BioDeviceHub

Limit of Detection and Quantitation Calculator

Calculate the limits of detection and quantitation from a low-range calibration curve (ICH), or the limits of blank and detection from replicates (CLSI EP17).

Formula

LoD=3.3 σS;LoQ=10 σS\mathrm{LoD} = \dfrac{3.3\,\sigma}{S};\quad \mathrm{LoQ} = \dfrac{10\,\sigma}{S}
LoB=xˉblank+1.645 sblank\mathrm{LoB} = \bar{x}_{\text{blank}} + 1.645\,s_{\text{blank}}
LoD=LoB+1.645 slow\mathrm{LoD} = \mathrm{LoB} + 1.645\,s_{\text{low}}
σ\sigma
standard deviation of the response: the residual SD of the regression or the SD of the intercept
SS
slope of the calibration curve

How it works

The limit of detection is the smallest amount that can be distinguished from nothing, and the limit of quantitation the smallest that can be measured with acceptable precision. In the ICH approach both come from the noise of the response and the sensitivity of the method: 3.3 and 10 times the standard deviation, divided by the slope of the calibration curve.

The CLSI EP17 approach works from replicates instead: the limit of blank is the level that 95% of blank results fall below, and the limit of detection is the level at which a sample is distinguished from a blank with 95% confidence, which also needs replicates of a sample near the limit. The two approaches answer slightly different questions, and their answers can differ.

Worked example

Six low-range standards from 0.5 to 8 with signals 0.052 to 0.795.

  1. The fit gives a slope S = 0.09981 and a residual standard deviation σ = 0.006449.
  2. LoD = 3.3 × 0.006449 / 0.09981 = 0.2132; LoQ = 10 × 0.006449 / 0.09981 = 0.6462.

LoD = 0.213 and LoQ = 0.646, in the units of the standards. LoQ is 3.03 times the LoD by construction.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • The calibration is linear at the low end and the scatter is constant there.
  • The blank and low-level replicates are independent, from separate preparations.
  • For CLSI, results are approximately normally distributed.

Common mistakes

  • Estimating a limit from a calibration spanning many orders of magnitude, where the scatter is dominated by the high standards.
  • Quoting an LoD without saying how it was calculated. The methods give different numbers.
  • Treating the LoD as the lowest concentration you can measure accurately. That is the LoQ.

Related tools

Calibration Curve Calculator (Standard Curve)Linear fit, residuals and an unknown with its uncertaintyOpen calculatorPercent Recovery CalculatorRecovery of a spike or a standard, with biasOpen calculatorReplicate Measurement Statistics (SD, %RSD, SE, CI)Mean, SD, %RSD, standard error and 95% CI of replicatesOpen calculatorELISA Standard Curve Calculator (4PL)Four-parameter logistic fit and sample concentrationsOpen calculator

Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.