A calibration curve connects known analyte concentrations or amounts with the response produced by an analytical method. The relationship is then used to estimate an unknown sample's value. Reading the curve means understanding its axes, model and supporting data, rather than treating a high correlation number as proof that every calculated result is reliable.
Identify what was put in and what was measured
The horizontal axis commonly shows assigned concentration; the vertical axis may show peak area, a signal ratio or another response. These are different quantities. A graph labelled only amount and intensity omits information needed to reproduce its calculation.
NIST's calibration guidance starts with plotting responses against known reference values, choosing a candidate model and evaluating the fit. It also calls for examining residuals and using suitable weighting where measurement variation is not constant across the interval.NIST — Calibration data analysis and model validation (opens in a new tab)
| Item | What to establish |
|---|---|
| Reference values | Concentration or amount, with units and preparation basis |
| Response | Area, height, ratio or another explicitly defined signal |
| Model | The fitted relationship and any transformation or weighting |
| Range | The interval supported by the calibration and method evidence |
Calculate the unknown in the correct direction
For an original linear example, let response y = 200x + 10, where x is concentration in µg/mL and y is an arbitrary response unit. A sample response of 610 gives x = (610 − 10)/200 = 3.00 µg/mL. The intercept is removed before division by the slope.
Ignoring the intercept would give 3.05 µg/mL. At a smaller response of 50, the proper result is 0.20 µg/mL, while ignoring the intercept gives 0.25 µg/mL. The same omitted response of 10 creates a much larger relative error at the lower concentration.
The equation describes the solution presented to the measurement under this model. A separate, documented dilution factor may be needed to recover the original sample concentration. Neither that factor nor a conversion to milligrams per vial should be silently built into a label that still says instrument response.
Look at deviations across the interval
A residual is an observed response minus the model's fitted response at that reference level. A pattern of deviations can expose curvature or another mismatch that a single summary statistic hides. Random-looking residuals are useful evidence, but they do not test every possible source of bias.NIST — Calibration data analysis and model validation (opens in a new tab)
In its worked weighting example, NIST models how variability changes with response before applying a weighted fit. Weighting is therefore a response to an evidence-based variance problem, not a choice made solely because it makes the displayed fit look better.NIST — Weighting to improve fit (opens in a new tab)
An unsuitable line should not be rescued by automatically discarding awkward levels. Review preparation, instrument behaviour and the model itself. If a level is excluded for a justified reason, retain that reason and the original record.
Keep interpolation distinct from an unsupported extension
If an illustrative calibration is supported from 1 to 5 µg/mL, a computed value of 3 lies inside that interval. A value of 8 lies outside it even though the equation can still produce a number. Mathematical calculability does not supply the missing performance evidence.
NIST's discussion of calibrated-value uncertainty treats the unknown result as its own measurement problem, including uncertainty arising through calibration. A precisely printed coefficient is not an uncertainty statement for a future sample.NIST — Uncertainties of calibrated values (opens in a new tab)
The practical conclusion should connect the unknown response to an appropriate curve, a supported interval and the sample calculation. Keep reference-value accuracy and sample-specific interference in view; a good fit to incorrectly assigned standards can still return biased sample values.
Sources and further detail
- NIST — Calibration data analysis and model validation (opens in a new tab)
Statistical handbook guidance on model fitting and residuals. The original peptide-concentration example does not reuse the load-cell dataset.
- NIST — Weighting to improve fit (opens in a new tab)
Worked statistical example for non-constant measurement variability; no universal weighting prescription inferred.
- NIST — Uncertainties of calibrated values (opens in a new tab)
Distinguishes uncertainty in calibrated future measurements from the fitted curve itself.
Sources checked 19 September 2026. Worked examples are illustrative unless a supplied report is explicitly identified. This article has not undergone independent scientific peer review.