Standard Curve Calculator – Calibration Curves, Interpolation and Acceptance
A standard curve (calibration curve) links what an instrument reads to how much analyte is present. You measure standards of known concentration, fit a model to them and read each unknown sample's concentration back off the curve. This calculator does that for Bradford and BCA protein assays, ELISA, colorimetric methods and LC-MS. Every replicate is fitted as its own point, and each result comes with a confidence interval, a status and a dilution suggestion.
Why R² ≥ 0.999 is not a good calibration
The coefficient of determination tells you how much of the response variation the curve explains, and the top standards dominate it. In the LC-MS example (1 to 1000 ng/mL), an unweighted line gives R² = 0.9998, yet the 1 ng/mL standard back-calculates to 2.13 ng/mL, an error of +113 %. A calibration is good when it gives back the concentrations you already know. So the tool back-calculates every standard, reports the %RE((x_back − x_nominal) / x_nominal × 100) and plots it against concentration. That residual plot is where problems at the low end show up.
Weighting in plain words
On many instruments the noise grows with the signal. Ordinary least squares treats every point equally, so the big standards pull the line wherever they need it, and the small ones pay the price. Weighting each point by 1/x or 1/x² evens this out. To pick a weighting, open Compare fits. It fits every model and weighting to your data and ranks them by the summed absolute %RE, Σ|%RE|. Don't compare R² values across weightings: they are computed on different scales.
Linear, quadratic or 4PL
- Linear (
y = a + b·x): absorbance methods within their linear range, and chromatography. Use through origin only if the blank truly reads zero. - Quadratic (
y = a + b·x + c·x²): gently bending curves such as the Bradford assay. The tool keeps the root on the calibrated side of the parabola's turning point. It reports “no real solution” when a response lies above the curve's maximum. - 4PL (
y = D + (A − D) / (1 + (x/C)^B)): sigmoidal immunoassays. A is the zero-dose response, D the top plateau, C the inflection point (EC₅₀ or IC₅₀) and B the Hill slope. It works for both sandwich (rising) and competitive (falling) ELISA.
LOD, LOQ and LLOQ: three different lowest numbers
The limit of detection is the smallest amount you can tell apart from the blank. The limit of quantitation is the smallest amount you can measure with acceptable precision. Under ICH Q2, LOD = 3.3σ/S and LOQ = 10σ/S, where S is the slope and σ is the residual SD or the SD of the blank. The LLOQ is simply your lowest accepted standard. A result can be above the LOQ but below the LLOQ, and it is then an extrapolation.
Blank subtraction and through-origin fits
Subtracting a blank shifts every response by the same amount. With a free intercept, the fitted intercept absorbs that shift, so no interpolated concentration changes. Blank subtraction matters only when you force the line through zero. Without it, a through-origin fit tilts to pass through the origin and biases low samples.
Results outside the curve
When a sample reads above the highest standard, the tool suggests a total dilution. It aims to bring the sample to about 80 % of the ULOQ and uses a standard step such as 1:2, 1:5 or 1:10. For a sample already diluted 1:2 that needs twice as much, it shows “re-assay at 1:4 (2× more than now)”.
How precise is an interpolated result?
The interval combines two sources of error: noise in the sample's own readings, and uncertainty in the fitted curve. For a straight line this is the textbook formula s_x0 = (s/b)·√(1/m + 1/n + (y₀ − ȳ)² / (b²·Σ(xᵢ − x̄)²)). Running more replicates of the unknown (a larger m) shrinks the first term. Results near the middle of the curve, where y₀ is close to ȳ, are the most precise.
To convert a fitted slope into a molar absorptivity, use the Beer–Lambert Law Calculator. To plan the standards themselves, use the Dilution Series Generator.