Linear regression standard curve
Calibration Curve Calculator
Free calibration curve calculator. Fit a linear regression to your standards, get the equation, R², and standard error, then interpolate an unknown concentration from its signal.
Calibration standards
| Concentration (x) | Signal (y) | |
|---|---|---|
Fitted calibration line
y = 0.0935x + 0.03
R² = 0.99877 · Good linearity
Slope (m)
0.0935
Intercept (b)
0.03
Std. error
0.01197
Solve an unknown sample
Formula reference
y = m·x + bx = (y − b) / mExample: quantify a protein by absorbance
- 1Enter your standards as concentration vs. signal pairs, e.g. 0→0.04, 2→0.21, 4→0.40, 6→0.58, 8→0.79.
- 2The calculator fits y = 0.0935·x + 0.030 with R² ≈ 0.9988.
- 3Check R² and the standard error to confirm the response is linear.
- 4Enter the unknown sample signal (e.g. 0.35) to interpolate its concentration: x = (0.35 − 0.030) / 0.0935 ≈ 3.42.
Common mistakes to avoid
- Reading an unknown whose signal falls outside the calibrated range — that is extrapolation, not interpolation.
- Trusting a high R² that hides curvature; always inspect the plotted residual pattern.
- Using too few standards (fewer than three leaves no degrees of freedom for the standard error).
Frequently asked questions
What is a calibration curve?
A calibration curve is a plot of known standard concentrations against the signal an instrument produces for each one. Fitting a line lets you convert a measured signal back into a concentration.
What does R² tell me?
R² is the fraction of the signal variance explained by the linear fit. Values at or above 0.99 indicate good linearity; below 0.95 suggests the response is not linear or contains outliers.
How do I find an unknown concentration?
Rearrange the fitted line: x = (y − b) / m, where y is the measured signal, b the intercept, and m the slope. The tool does this for you and warns if the signal is outside the standard range.
Ready to use the calculator?
Open the working LabTools calculator with units, validation, and prep-sheet output.