Enter calibration data
Example data table
| Standard | Known concentration (mg/L) | Measured response |
|---|---|---|
| 1 | 0.00 | 0.03 |
| 2 | 2.00 | 1.05 |
| 3 | 4.00 | 2.09 |
| 4 | 6.00 | 3.08 |
| 5 | 8.00 | 4.11 |
| 6 | 10.00 | 5.12 |
Example blank responses: 0.00, 0.01, 0.01, 0.02
Example unknown response: 2.65
Formula used
This calculator fits a linear calibration model and then evaluates error in both response space and back-calculated concentration space.
Fitted response: ŷ = a + b x
Weighted slope: b = Σ[w(x - x̄w)(y - ȳw)] / Σ[w(x - x̄w)²]
Intercept: a = ȳw - b x̄w
Response residual: e = y - ŷ
Back-calculated concentration: x̂ = (y - a) / b
Concentration error: Δx = x̂ - x
Percent error: % error = (Δx / x) × 100
Recovery: Recovery % = (x̂ / x) × 100
SEE = √(Weighted SSE / (n - 2))
RMSE = √(Σe² / n)
MAE = Σ|e| / n
LOD = 3.3 σ / |b| and LOQ = 10 σ / |b|
Here, σ comes from blank-response standard deviation when blanks are supplied. Otherwise, the residual standard error is used as the noise estimate.
How to use this calculator
- Enter known concentrations and measured responses in matching order.
- Add blank responses if you want LOD and LOQ based on blanks.
- Select an appropriate weighting scheme for your calibration behavior.
- Choose the confidence level for slope and intercept intervals.
- Optionally enter an unknown response to estimate concentration.
- Optionally add the actual unknown concentration to assess recovery and error.
- Press the calculate button to display summary metrics, table output, and graph.
- Use the CSV and PDF buttons to export the analysis.
FAQs
1. What does this calculator measure?
It measures regression fit, response residuals, back-calculated concentration error, percent error, recovery, detection limits, and uncertainty indicators for a linear calibration curve.
2. When should I use weighting?
Use weighting when response variance changes across concentration levels. Lower levels often need more influence, especially in analytical chemistry, assay validation, and instrument method development.
3. Why is back-calculated concentration important?
Back-calculation shows how well the regression reproduces known standards. Large concentration errors can reveal poor fit, wrong weighting, outliers, or nonlinearity in the method.
4. What is the difference between RMSE and SEE?
RMSE summarizes average residual size across all points. SEE adjusts for regression degrees of freedom and is commonly used as the calibration noise estimate.
5. How are LOD and LOQ estimated here?
LOD and LOQ use 3.3σ/|b| and 10σ/|b|. The calculator uses blank-response standard deviation when blank data exists, otherwise residual standard error.
6. Can I include a zero standard?
Yes, for unweighted analysis. However, x-based weighting options like 1/x and 1/x² cannot handle zero concentration because they create division problems.
7. What does the unknown estimate represent?
It is the concentration predicted from the fitted calibration line using the entered unknown response. If an actual value is supplied, the calculator also reports error and recovery.
8. Is this calculator suitable for nonlinear curves?
No. This version is built for linear calibration models only. Curved responses should be evaluated with polynomial, logistic, or other validated nonlinear models.