Detection Limit Calculator Formula
Understand the math behind the detection limit calculator. Each variable explained with a worked example.
Formulas Used
Limit of Detection (LOD, 3sigma)
lod = 3 * blank_std / slopeLimit of Quantitation (LOQ, 10sigma)
loq = 10 * blank_std / slopeVariables
| Variable | Description | Default |
|---|---|---|
blank_std | Standard Deviation of Blank (sigma) | 0.005 |
slope | Calibration Slope (m) | 2500 |
How It Works
Limit of Detection and Quantitation
LOD is the lowest analyte concentration that can be reliably detected (S/N ≈ 3). LOQ is the lowest concentration that can be quantified with acceptable precision (S/N ≈ 10).
Formulas (ICH Method)
LOD = 3.3 × sigma / S (often simplified to 3 × sigma / S)
LOQ = 10 × sigma / S
where sigma is the standard deviation of the blank response and S is the slope of the calibration curve. This is the most common approach in pharmaceutical and environmental analysis.
Worked Example
Blank standard deviation = 0.005, calibration slope = 2500 signal/M.
blank_std = 0.005slope = 2500
- 01LOD = 3 × 0.005 / 2500 = 0.015 / 2500 = 6.0 × 10⁻⁶ M = 6.0 uM
- 02LOQ = 10 × 0.005 / 2500 = 0.05 / 2500 = 2.0 × 10⁻⁵ M = 20 uM
Ready to run the numbers?
Open Detection Limit Calculator