N2V2. These are the tools I reach for every single day. You probably do too.
All of it works offline, which matters when you are standing at the bench with one bar of signal and a pipette in your hand.