The Dilution Calculator:
C1V1 = C2V2
The Equation You Use Every Day
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 applies to anything from diluting a 10x PBS stock to preparing working concentrations of antibiotics.
When C1V1 = C2V2 Is Not Enough
The simple 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 and the error per step is controlled, but planning the steps requires more thought than the simple equation, especially when you need specific final concentrations at each point.
Common Mistakes
Confusing "volume to add" with "total volume". V2 is the total volume of the final solution, not the amount of diluent you add. The diluent volume is V2 minus V1.
Unit mismatches. If C1 is in mg/mL and C2 is in ug/mL, the equation still works, but only if you handle the conversion. Mixing units without noticing wastes time.
Not accounting for the volume contribution of the solute 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 C1V1 = C2V2, a serial dilution planner that works out step-by-step pipetting volumes, 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. All offline.