Serial dilution
Serial dilution is a step-by-step way to reduce a concentration by repeating a consistent dilution factor (like 1:10)
or using a custom factor at each step. It is widely used in biology labs for plating, assays, standards, and calibration curves.
Key definitions
- Stock concentration: \( C_0 \) (the starting concentration).
- Tube concentration: \( C_i \) (after step \( i \)).
- Transfer volume: \( V_{\mathrm{transfer},i} \) (volume moved from the previous tube).
- Diluent volume: \( V_{\mathrm{diluent},i} \) (buffer/water added).
- Final volume: \( V_{\mathrm{final},i} = V_{\mathrm{transfer},i} + V_{\mathrm{diluent},i} \).
- Dilution factor: \( DF_i \) describes how strong the dilution is at step \( i \).
How to read “1:10”
In this calculator, “1:10” means: take 1 part sample and bring to 10 parts total.
So the dilution factor is \( DF = 10 \).
Core formulas
Dilution factor definition:
\[
DF_i = \frac{V_{\mathrm{final},i}}{V_{\mathrm{transfer},i}}
\]
Concentration after each step:
\[
C_i = \frac{C_{i-1}}{DF_i}, \qquad C_0 = \text{stock concentration}
\]
Volumes (two common lab ways to plan a step):
\[
\begin{aligned}
\text{If you choose } V_{\mathrm{final},i}:\quad
&V_{\mathrm{transfer},i} = \frac{V_{\mathrm{final},i}}{DF_i},
\qquad
V_{\mathrm{diluent},i} = V_{\mathrm{final},i} - V_{\mathrm{transfer},i} \\[6pt]
\text{If you choose } V_{\mathrm{transfer},i}:\quad
&V_{\mathrm{final},i} = V_{\mathrm{transfer},i}\cdot DF_i,
\qquad
V_{\mathrm{diluent},i} = V_{\mathrm{final},i} - V_{\mathrm{transfer},i}
\end{aligned}
\]
Fixed factor vs custom list
- Fixed factor: you pick one dilution factor \( DF \) and repeat it for every step (common in practice).
- Custom list: you provide \( DF_1, DF_2, \dots, DF_N \) (useful if pipetting constraints change per step).
Overall dilution
After \( N \) steps, the total dilution relative to stock is:
\[
\frac{C_N}{C_0} = \frac{1}{DF_1 DF_2 \cdots DF_N}
\]
If \( DF \) is constant each step, then \( C_N = \dfrac{C_0}{DF^N} \).
Choosing steps and factor to hit a target
Sometimes you know a target concentration \( C_t \) you want to reach (for example for a standard curve).
If the dilution factor is fixed, you can estimate the number of steps needed.
\[
C_t \approx \frac{C_0}{DF^N}
\quad\Rightarrow\quad
N \approx \frac{\log\!\left(\frac{C_0}{C_t}\right)}{\log(DF)}
\]
Or if you already know \( N \), you can estimate the required fixed dilution factor:
\[
DF \approx \left(\frac{C_0}{C_t}\right)^{1/N}
\]
Practical note
In real lab work you typically round to a convenient DF (like 2, 5, 10) that matches pipetting accuracy and available tube volumes.
Worked example
Stock: \( C_0 = 1.0 \,\mathrm{mg/mL} \), repeat 1:10 dilution (so \( DF=10 \)), and set final volume per tube to \( 1.0\,\mathrm{mL} \).
\[
\begin{aligned}
V_{\mathrm{transfer}} &= \frac{1.0\ \mathrm{mL}}{10} = 0.10\ \mathrm{mL} \\
V_{\mathrm{diluent}} &= 1.0\ \mathrm{mL} - 0.10\ \mathrm{mL} = 0.90\ \mathrm{mL} \\
C_1 &= \frac{1.0}{10} = 0.10\ \mathrm{mg/mL} \\
C_2 &= \frac{0.10}{10} = 0.010\ \mathrm{mg/mL}
\end{aligned}
\]
The pattern continues: each step divides concentration by 10, while volumes stay the same if final volume stays fixed.
Common mistakes and lab tips
- Mixing: always mix thoroughly after adding transfer + diluent (vortex or pipette-mix).
- Pipetting limits: very small transfer volumes (like 1–5 µL) can be inaccurate; consider changing DF or tube volume.
- Units: keep your concentration unit consistent across steps (the calculator tracks everything in the unit you choose).
- Log plot: if the concentrations span orders of magnitude, log y-axis usually gives a clearer picture.
