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How low can this method measure?

LOD and LOQ calculator (ICH Q2)

From the standard deviation of the response (σ) and the slope of the calibration curve, calculates the smallest amount you can say is present (limit of detection, LOD) and the smallest amount you can put a number on (limit of quantitation, LOQ).

When to use itUse it to set detection and quantitation limits in analytical method validation, or to check whether an impurity such as residual DNA can be measured down to its specification.

Prefilled with an example: a response standard deviation (σ) of 1.5 and a calibration slope of 0.5. Change any value and the result updates.

response units

The standard deviation of blank measurements, of the residuals of the calibration curve, or of its y-intercept. Use the same response unit as the slope (fluorescence intensity, absorbance and so on).

response units ÷ concentration units

How much the response rises for each unit increase in concentration. LOD and LOQ come out in concentration units.

Limit of detection (LOD)9.9 concentration units
Limit of quantitation (LOQ)30 concentration units

With this method you can say the analyte is present from 9.9, and give an amount from 30 (both in the concentration units of the calibration curve). If the specification limit you need to control is below the LOQ, this method cannot measure it, and you need more sensitivity.

How to read the result

  • Measured value below the LODNot detectedThe signal cannot be clearly told apart from a blank. Report it as below the detection limit.
  • At or above the LOD, below the LOQPresent, but not quantifiableYou can confirm it is there, but cannot give an amount with the required accuracy.
  • At or above the LOQQuantifiableYou can report an amount with the required accuracy. Decide conformance to specification in this range.
  • Acceptance criteriaNo pass line for LOD and LOQ themselvesICH Q2(R2) gives the method of calculation, not acceptable LOD or LOQ values. Acceptable values are set case by case from the product specification (for example, the guide of 10 ng of residual DNA per dose) and the method validation acceptance criteria.

How it is calculated

Enter σ and the slope in the same response unit, and LOD and LOQ come out in concentration units. If your axes use Cq values as the response and log copy number as the concentration, as in qPCR, read the results in those units.

LOD = 3.3 × σ ÷ slope LOQ = 10 × σ ÷ slope

Source: Detection limit LOD = 3.3σ ÷ S and quantitation limit LOQ = 10σ ÷ S. This is one of the approaches given in ICH Q2(R2), Validation of Analytical Procedures.

With your numbers

  1. LOD = 3.3 × σ (standard deviation) ÷ slope S = 3.3 × 1.5 ÷ 0.5 = 9.9
  2. LOQ = 10 × σ ÷ slope S = 10 × 1.5 ÷ 0.5 = 30

Limits of this calculation

  • ICH Q2(R2) presents 3.3σ/S and 10σ/S as one of several approaches, alongside others such as signal-to-noise. Which σ to use (the standard deviation of the blank, of the residuals or of the intercept) depends on the method design, and the result changes with that choice.
  • σ and the slope must be in the same response unit. Otherwise, the result is not in correct concentration units.
  • In systems that use Cq values (cycle numbers) as the response, such as qPCR, the slope and σ do not necessarily mean what they do in this linear model, so take care applying it directly. (The related article covers qPCR and ddPCR, but this equation assumes an ordinary linear calibration curve.)
  • The calculated LOD and LOQ are not acceptance criteria. Acceptable values are set separately, as product specifications, per-dose control limits (for example, residual DNA 10 ng/dose) or method validation acceptance criteria.
  • The factors 3.3 and 10 are conventions. Some literature writes 3.3 as 3 or 3.29, and the numbers shift slightly with rounding and assumptions.

Primary sources

Every calculator gives an estimate for learning, built on published information and primary sources. Real decisions follow the applicable guidance and expert judgment.