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.
- 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
Frequently Asked Questions
What is the difference between LOD and LOQ?
LOD answers "is the analyte present?" (qualitative). LOQ answers "how much is present?" (quantitative). LOQ is about 3× higher than LOD because greater S/N is needed for reliable quantitation.
How is the blank standard deviation determined?
Measure the response of 10-20 blank samples (same matrix as unknowns but without analyte). The standard deviation of these measurements is sigma. Use the same instrumental conditions as actual samples.
Are there other methods to determine LOD?
Yes. Visual evaluation (lowest visible S/N ≈ 3), signal-to-noise method (directly measuring S/N at low concentrations), and EPA method detection limit (MDL) using t-distribution statistics on replicate measurements.
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