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About this tool
Enter calibration points to compute the linear fit, residuals, and R², then derive the LOD and LOQ.
The Calibration Curve LOD/LOQ Workbench fits a straight calibration line to your concentration/response pairs by unweighted ordinary least squares, then derives detection limits from the scatter around that line: LOD = 3.3 × σ ÷ |slope| and LOQ = 10 × σ ÷ |slope|, the sigma-factor convention used in ICH Q2. σ here is the residual standard deviation, √(Σresiduals² ÷ (n − 2)). You paste one "concentration | response" pair per line and get the slope, intercept, R², residual SD and a per-point residual table alongside the two limits.
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Paste one standard per line into the Calibration points textarea in concentration x | response y form — it opens with a six-point curve running 0 | 0.02 to 5 | 5.11, and needs at least three valid pairs whose x values vary.
Set the LOD sigma factor and LOQ sigma factor number fields (3.3 and 10 by default, so entering 3 reproduces the 3σ convention), or press the Six-point curve chip under Examples; the fit recomputes on every keystroke.
Read the LOD · LOQ result line above the y = slope·x + intercept caption, the Slope, Intercept, Residual SD, R² and Points rows, and the x / y / Fitted y / Residual table. Download saves calibration-curve-lod-loq-workbench.txt and Reset restores the defaults.
Every point gets its fitted y and residual in a table, so curvature or a bad standard at the low end is visible instead of hidden inside a good-looking R².
The 3.3 and 10 defaults follow the common convention, but both are editable, so you can reproduce a 3σ/10σ house method or a protocol that specifies something else.
The tool is explicit that this is an unweighted OLS and residual-SD illustration, so you know what it did not do before quoting the number.
LOD = 3.3 × σ ÷ |slope| and LOQ = 10 × σ ÷ |slope|, where σ is the residual standard deviation of the calibration line and slope is its sensitivity. Both sigma factors are editable inputs, so setting LOD to 3.0 reproduces the 3σ convention some methods use instead.
The residual standard deviation of the regression: the square root of the sum of squared residuals divided by n − 2. It uses n − 2 degrees of freedom because two parameters, slope and intercept, were estimated from the data. Some validated methods instead require the standard deviation of the blank or of replicate low-level standards — that is a different σ and will give a different limit.
At least three valid pairs, and the x values must actually vary or the slope is undefined. Three is the arithmetic minimum, not a good practice — analytical guidelines typically expect five or six concentration levels across the working range, and n − 2 degrees of freedom at n = 3 makes σ very unstable.
Treat it as an illustration rather than a validated result. It performs an unweighted ordinary least-squares fit only, and does not handle blank SD, replicate low-level standards, weighting such as 1/x or 1/x², heteroscedasticity checks or matrix effects. Follow your jurisdiction's guidance and your laboratory's validation protocol for anything you submit.
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