Calibration Curve Calculator
Fit a linear analytical calibration curve from concentration-response pairs, calculate slope, intercept and R², and estimate an unknown concentration.
Fit a linear calibration curve
Paste concentration,response pairs to calculate least-squares slope, intercept, R² and an unknown concentration from measured response.
| x concentration | Observed y | Fitted y | Residual |
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How the Calibration Curve Calculator works
NIST describes calibration as relating known analyte quantities to measured instrumental response through a mathematical model. This tool performs an ordinary least-squares linear fit y = slope×x + intercept from entered concentration-response pairs, calculates R², displays residuals and back-calculates an unknown x from its measured y.
How to use this calibration curve calculator
Paste at least two numeric x,y pairs, ideally several standards covering the validated analytical range. Review the fitted-vs-observed table rather than relying only on R². Enter the unknown response only when it falls within a range and method context where inverse prediction is appropriate. Replicates can be entered as separate points if that matches your method.
How to interpret the result
Slope represents response change per concentration unit, while the intercept estimates response at x=0 under an unconstrained fit. R² describes the fraction of response variation accounted for by the line, but a high R² alone does not prove unbiased calibration. Residual pattern, back-calculated standards, blanks and uncertainty are also important.
Assumptions and limitations
The tool fits an unweighted straight line and does not test heteroscedasticity, outliers, limit of detection/quantitation, replicate weighting, uncertainty or matrix effects. NIST guidance emphasizes choosing an appropriate calibration model; do not force a linear fit simply because the software can calculate one. Extrapolating unknowns beyond standards is especially risky.
Practical example and workflow
With standards spanning 0–6 concentration units and responses near a straight line, the table shows fitted response and residual for every point. If a mid-range unknown response of 3.05 back-calculates near 3 concentration units, the analyst can still verify QC acceptance and calibration-range rules before reporting the result.