How It Works
This calculator works in 4 steps.
Enter the top concentration
Type the highest value.
Enter the bottom value or the ratio
Type the lowest value, or type the constant ratio such as 3 or √10.
Enter the point count
Type the number of concentrations, including both ends.
Read the series
The calculator lists each concentration, its log₁₀ value, and its preparation volumes.
The Formula
The formula divides the top concentration by the constant ratio raised to the point index.
Cᵢ = C_top / rⁱ (i = 0 … k − 1)r = (C_top / C_bottom)^(1/(k − 1))Δlog = log₁₀(r)- Cᵢ:
- Concentration at index i
- C_top / C_bottom:
- Highest and lowest concentrations
- r:
- Constant ratio
- k:
- Number of points
Seven points from 100 µM to 0.1 µM give r = 1,000^(1/6) = 3.162. The series is 100, 31.6, 10, 3.16, 1, 0.316, and 0.1 µM.
Conversion Table
The conversion table shows the ratio and first 5 points for 5 geometric series.
| Top | Bottom | Points | Ratio | First points |
|---|---|---|---|---|
| 100 | 0.1 | 7 | 3.162 | 100, 31.6, 10, 3.16, 1 … |
| 10 | 0.01 | 10 | 2.154 | 10, 4.64, 2.15, 1, 0.464 … |
| 1,000 | 1 | 4 | 10 | 1,000, 100, 10, 1 |
| 64 | 0.5 | 8 | 2 | 64, 32, 16, 8, 4 … |
| 50 | 0.05 | 13 | 1.778 | 50, 28.1, 15.8, 8.89, 5 … |
What Is the Geometric Concentration Series Calculator?
The Geometric Concentration Series Calculator is a tool that generates a set of concentrations with a constant ratio between neighbors, so the points are evenly spaced on a logarithmic axis. The user sets 2 of the 3 inputs, ratio, point count, or end points, and the calculator solves the third.
Geometric spacing suits responses that follow a log-dose pattern, such as receptor binding and enzyme inhibition. Equal log spacing gives each decade the same number of points. The calculator lists each concentration, its log₁₀ value, and the volume to prepare it from a common stock.
Common Uses
There are 5 main uses of this calculator.
Dose-response curves
Pharmacologists fit sigmoid curves with even log spacing.
Receptor binding studies
Biochemists span 2 decades above and below the dissociation constant (Kd).
Toxicity tests
Ecotoxicology labs space test levels by a constant factor, such as 2 or 3.2.
Antibiotic MIC ranges
Microbiologists use twofold geometric ranges for susceptibility tests.
Calibration across decades
Analysts calibrate wide-range instruments with log-spaced standards.