Why dilute in steps rather than all at once
Consider making a 1,000-fold dilution into one millilitre. Done in a single step it means transferring one microlitre, a volume at the very bottom of most pipettes' range, where a two percent volumetric error is optimistic. Done as three tenfold steps, each transfer is 100 microlitres, comfortably within the accurate range of a standard pipette.
The errors still compound across the steps, but they compound from a much smaller base. Three steps each accurate to one percent give a final accuracy near three percent; one step accurate to fifteen percent gives fifteen percent, and there is nothing you can do about it afterwards.
How a constant-volume series works
In the standard scheme, every tube ends up with the same final volume. You transfer a fixed fraction of that volume from the previous tube, top up with diluent, mix, and repeat. Because the fraction is the same each time, the concentration falls by the same factor at every step and the series is geometric.
One consequence catches people out: after you transfer out of a tube to feed the next one, that tube no longer holds the full volume. If you need a specific volume at every level, set the final volume to include what will be withdrawn for the next step.
Choosing the factor
Tenfold steps are easy to reason about and give one order of magnitude per tube, which suits a wide-range screen. Twofold and threefold steps give finer resolution, which is what you want when the interesting range is already known and you are trying to fit a curve through it.
Half-log steps, a factor of about 3.16, are a common compromise: two steps per order of magnitude, evenly spaced on a log axis, which is how dose-response data is usually plotted.
Mixing between steps
Every step must be mixed thoroughly before the next transfer, because an unmixed tube has a concentration gradient and the aliquot you take from it is not representative. This is the most common source of a dilution series that does not behave geometrically.
Changing pipette tips between steps matters for the same reason: a tip carrying residue from a more concentrated tube contaminates the next one, and the effect grows as the series gets more dilute.
Where the series stops being reliable
At the dilute end, adsorption becomes the dominant loss. A peptide at low nanomolar concentration in a standard polypropylene tube can lose a substantial fraction of itself to the walls, and the loss is proportionally larger the more dilute the solution. Low-binding plasticware and a carrier protein such as bovine serum albumin both help.
At the concentrated end, the limit is solubility. A stock that is at or near its solubility limit may be carrying undissolved material, and an aliquot from it is not at the concentration you calculated.
How the serial dilution scheme is calculated
A constant-volume geometric series. Each step transfers the same fraction of the final volume and is topped up with the same volume of diluent, so the concentration falls by a constant factor.
transfer volume = final volume / dilution factor diluent volume = final volume - transfer volume C(step n) = starting concentration / factor^n steps to target = ceil( ln(C_start / C_target) / ln(factor) )
- Fix the final volume per tube. Every tube in the series ends at this volume. Setting it once keeps the transfer and diluent volumes identical at every step, which is what makes the series easy to execute without a written table.
- Divide by the dilution factor for the transfer. A tenfold series into 1 mL transfers 100 microlitres. The transfer volume is the same at every step, so one pipette setting covers the whole series.
- Take the diluent volume as the remainder. Final volume minus transfer volume. Pre-loading every tube with the diluent before starting turns the series into a sequence of identical transfers.
- Apply the factor cumulatively. Step n is the starting concentration divided by the factor raised to the power n, so a tenfold series reaches one thousandth at step three.
- Solve for the number of steps when a target is given. The logarithm of the concentration ratio over the logarithm of the factor, rounded up. Rounding up means the series always reaches at least the target rather than stopping just above it.
What this method cannot tell you
- •It assumes complete mixing at every step. An unmixed tube breaks the geometric relationship, and no downstream arithmetic can detect that it happened.
- •It does not model adsorption to tube and tip surfaces, which is the dominant loss at the dilute end of a long series.
- •It assumes the starting concentration is what you believe it is. Every step inherits an error in the stock.
- •It does not check that the transfer volume is within your pipette's accurate range. A calculated 0.5 microlitre transfer is arithmetically fine and practically unusable.
Serial dilution calculator: frequently asked questions
A sequence of dilutions in which each one is made from the previous one rather than from the original stock. Each step reduces the concentration by the same factor, so the series steps down geometrically.
Three tenfold steps take you to one thousandth of the starting concentration, with every transfer a comfortable, measurable volume.
Because the accuracy of a single large dilution is limited by the smallest volume you have to measure, and that volume shrinks as the dilution factor grows.
A 1,000-fold dilution into 1 mL means transferring 1 microlitre. Most pipettes cannot deliver that reproducibly, and the error goes straight into your final concentration with no way to detect it.
Divide the final volume by the dilution factor to get the transfer volume, and the remainder is the diluent volume. Both stay the same at every step.
A tenfold series into 1 mL tubes is 100 microlitres transferred into 900 microlitres of diluent, repeated for as many steps as you need.
It depends on how wide a range you need to cover and how finely.
- •Tenfold: one order of magnitude per tube, good for a first wide screen
- •Half-log, about 3.16-fold: two points per order of magnitude, standard for dose-response curves
- •Twofold or threefold: fine resolution across a narrow known range
Take the logarithm of the ratio between the starting and target concentrations, divide by the logarithm of the dilution factor, and round up.
The calculator does this when you enter a target, and reports the concentration the rounded-up number of steps actually reaches, which is usually a little below the target rather than exactly on it.
Because you took an aliquot out of each tube to feed the next one, and only the last tube in the series was never drawn from.
If you need a specific usable volume at every level, set the final volume high enough to cover both the transfer out and the volume you want to keep.
Yes. A tip carrying residue from a more concentrated tube carries that residue into the next one, and the proportional effect grows at every step as the series gets more dilute.
Reusing a tip is one of the two most common causes of a series that does not follow the geometric relationship. The other is not mixing.
Enough that the tube is uniform, which for a small volume usually means pipetting up and down several times or vortexing briefly.
An unmixed tube has a gradient, so the aliquot you take next is not at the concentration you calculated, and every subsequent step inherits the error.
Yes, but expect losses at the dilute end and take steps to limit them. Surface adsorption removes a proportionally larger fraction the more dilute the solution.
- •Use low-binding tubes and tips
- •Add a carrier protein such as 0.1 percent bovine serum albumin, where the assay allows
- •Prepare dilute working solutions shortly before use rather than storing them
No, but a constant factor is far easier to execute and to reason about, and it puts the points at even intervals on a log axis.
The assay prep calculator handles the case where you want an arbitrary list of dilutions made independently from the stock rather than in a chain.
In dilution notation they usually mean the same thing: one part sample brought to ten parts total, which is a tenfold dilution.
Ambiguity creeps in when 1:10 is read as one part sample to ten parts diluent, which is eleven parts total and an elevenfold dilution. This calculator uses the tenfold reading, and states the transfer and diluent volumes explicitly so there is nothing to interpret.
Each step contributes its own error, and the errors compound. Three steps at one percent each give roughly three percent at the end.
That is still far better than a single step forced to transfer a volume at the edge of a pipette's range, which is the alternative.
Yes. Pre-loading every tube with its diluent volume turns the series into a sequence of identical transfers, which is faster and much harder to lose your place in.
Dilute peptide solutions are the least stable form the material takes: more surface contact per molecule, less protection from adsorption, and often no preservative.
Prepare working dilutions close to the time of use and keep the concentrated stock as the thing you store.
Any of them, as long as you are consistent. The arithmetic is a ratio, so the units cancel and the series is the same in mg/mL as in nanomolar.
To convert between mass and molar units, run the starting concentration through the molarity calculator first.
So the series always reaches at least the target concentration. Rounding down would leave the last tube more concentrated than you asked for, which is the error more likely to go unnoticed.
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