Calculator
Enter calibration standards, optional blank responses, and unknown signals. Results appear above this form after submission.
Example data table
This example represents a simple photodiode calibration using irradiance standards and voltage output.
| Reference irradiance (W/m²) | Measured voltage (V) |
|---|---|
| 0 | 0.11 |
| 50 | 0.62 |
| 100 | 1.16 |
| 150 | 1.71 |
| 200 | 2.27 |
| 250 | 2.79 |
Formula used
1) Linear calibration
Model: y = mx + b
Use this when the detector response is approximately proportional to the reference quantity over the chosen range.
2) Linear through origin
Model: y = mx
Use this only when physics and instrumentation justify zero signal at zero reference after correction.
3) Quadratic calibration
Model: y = ax² + bx + c
Use this when detector response bends slightly and a straight line leaves structured residuals.
4) Solving unknowns
For a linear fit, x = (y - b) / m. For a quadratic fit, the calculator solves ax² + bx + c - y = 0 and chooses the physically reasonable root near the calibrated span.
5) Detection estimates
When blank responses are supplied, blank mean can be subtracted from signals. The solver estimates LOD = 3.3σ / slope and LOQ = 10σ / slope using blank standard deviation and the effective low-end sensitivity.
How to use this calculator
- Enter the known reference values in the first box.
- Enter the measured instrument responses in the second box.
- Add optional blank responses if you want correction, LOD, and LOQ.
- Enter one or more unknown signals to estimate their reference values.
- Choose linear or quadratic fitting and optional weighting.
- Submit the form to see the fit, diagnostics, solved unknowns, and graph above the form.
- Use the CSV or PDF buttons to export a clean calculation report.
FAQs
1) What does a calibration curve solver do?
It fits a mathematical relationship between known reference values and measured responses, then inverts that relationship to estimate unknown values from new instrument signals.
2) When should I choose a linear fit?
Choose linear fitting when residuals stay small and random, the response is proportional across the working range, and detector physics suggests nearly constant sensitivity.
3) When is a quadratic fit better?
Quadratic fitting is useful when response curvature appears at higher reference values, or when a straight line leaves systematic residual patterns rather than random scatter.
4) What does weighting change?
Weighting changes how strongly each calibration point influences the fit. It is often used when variance grows with signal size and lower standards need stronger emphasis.
5) Why use blank correction?
Blank correction removes baseline offset from standards and unknowns. This often improves physical interpretability, reduces intercept bias, and supports LOD and LOQ estimation.
6) What does R² tell me?
R² measures how much of the response variation is explained by the fit. High R² helps, but residual behavior and physics still matter before trusting a model.
7) Can I solve multiple unknown signals at once?
Yes. Enter several unknown signals separated by commas or lines. The calculator solves each one, labels extrapolations, and lists all estimates in a results table.
8) What if the unknown lies outside calibration range?
The solver still reports a value when possible, but marks it as extrapolated. Such estimates are less reliable and should be confirmed with a wider calibration span.