Almost every method-validation report contains an LOD and an LOQ, and a surprising share of them are wrong — not because the arithmetic is hard, but because the number depends entirely on which definition was used and on how the blank was measured. This guide gives the three accepted routes, the exact formulas, and the traps that make two labs report values differing by a factor of five on the same instrument.

What the two limits actually mean

LOD (limit of detection) — the lowest concentration that can be reliably distinguished from a blank. It answers "is the analyte there?" It is not a concentration you may report as a number.
LOQ (limit of quantitation) — the lowest concentration that can be measured with acceptable precision and accuracy (conventionally CV ≤ 20 % and recovery 80–120 % for immunoassays). It answers "how much is there?"

Everything below LOQ is reported as < LOQ, never as the point estimate. Everything below LOD is reported as not detected with the LOD stated.

Method 1 — blank standard deviation (ICH Q2(R2), most common)

Measure the blank at least 10 times independently (not 10 reads of one well), take the SD of the blank signal, and convert to concentration with the calibration slope S:

LOD = 3.3 x SD_blank / S
LOQ = 10  x SD_blank / S

Some fields use the decision limit form LOD = mean_blank + 3 x SD_blank in signal units and then back-calculate. Both are defensible; state which one you used.

Worked example. Blank OD over 12 replicates: mean 0.052, SD 0.0061. Calibration slope near the bottom of the curve: 0.0042 OD per pg/mL.

LOD = 3.3 x 0.0061 / 0.0042 = 4.8 pg/mL
LOQ = 10  x 0.0061 / 0.0042 = 14.5 pg/mL

Method 2 — calibration curve residuals

When blanks are unavailable or dominated by matrix, use the residual standard deviation of the regression (σ) in place of SD_blank:

LOD = 3.3 x sigma / S
LOQ = 10  x sigma / S

Two rules make this valid: fit the curve over the low range only (roughly the bottom third), and use a linear segment. Taking σ from a full-range 4PL fit mixes in variance from the high asymptote and inflates both limits.

Method 3 — signal-to-noise (chromatography)

For methods with a visible baseline, LOD is the concentration giving S/N ≈ 3 and LOQ the concentration giving S/N ≈ 10. Simple and widely accepted for HPLC/GC, but it depends on how the software windows the noise, so record the noise window.

LOQ vs LLOQ: not the same thing

In immunoassay practice you will meet LLOQ — the lowest standard on the curve that meets the precision and accuracy criteria. It is an empirical limit tied to your calibrators, whereas LOQ from the formulas above is a statistical estimate. When your lowest calibrator sits above the calculated LOQ, the calibrator wins: you cannot quantify below the range you actually measured.

This is also why a zero standard never becomes the LLOQ. The log-scale 4PL/5PL model is undefined at zero concentration, so the zero well anchors the lower asymptote (background) while the lowest non-zero standard defines the quantifiable floor.

Five mistakes that change the number

Pseudo-replicates. Reading one blank well ten times measures instrument noise, not method noise. Use independent preparations.
Wrong slope. Using the mid-curve slope of a sigmoidal fit instead of the slope near the blank underestimates LOD, sometimes twofold.
Matrix-free blanks. A buffer blank ignores matrix interference; use blank matrix when the assay is run in serum, plasma, or sediment extract.
Skipping the dilution factor. LOD/LOQ must be expressed in original-sample units. Multiply by the dilution factor before reporting.
Reporting values below LOQ as numbers. They pass into means and inflate or deflate group comparisons. Apply a documented rule (< LOQ, or LOD/2 imputation where the field accepts it) and state the censoring rate.

Reporting checklist

Method used (blank SD, residual SD, or S/N) named explicitly
Number of independent blank replicates
Slope source and range used for its estimation
Blank type (buffer vs matrix)
Units after dilution correction
Rule applied to values below LOQ, plus how many samples were affected

Doing it in Labreador

Labreador's ELISA module fits 4PL/5PL curves, reports the working range with explicit LLOQ/ULOQ flags, and marks every sample that falls outside it or was extrapolated, so out-of-range values never quietly enter your summary statistics. The Method Health panel additionally checks curve span, R², back-calculated standard recovery, and confidence-interval width — the signals that tell you whether an LOQ estimate is trustworthy at all. All computation happens in your browser; no data is uploaded.

References

ICH (2023). Q2(R2) Validation of Analytical Procedures. International Council for Harmonisation.
Armbruster, D. A., & Pry, T. (2008). Limit of blank, limit of detection and limit of quantitation. Clinical Biochemist Reviews, 29(Suppl 1), S49-S52.
CLSI (2012). EP17-A2: Evaluation of Detection Capability for Clinical Laboratory Measurement Procedures.
Currie, L. A. (1999). Detection and quantification limits: origins and historical overview. Analytica Chimica Acta, 391(2), 127-134.

Cite Labreador

If Labreador supported your analysis, please cite it: Labreador - Bioassay Analysis Platform (Version 1.6.0) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.21676846

How to Calculate LOD and LOQ: Formulas, Methods and Common Mistakes