# Serial dilution: what is in each tube?

Plans a serial dilution: the concentration in every tube, the total dilution factor, and how much sample and diluent go in each tube for a chosen factor per step and final volume.

- Page: https://www.acalculator.org/biology/serial-dilution-calculator
- JSON spec: https://www.acalculator.org/biology/serial-dilution-calculator.json
- Version: c9c29d115c26

## Default answer

Example with the default inputs (Starting concentration 1,000,000, Dilution factor per step 10, Number of dilution steps 6, Final volume in each tube 10 mL): After 6 steps of 1:10, the last tube holds 1, a total dilution of 1,000,000.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| c0 | Starting concentration | The concentration of the stock or culture before the first step, in any unit (M, mg/mL, cells/mL). |
| f | Dilution factor per step | How many times each step dilutes the tube before it: 10 for a 1:10 (ten-fold) series. |
| n | Number of dilution steps | How many tubes the series makes after the stock. |
| v | Final volume in each tube | The total volume in each tube after mixing: sample plus diluent. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| final | Concentration in the last tube | The starting concentration ÷ (dilution factor per step) ^ steps, in the starting unit. |
| total | Total dilution factor | (Dilution factor per step) ^ steps: how many times the last tube is diluted from the stock. |
| transfer | Sample to move each step | The volume taken from one tube into the next: final volume ÷ dilution factor per step. |
| diluent | Diluent in each tube | The diluent put in each tube before the sample: final volume − sample moved. |
| tubes | Each tube | Every tube in order, with its dilution from the stock and its concentration. |

## Method

Tube k = C₀ ÷ Fᵏ; total dilution factor = Fⁿ; sample moved each step = V ÷ F; diluent in each tube = V − V ÷ F.

## Assumptions

- Every step uses the same dilution factor F and the same final volume V.
- Each tube is mixed well before its sample is moved on, and volumes add up.
- The concentration keeps the unit of the starting concentration (M, mg/mL, cells/mL).

## Worked examples

1. c0 = 1,000,000, f = 10, n = 6, v = 0.00001 gives final = 1, total = 1,000,000, transfer = 0.000001, diluent = 0.000009. Source: OpenStax, Microbiology, section 9.1 How Microbes Grow (1.0 mL of culture into 9.0 mL of broth is a dilution factor of 10, or 1:10; a second 1.0 mL into 9.0 mL makes 1:100 of the original culture), CC BY 4.0, https://openstax.org/books/microbiology/pages/9-1-how-microbes-grow (retrieved 2026-10-03).
2. c0 = 1, f = 10, n = 2, v = 0.00001 gives final = 0.01, total = 100, transfer = 0.000001, diluent = 0.000009, tubes = Tube 1: 1:10 of the stock, 0.1; Tube 2: 1:100 of the stock, 0.01. Source: OpenStax, Microbiology, section 9.1 How Microbes Grow (1.0 mL of culture into 9.0 mL of broth is a dilution factor of 10, or 1:10; a second 1.0 mL into 9.0 mL makes 1:100 of the original culture), CC BY 4.0, https://openstax.org/books/microbiology/pages/9-1-how-microbes-grow (retrieved 2026-10-03).
3. c0 = 2, f = 2, n = 5, v = 0.000001 gives final = 0.0625, total = 32, transfer = 0.000001, diluent = 0.000001. Source: OpenStax, Microbiology, section 9.1 How Microbes Grow (1.0 mL of culture into 9.0 mL of broth is a dilution factor of 10, or 1:10; a second 1.0 mL into 9.0 mL makes 1:100 of the original culture), CC BY 4.0, https://openstax.org/books/microbiology/pages/9-1-how-microbes-grow (retrieved 2026-10-03).

## FAQ

### What is a serial dilution?

A series of dilutions in which each tube is made from the tube before it, not from the stock. A 1:10 series takes 1 mL of the stock into 9 mL of diluent, then 1 mL of that tube into 9 mL more, and so on. Each tube is ten times weaker than the last.

### How do I work out the total dilution factor?

Multiply the factors of the steps. Six 1:10 steps give 10 × 10 × 10 × 10 × 10 × 10 = 10⁶, so the last tube is 1:1,000,000 of the stock. With the same factor F in each of n steps, the total is Fⁿ.

### How much sample and diluent go in each tube?

Sample = final volume ÷ factor; diluent = final volume − sample. For 10 mL tubes in a 1:10 series that is 1 mL of sample and 9 mL of diluent. For a two-fold series it is half and half.

### What is the difference between 1:10 and 1 to 10?

In this calculator 1:10 means 1 part sample in 10 parts total (1 mL in a final 10 mL). Some labs write 1:9 for 1 part sample to 9 parts diluent. Both describe the same tube; check which one your protocol uses.

### Why use a serial dilution instead of one big dilution?

A single 1:1,000,000 dilution would need 1 µL in a litre, which is hard to measure well. Small steps keep each pipetting volume easy to measure, and the series gives a range of concentrations, such as plates of 30 to 300 colonies in a plate count.

### Does the unit of the concentration matter?

No. The result keeps the unit you type the stock in: molar, mg/mL, cells/mL or colony-forming units per mL. Only the volumes need a unit.

## Sources

- OpenStax, Microbiology, section 9.1 How Microbes Grow (serial dilutions for plate counts: 1.0 mL of culture into 9.0 mL of broth is a dilution factor of 10, or 1:10; the next 1.0 mL into 9.0 mL is 1:100 of the original culture; plates of 30 to 300 colonies), CC BY 4.0, retrieved 2026-10-03. https://openstax.org/books/microbiology/pages/9-1-how-microbes-grow