Limit of Quantitation Calculator

The limit of quantitation is the lowest analyte concentration at which a method can report a number rather than merely a yes-or-no answer. ICH Q2 expresses it as LOQ = 10 sigma / S and the companion limit of detection as LOD = 3.3 sigma / S, where sigma is the standard deviation of the response and S is the slope of the calibration line in response units per concentration unit. Because both share the same sigma and S, the ratio of LOQ to LOD is always about 3.03. The multiplier 10 is chosen so that the relative standard deviation at the LOQ is roughly 10 percent, the precision most laboratories accept as the floor for reporting a numerical result. In chromatography the equivalent convention is a peak height ten times the peak-to-peak baseline noise, with 3 to 1 used for detection. The estimate is only as good as the sigma that goes into it. Blank standard deviation, the residual standard deviation of the regression line, and the standard deviation of replicate low-level spikes can differ by a factor of two or more for the same method, so the source must be stated. A calculated LOQ is a starting hypothesis: regulators expect it to be confirmed by analysing about six independent replicates at that level and demonstrating acceptable precision and recovery, commonly 80 to 120 percent. LOQ is also condition-specific, shifting with column age, detector lamp hours, matrix, and injection volume, and it must sit below the relevant specification, such as the ICH Q3B identification threshold of 0.10 percent for drug product impurities.

Formal treatment of detection limits began with Heinrich Kaiser, who in papers published in Zeitschrift fur Analytische Chemie during the 1940s and again in the mid-1960s argued that a decision about the presence of an analyte should be tied to a multiple of the standard deviation of the blank, popularising the three-sigma criterion still used today. Kaiser worked from emission spectroscopy, where fluctuating background was the dominant obstacle to trace analysis. His framework addressed detection only, and said little about the higher concentration at which a measurement becomes numerically trustworthy. Lloyd Currie of the US National Bureau of Standards supplied that missing tier in a 1968 paper in Analytical Chemistry, which separated the critical level, the detection limit, and the determination limit and analysed each in terms of false positive and false negative error rates. Currie proposed a multiplier of 10 for the determination limit, corresponding to a 10 percent relative standard deviation, and this became the basis of the modern LOQ. IUPAC issued harmonised recommendations along these lines in 1995. Regulators codified the concepts separately: the US EPA published its method detection limit procedure in 40 CFR Part 136 Appendix B in 1984, while the ICH adopted Q2A in 1994 and Q2B in 1996, later merged as Q2(R1) and revised as Q2(R2) in 2023.