LabCalc

Calibration Curve Calculator

y = m·x + b, x = (y − b) / m

Fit a linear calibration curve by least squares, with optional 1/x or 1/x² weighting, and back-calculate unknown concentrations.

Standards

1
2
3
4
5

Result

y = 0.0410777x + 0.00141262

R² = 0.999986 over 5 standards • first unknown ≈ 3.61723 mg/L

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Calculation

  1. Least-squares fit

    y = m·x + b

    Unweighted (ordinary least squares), n = 5 standards

    y = 0.0410777·x + 0.00141262

  2. Goodness of fit

    R² = Sxy² / (Sxx · Syy)

    R² = 0.999986

  3. Residual standard deviation

    Sy/x = √(Σ(yᵢ − ŷᵢ)² / (n − 2))

    Sy/x = 0.00068973

  4. Unknown, response 0.15

    x = (y − b) / m

    x = (0.15 − 0.00141262) / 0.0410777

    3.61723 mg/L

Inputs

Standards
5 points
Weighting
Unweighted (ordinary least squares)
Concentration unit
mg/L
Standard 1
0.5 mg/L → 0.021
Standard 2
1 mg/L → 0.043
Standard 3
2 mg/L → 0.084
Standard 4
5 mg/L → 0.207
Standard 5
10 mg/L → 0.412

R² alone does not validate a calibration: inspect the residuals, the working range and the behaviour near the lowest standards.

Weighting is applied only when you select it. No weighting model is chosen automatically.

Replicate standards are kept as individual points unless you explicitly average them.

About this calculator

Enter your standards as concentration and response pairs. The calculator performs an ordinary or weighted least-squares fit and reports the slope, intercept, R² and — when you have at least three standards — the residual standard deviation and the standard error of the slope.

Weighting (1/x or 1/x²) is applied only when you select it, and a standard at concentration zero cannot be included in a weighted fit because its weight would be infinite. Replicate standards stay as individual points unless you choose to average them. R² alone does not validate a calibration — inspect the residuals and the working range.

LabCalc is provided as a calculation aid. Users remain responsible for verifying calculations, units, chemical compatibility, experimental procedures and applicable safety requirements before laboratory use.

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