How It Works
This calculator works in 4 steps.
Enter the starting concentration (C₀)
Type the stock value.
Enter the target concentration
Type the lowest concentration needed, in the same unit.
Enter the step factor (F)
Type the factor per tube, such as 2 or 10.
Read the step count
The calculator returns n = log(C₀ / C_target) / log(F), rounded up, plus the concentration in the last tube.
The Formula
The formula divides the log of the concentration ratio by the log of the step factor.
n = log(C₀ / C_target) / log(F)n_whole = ⌈n⌉C_last = C₀ / F^n_whole- n:
- Number of serial steps
- C₀:
- Starting concentration
- C_target:
- Target concentration
- F:
- Step factor
Reaching 0.25 µg/mL from 128 µg/mL in twofold steps needs n = log(512) / log(2) = 9 steps exactly.
Conversion Table
The conversion table gives exact and whole step counts for 6 start, target, and factor combinations.
| Start (C₀) | Target | Factor | Exact steps | Whole steps | Last tube |
|---|---|---|---|---|---|
| 10⁹ | 100 | 10 | 7 | 7 | 100 |
| 128 | 0.25 | 2 | 9 | 9 | 0.25 |
| 10 | 0.001 | 10 | 4 | 4 | 0.001 |
| 1,000 | 1 | 3 | 6.29 | 7 | 0.457 |
| 5 | 0.01 | 5 | 3.86 | 4 | 0.008 |
| 2 × 10⁷ | 20 | 10 | 6 | 6 | 20 |
What Is the Serial Dilution Step Count Calculator?
The Serial Dilution Step Count Calculator is a planning tool that returns the number of serial steps a fixed factor needs to bring a starting concentration to or below a target concentration. The calculator uses a logarithm of the concentration ratio and rounds up to the next whole step.
The step count sets the number of tubes, wells, and pipette tips for a series. When the exact answer falls between 2 whole numbers, the last step overshoots the target. The calculator reports the exact step value and the concentration reached after rounding, so the user sees the overshoot before preparing tubes.
Common Uses
There are 5 main uses of this calculator.
Tube count planning
Users label the right number of tubes before starting.
Plate layout planning
Researchers check whether a series fits in 12 columns of a 96-well plate.
Consumable estimates
Lab managers count tips and tubes per series.
Plating targets
Microbiologists find the step that lands near 300 CFU per plate.
Protocol checks
QC staff confirm that a written step count reaches the stated low point.