How It Works
This solver works in 4 steps.
Enter the top concentration
Type the first and highest concentration in the series.
Enter the bottom concentration
Type the last and lowest concentration in the series.
Enter the number of steps
Type the count of dilution steps between the endpoints, which is the number of points minus 1.
Read the step factor
The calculator returns F = (C_top / C_bottom)^(1/n) and a rounded factor with its bottom value.
The Formula
The formula takes the n-th root of the ratio between the top and bottom concentrations.
F = (C_top / C_bottom)^(1/n)log(F) = [log(C_top) − log(C_bottom)] / nV_t = V_d / (F − 1)- F:
- Constant factor per step
- C_top:
- Highest concentration
- C_bottom:
- Lowest concentration
- n:
- Number of steps (points − 1)
Ten points from 10 µM to 1 nM span a 10,000-fold range in 9 steps. F = 10,000^(1/9) = 2.783.
Conversion Table
The conversion table lists the exact step factor for 6 endpoint pairs and step counts.
| Top | Bottom | Steps | Step factor | Check: total DF |
|---|---|---|---|---|
| 1,000 | 1 | 3 | 10 | 1,000 |
| 1,000 | 1 | 6 | 3.162 | 1,000 |
| 100 | 0.1 | 8 | 2.371 | 1,000 |
| 500 | 2 | 5 | 3.017 | 250 |
| 10 | 0.01 | 9 | 2.154 | 1,000 |
| 64 | 1 | 6 | 2 | 64 |
What Is the Serial Dilution Factor Solver?
The Serial Dilution Factor Solver is a planning tool that returns the constant step factor needed to move from a chosen top concentration to a chosen bottom concentration in a set number of steps. The solver takes the n-th root of the overall dilution factor.
Fixed endpoints are common in assay design. A dose-response curve often needs exactly 10 points from 10 µM to 1 nM. The solver returns the exact factor, rounds it to a practical value such as 3 or 2.5, and shows how far the rounded factor moves the bottom concentration.
Common Uses
There are 5 main uses of this solver.
Dose-response design
Pharmacologists fit 8 to 12 points between set top and bottom doses.
Standard curve design
Analysts spread a fixed number of standards across a validated range.
Fixed plate formats
Users fit a series into 11 dilution columns plus 1 control column.
Regulatory ranges
Labs match the lowest standard to a required limit of quantitation (LOQ).
Range compression
Researchers find the factor that compresses 6 decades into 8 points.