Serial Dilution Calculator
Steps, volumes and compounded error for a serial dilution — where six steps at 2% error apiece is 12.6%, not 2%.
The error model here is deliberately pessimistic: it assumes every transfer errs the same way, so the errors compound rather than partly cancelling. Random errors would grow more slowly — as the square root of the steps — so treat this as the worst case rather than the expected one. Nothing is uploaded.
Serial dilution exists because the direct route is impossible
A millionfold dilution into one millilitre needs a thousandth of a microlitre of stock. No pipette does that. Doing it in stages turns an impossible transfer into six easy ones — or three, or twenty, depending how big you make each step.
| Step size | Steps needed | Reaches | Stock per step | Compounded error |
|---|---|---|---|---|
| 1:2 | 20 | 1:1,048,576 | 500 µL | 48.6% |
| 1:5 | 9 | 1:1,953,125 | 200 µL | 19.5% |
| 1:10 | 6 | 1:1,000,000 | 100 µL | 12.6% |
| 1:100 | 3 | 1:1,000,000 | 10 µL | 6.1% |
| 1:1000 | 2 | 1:1,000,000 | 1 µL | 4.0% |
Steps have to be whole, so a scheme usually overshoots slightly rather than landing exactly — twenty two-fold steps reach 1:1,048,576 rather than the million asked for. The tool rounds up, so the target is always met or beaten and never missed.
And the errors multiply rather than average out
Each transfer carries its own pipetting error, and they compound. Six steps at 2% apiece is not 2% but 12.6%; twenty steps is nearly half again. More steps is not more careful — it is more chances to be wrong in the same direction.
| Steps | Compounded error | If it simply added |
|---|---|---|
| 1 | 2.00% | 2% |
| 2 | 4.04% | 4% |
| 3 | 6.12% | 6% |
| 6 | 12.62% | 12% |
| 10 | 21.90% | 20% |
| 20 | 48.59% | 40% |
Which makes the choice of step size a genuine trade rather than a preference. Three hundredfold steps compound to 6.1% against 12.6% for six tenfold ones — but they ask you to pipette 10 µL instead of 100, and a small volume is exactly where pipetting error comes from in the first place.
How to use
- Enter the total dilution factor you need.
- Enter the factor per step.
- Enter the volume per tube and your pipetting error.
- Compare step sizes on error and on pipettable volume.
Frequently asked questions
Why dilute serially instead of in one step?
Because the direct route often asks for a volume that does not exist. A millionfold dilution into one millilitre needs a thousandth of a microlitre of stock — no pipette does that, but six tenfold steps are all easy.
How many steps do I need?
The log of the total factor over the log of the step factor, rounded up. A millionfold is six steps of ten, three of a hundred, or twenty of two. Steps must be whole, so a scheme usually overshoots slightly rather than landing exactly.
Does the error really compound?
Yes, and multiplicatively rather than additively. Six transfers at 2% apiece is 12.6%, not 2% and not 12% — each step scales what came before, so the errors ride on top of one another.
So should I use fewer, bigger steps?
It is a genuine trade rather than an improvement. Three hundredfold steps compound to 6.1% against 12.6% for six tenfold ones — but they ask you to pipette 10 microlitres instead of 100, and small volumes are exactly where pipetting error comes from.
Is the error model realistic?
It is deliberately pessimistic. It assumes every transfer errs the same way, so the errors compound rather than partly cancelling. Genuinely random errors would grow as the square root of the steps, so treat this as the worst case.
What volume does each step move?
The tube volume divided by the step factor. A tenfold step into 1 mL moves 100 microlitres of the previous tube into 900 of fresh diluent, which is comfortable; a thousandfold step into the same tube moves 1 microlitre, which is not.
Does the scheme always hit the target exactly?
Rarely. Because the step count rounds up, twenty two-fold steps reach 1:1,048,576 rather than the million asked for. The tool always meets or beats the target rather than falling short of it.
Does this send anything anywhere?
No. Every figure is computed in your browser, and nothing is uploaded or stored.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.