A serial dilution is a chain of identical dilution steps, where concentration at step i = initial concentration / (dilution factor ^ i). This post covers that arithmetic, how it differs from a single C1V1 dilution, and how to check a planned series has enough volume at every step.
How do you calculate a serial dilution series?
A single dilution step reduces concentration by a fixed factor. Starting from an initial concentration and applying the same dilution factor at every step:
concentration at step i = initial concentration / (dilution factor ^ i)Step 0 is the undiluted starting concentration. A ten-fold serial dilution (factor of 10) starting at 1000 micrograms per milliliter produces 100 at step 1, 10 at step 2, 1 at step 3, and so on, each step an order of magnitude below the last. The serial dilution calculator runs this exponent directly for as many steps as you specify and reports the full series at once, rather than requiring the same division to be repeated by hand for every step.
How it differs from a single dilution
A single dilution, the kind covered by C1V1, moves from one concentration to one target concentration in one step:
C1V1 = C2V2A serial dilution is that same relationship applied repeatedly, each output becoming the next input. If you only need one target concentration, a single C1V1 dilution is the more direct tool; the C1V1 dilution calculator solves that equation for whichever one of the four quantities you leave blank. The arithmetic behind a single dilution vial is also covered in how to reconstitute a peptide vial, which works through the same C1V1 relationship for a single vial rather than a chain of steps.
A serial dilution series is worth building instead of several one-off dilutions when you need a whole range of concentrations at once, for example a standard curve, and want each one to be a known, consistent multiple of the last rather than mixed independently and prone to compounding measurement error at each independent mix.
Checking there is enough volume for every step
The concentration arithmetic above assumes each step actually has enough volume to both transfer forward into the next step and, usually, leave a usable sample behind. Before running a series, work out how much volume each step needs: the transfer volume into the next tube, plus whatever volume the step itself requires for its own use. If a series has five steps and each needs 100 microliters transferred forward plus 400 microliters retained, the first tube needs to hold at least the total across every downstream step, not just enough for the next one. Planning that total before starting avoids running short partway through the series and having to restart with a larger initial volume.
Two related but distinct dilution numbers
The dilution factor itself, and the general idea of “how much did this get diluted”, comes up outside of serial dilution too. The dilution factor calculator computes the factor between any initial and final concentration directly:
dilution factor = initial concentration / final concentrationThat is a useful check on a single step of a series, or on any dilution at all: given the before and after concentrations, what factor actually happened, independent of whether it was intended to be part of a chain.
Preparing the solutions a series starts from
A serial dilution series usually starts from a stock solution prepared separately. The stock solution calculator computes how much solute is needed to hit a target starting concentration in a given volume, and the working solution calculator covers diluting a stock down to one working concentration, splitting the result into stock volume and diluent volume. Either is a natural first step before a serial dilution takes that starting point through a chain of further steps.
In short: a serial dilution’s concentration at step i is initial concentration / (dilution factor ^ i), the same relationship applied repeatedly rather than a single C1V1 step.