Last updated: 2026-07-01

What a serial dilution does

A serial dilution lowers a concentration in a chain of equal steps instead of one big jump. At every step you take a small portion of the previous solution and dilute it by the same fold factor, so the diluted solution from one step becomes the stock for the next. Because the same factor applies repeatedly, the concentration falls geometrically, letting you reach very low and accurately known concentrations that a single dilution could not deliver reliably.

The serial dilution formula

Let $C_0$ be the stock concentration, $D$ the dilution factor applied at each step, and $k$ the number of steps. Each step divides the concentration by $D$, so after $k$ steps:

$$C_k = \frac{C_0}{D^{k}}$$

The total dilution factor — the overall reduction from the first tube to the last — is the per-step factor raised to the number of steps:

$$D_{tot} = D^{k}$$

Symbol	Quantity	Unit
C₀	Stock concentration	mol/L (M)
D	Dilution factor per step	—
k	Number of steps	—
Cₖ	Final concentration	mol/L (M)
D_tot	Total dilution factor	—

Worked example

Start with a 1 M stock and run a tenfold (1:10) dilution for 5 steps. The total dilution factor is:

$$D_{tot} = D^{k} = 10^{5} = 100000$$

So the final concentration is:

$$C_k = \frac{C_0}{D^{k}} = \frac{1\ \text{M}}{10^{5}} = 1 \times 10^{-5}\ \text{M} = 10\ \unicode{x00B5}\text{M}$$

The concentration at each step follows a clean power-of-ten pattern:

Step (k)	Total dilution (Dᵏ)	Concentration
0	1	1 M
1	10	0.1 M
2	100	0.01 M
3	1000	0.001 M
4	10000	0.0001 M
5	100000	0.00001 M

Setting up the transfers

For a tenfold series, a common bench recipe uses 100 µL transfers into 900 µL of diluent, so each step mixes 1 part into 9 parts for a total of 10 parts:

• Add 900 µL of diluent to each tube after the first.
• Transfer 100 µL of stock into the first diluent tube and mix well.
• Transfer 100 µL of that mixture into the next tube, mix, and repeat.
• Change pipette tips between steps so carryover does not inflate the concentration.

Mix thoroughly before each transfer; incomplete mixing is the most common source of error in a dilution series.

Dilution factor vs total dilution

The dilution factor per step is the fold reduction at a single step — 10 for a 1:10 dilution. The total dilution factor is the cumulative reduction across the whole chain, $D^{k}$. Three tenfold steps keep a per-step factor of 10 but reach a total dilution of $10^{3} = 1000$, a 1:1000 dilution overall. Keeping the two apart avoids the frequent mistake of multiplying by the number of steps ($10 \times 3 = 30$) rather than raising to the power of the number of steps ($10^{3} = 1000$).

Common uses

• Standard curves for spectrophotometry, ELISA, and qPCR, where evenly spaced concentrations are needed.
• Plate counts in microbiology, diluting a sample until colonies are countable.
• Preparing trace-level reference standards for analytical chemistry.

Frequently Asked Questions (FAQ)

What is a serial dilution?

A serial dilution is a stepwise dilution in which the diluted solution from one step becomes the stock for the next step. Each step reduces the concentration by the same fold factor, so the concentration drops geometrically. This is the standard way to reach very low, accurately known concentrations, because a single large dilution would need impractically small or large volumes.

What is the serial dilution formula?

After k steps of dividing by a fold factor D, the concentration is Cₖ = C₀ ÷ Dᵏ, where C₀ is the stock concentration. The total dilution factor is Dᵏ. For example, five tenfold steps give a total dilution of 10⁵ = 100000, so a 1 M stock ends at 0.00001 M.

What is the difference between the dilution factor and the total dilution?

The dilution factor per step is the fold reduction at a single step — for a 1:10 dilution it is 10. The total dilution factor is the cumulative reduction across every step, equal to the per-step factor raised to the number of steps. Three 1:10 steps give a per-step factor of 10 but a total dilution of 10³ = 1000 (a 1:1000 dilution overall).

How do I set up a tenfold serial dilution?

Prepare a row of tubes. Add 900 µL of diluent to each tube after the first. Transfer 100 µL of the stock into the first diluent tube and mix, then transfer 100 µL of that mixture into the next tube, and repeat. Each transfer of 1 part into 9 parts diluent gives a 1:10 (tenfold) dilution, so tube k holds a concentration of C₀ ÷ 10ᵏ.