Serial Dilution Calculator: Tube-by-Tube Plan and Volumes

A serial dilution takes a stock down by the same factor again and again. Six easy pipetting steps reach one millionth of the starting concentration, which a single dilution could only manage with a volume too small to pipette. The planner turns the series into a table for the bench.

How to use the planner

Starting concentration: the stock you dilute from. The default is 1e6. Every box also accepts thousands separators (1,000,000), a lone decimal comma (2,5) and forms such as 1.2 × 10^5. A comma followed by exactly three digits counts as a thousands separator, so 1,234 means 1234.
Unit label: free text, up to 16 characters, printed after every concentration. It starts as cells/mL, but CFU/mL, µg/mL or mM work just as well, because the arithmetic never converts units.
Dilution factor per step: how many times weaker each tube is than the one before, 10 for a tenfold series, 2 for a twofold series. Any number above 1 works, so 3.162 (the square root of 10) gives half-log steps.
Number of tubes: the plan stops at 24 tubes and says so if you ask for more.
Volume in each tube, in mL or µL: what a tube holds right after mixing, before you take the next transfer out of it.

For each tube the table shows its concentration, the volume to transfer in from the tube before it (tube 1 receives from the stock) and the diluent to put in first. The line under the table repeats the one instruction that holds for every step. An empty or out-of-range box (a factor of 1 or less, no tubes, zero volume) gives a warning instead of a table.

The formula

Two lines run the whole series:

transfer = V ÷ f, and diluent = V - transfer
C(n) = C0 ÷ f^n

V is the volume in each tube, f the dilution factor per step, n the tube number, C0 the starting concentration and C(n) the concentration in tube n. The total dilution after n steps is f^n, which is why six tenfold steps give 10^6.

Each step is an ordinary single dilution whose stock is the previous tube, so the C1V1 dilution calculator gives the same numbers one tube at a time.

Worked example with the default values

The planner opens with 1e6 cells/mL, a factor of 10, 6 tubes and 1 mL per tube.

transfer = 1 mL ÷ 10 = 0.1 mL
diluent = 1 - 0.1 = 0.9 mL

The result line reads "Each step: 0.1 mL of the previous tube into 0.9 mL of diluent", and the table fills in like this:

Tube	Concentration	Transfer in	Diluent
1	100000 cells/mL	0.1 mL	0.9 mL
2	10000 cells/mL	0.1 mL	0.9 mL
3	1000 cells/mL	0.1 mL	0.9 mL
4	100 cells/mL	0.1 mL	0.9 mL
5	10 cells/mL	0.1 mL	0.9 mL
6	1 cells/mL	0.1 mL	0.9 mL

At the bench: put 0.9 mL of diluent in six tubes, add 0.1 mL of stock to tube 1, mix, move 0.1 mL from tube 1 to tube 2, mix, and carry on. Two things follow. You need only 0.1 mL of stock (V ÷ f). And once the last transfer is done, tubes 1 to 5 hold 0.9 mL while tube 6 keeps the full 1 mL. If every tube must end at the same volume, take 0.1 mL out of tube 6 and discard it.

Where serial dilutions turn up

Plate counts for bacteria or yeast: a tenfold series, a fixed volume spread from several tubes, and the plate with a countable number of colonies (the usual window is about 30 to 300) multiplied back by its dilution.
Standard curves for absorbance assays and ELISA, usually twofold or threefold. The Beer-Lambert calculator covers reading them.
Twofold drug or antibiotic series and antibody titers.
Thinning a dense cell suspension before counting it on a hemocytometer.

Common mistakes

One tip for the whole series. A trace of liquid carried from a concentrated tube can swamp a dilute one further down. Use a fresh tip for every transfer.
Skipping the mix. Pipette up and down or vortex briefly (gently for cells) before taking the next transfer.
Calling the stock tube 1. Here tube 1 is already one step down. The stock is tube 0.
Transfers too small to pipette. A factor of 100 with 100 µL tubes means 1 µL transfers. Raise the tube volume or split each step into two tenfold steps.
Forgetting that errors compound. A 2 percent volume error at every step leaves tube 6 about 13 percent off (1.02^6 is about 1.13).

Limits

The planner assumes volumes simply add, which holds for dilute water-based solutions but not exactly for mixtures such as ethanol and water. At very low cell or microbe numbers, chance takes over: with an average of 1 cell per mL, Poisson statistics say about 37 percent of 1 mL samples contain no cell at all, so the last tubes of a series are estimates, not guarantees.

FAQ

What is a serial dilution?

It is a chain of dilutions where each tube is made from the one before, by the same factor each time. Concentrations fall geometrically: 10, 100 and 1,000 times weaker after one, two and three tenfold steps.

How do I work out the total dilution factor?

Multiply the step factors together. Six tenfold steps give 10 × 10 × 10 × 10 × 10 × 10, so 10^6, and the last tube is one millionth of the stock. If the steps differ, multiply each one in turn.

Is a 1:10 dilution 1 part in 10 or 1 part to 10?

Both readings are in use, which causes real mix-ups. In most biology protocols "1:10" means 1 part in 10 parts total, and that is how this planner works: a factor of 10 is 0.1 mL in a 1 mL total. If a protocol means 1 part plus 10 parts of diluent, the true factor is 11.

How do I make a twofold serial dilution?

Set the factor to 2. With 1 mL tubes the planner gives 0.5 mL of the previous tube into 0.5 mL of diluent, and each tube holds half the concentration of the one before.

How much stock do I need?

One transfer volume, V ÷ f, because only tube 1 draws from the stock: 0.1 mL with the defaults.