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Calibration Curve

A calibration curve relates analyte concentration to instrument response (e.g., absorbance). Linear regression fits y = mx + b; unknown concentration x = (y − b) / m. LOD and LOQ define detection limits.

Concept Fundamentals
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Slope (m)
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R²
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Unknown
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SE
Build Calibration Curvey = mx + b | Linear Regression | LOD/LOQ

Why This Chemistry Calculation Matters

Why: Calibration curves are essential for quantitative analysis. Beer's law (A = εlc) underlies absorbance-based calibration; linear regression provides slope, intercept, and R².

How: Enter standard concentrations and absorbances. Least-squares regression yields y = mx + b. For unknown absorbance y, concentration x = (y − b) / m. R² ≥ 0.99 excellent.

  • ●Linear regression: y = mx + b. R² = 1 − SS_res/SS_tot.
  • ●Beer's law: A ∝ c. Calibration converts A to concentration.
  • ●LOD = 3×SD blank; LOQ = 10×SD blank.
  • ●Never extrapolate beyond the standard range.
Sources:IUPAC AnalyticalISO 8466

📊 Calibration Curve Calculator

y = mx + b | Linear Regression | R² | Unknown Concentration

📋 Sample Examples

Standard Points

Select the unit for concentration values
Standard 1
Standard 2
Standard 3
Standard 4
Standard 5
Enter absorbance of unknown sample to calculate its concentration
Display residuals plot to assess curve quality

For educational and informational purposes only. Verify with a qualified professional.

🔬 Chemistry Facts

📊

y = mx + b. R² ≥ 0.99 excellent fit.

— IUPAC

🧪

Beer's law: A = εlc. Calibration links A to c.

— Spectroscopy

📐

LOD = limit of detection; LOQ = limit of quantitation.

— ISO

💡

Use 5–7 standards; never extrapolate.

— Analytical

📋 Key Takeaways

  • • y = mx + b — Linear regression for calibration
  • • R² ≥ 0.99 excellent, ≥ 0.95 good, ≥ 0.90 acceptable
  • • Unknown: x = (y − b) / m
  • • Use 5–7 standards; never extrapolate beyond range

What is a Calibration Curve?

A calibration curve relates analyte concentration to instrument response (e.g., absorbance). Use least-squares regression to fit y = mx + b, then interpolate unknown concentrations.

How Does It Work?

Prepare standards → measure responses → perform linear regression → calculate unknowns from x = (y − b) / m.

When to Use

ELISA, protein assays, enzyme assays, metal analysis (AAS), DNA quantification, environmental and pharmaceutical analysis.

Formulas

y = mx + b
R² = 1 − (SSres/SStot)
x = (y − b) / m

Best Practices

Use 5–7 standards, include blank, ensure linear range, check R², analyze residuals, never extrapolate.

📚 Official Data Sources

IUPAC Analytical Division ↗
Analytical method validation standards
ISO 8466 Standards ↗
Calibration and linear regression standards
Eurachem Guide ↗
Method validation and uncertainty estimation

⚠️ Disclaimer: Uses ISO 8466 and IUPAC standards.

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