Type in a starting concentration, a dilution factor and how many steps you want, and it prints the concentration at every step of a serial dilution. The first row is always the undiluted starting material, so five dilutions give six rows.
It is for the prep bench and the lab report: standard curves, overnight cultures, anything where you dilute by the same factor again and again and need the numbers without working them out on the back of a glove box.
The honest detail: it does arithmetic and nothing else. No volumes, no pipette sizes, no unit conversion, and no judgement about whether the concentration is realistic.
Calculate concentrations through a series of dilutions. Enter the starting concentration, dilution factor, and number of dilution steps.
How the calculation works
Each step divides the previous concentration by the same factor, so the concentration at step n is the starting concentration divided by the factor raised to the power of n. A factor of 10 means one part in ten total, which is one part sample plus nine parts diluent, and it is the most common setup in a teaching lab.
Results come back in scientific notation with four digits after the decimal point, so a starting concentration of 1000 with a factor of 10 gives 1.0000e+3, then 1.0000e+2, then 1.0000e+1, then 1.0000e+0, then 1.0000e-1, and 1.0000e-2 at the fifth dilution. The units you started with carry through untouched, whether that was micromolar, micrograms per millilitre or cells per millilitre.
Row count follows the number in the steps box. Put in 5 dilutions and you get 6 rows, because step 0 is the original; put in 1 and you get 2. The field allows 1 to 50, and an empty box, a factor of zero or a negative starting concentration stops the calculation with a message telling you the factor has to be at least 1.
Two worked examples
Start at 1000 with a factor of 10 over 5 dilutions. The six rows read 1.0000e+3, 1.0000e+2, 1.0000e+1, 1.0000e+0, 1.0000e-1 and 1.0000e-2, the classic tenfold series you have probably already pipetted by hand. The row at step 3 reads 1.0000e+0, so the concentration there is one of whatever unit you started with.
Now start at 1500 with a factor of 3 over 3 dilutions. You get 4 rows: 1.5000e+3, 5.0000e+2, then 1.6667e+2, then 5.5556e+1. Those last two are 166.6666 and 55.5555 with four digits kept after the decimal point of the mantissa, which is five significant figures, so the display is doing the rounding rather than losing the value.
A non-integer factor works too. Start at 50 with a factor of 2.5 over 4 dilutions and the five rows are 5.0000e+1, 2.0000e+1, 8.0000e+0, 3.2000e+0 and 1.2800e+0. That is the case where the maths runs ahead of the pipetting, because a 2.5 fold dilution is awkward to measure by hand.
What it does not do
There are no volumes anywhere in the output. Knowing that step 4 sits at 1.0000e-1 does not tell you to transfer 100 microlitres into 900 microlitres of diluent, and if you need the transfer scheme you have to work it out separately. This is a concentration table, not a protocol.
The factor is constant across every step, which is what serial dilution normally means, but not what every real procedure does. Variable factors, back dilutions and combining two series all need arithmetic this page will not do, and the same goes for anything that changes volume part way through.
It also does not know your detection limit or your pipette’s error. Start at 1000 and run 50 steps of a factor of 10 and the table happily reports 1.0000e-47, a number rather than something you could ever measure, and cumulative error is why most real series stop well before that.
Two edge cases are worth stating plainly. A factor of exactly 1 returns the same concentration on every row, since nothing is being diluted, and a factor below 1 is accepted even though the field is marked from 1 upwards, which produces rising concentrations instead of falling ones. Confusing rather than dangerous.
Finally, this is arithmetic rather than safety advice. Handling procedures, spill response and waste routes are governed by your institution’s own chemical hygiene plan, and that document outranks anything on this page.
Other tools
- spill response checklist – the steps to take before the maths matters
- sterile technique checklist – keeping the contamination out of your dilutions
- waste label generator – what to do with the tubes when the series is done
Frequently asked questions
What counts as a dilution factor?
Final volume divided by initial volume. A tenfold dilution is one part sample taken to ten parts total, so 1 part sample with 9 parts diluent. The factor you enter is that single number, 10, not the 1 to 9 ratio written in a protocol.
Why is there one more row than the number of dilutions?
Because step 0 is the starting material before any dilution has happened. Six dilutions give seven rows, from the original down to the last tube. If you only want the diluted tubes, ignore the first line.
How many steps should I use?
As many as your protocol and your pipette allow. Five or six is typical for a teaching standard curve, and past about eight the concentrations reach places where the arithmetic is correct but the measurement is not. The field permits up to 50.
Can I use different factors at each step?
Not here. The tool divides by one constant factor every time, so a series with a changing factor has to be worked out by hand. Doing it manually is often just as quick for three or four tubes.
Does it convert units?
No. It carries your starting unit through every row unchanged, so 1000 micromolar becomes 1.0000e-2 micromolar after five dilutions. Convert the starting value first if you want the table in something else.