Calibration Curve Calculator Formula
Understand the math behind the calibration curve calculator. Each variable explained with a worked example.
Formulas Used
Unknown Concentration
concentration = (signal - intercept) / slopeBack-Calculated Signal
predicted_signal = slope * ((signal - intercept) / slope) + interceptVariables
| Variable | Description | Default |
|---|---|---|
slope | Calibration Slope (m) | 2500 |
intercept | Calibration Intercept (b) | 0.05 |
signal | Measured Signal (y) | 1.3 |
How It Works
Linear Calibration Curve
A calibration curve relates instrument signal to analyte concentration. With a linear model y = mx + b, an unknown concentration is found by inverting this relationship.
Formula
c_unknown = (y_measured - b) / m
where y is the measured signal, m is the slope from standard curve regression, and b is the y-intercept. The calibration curve should be established from at least 5 standard concentrations spanning the expected range.
Worked Example
A calibration with slope = 2500 (signal/M), intercept = 0.05, and measured signal = 1.3.
- 01c = (1.3 - 0.05) / 2500
- 02c = 1.25 / 2500 = 0.000500 M = 0.500 mM
Frequently Asked Questions
How many standards do I need?
A minimum of 5 standards (plus a blank) is recommended. More points give better statistics. Standards should span the range of expected sample concentrations, ideally with the unknowns in the middle third of the curve.
What R² value is acceptable?
For quantitative analysis, R² > 0.995 is typically required. R² > 0.999 is excellent. If R² is low, check for preparation errors, instrument issues, or non-linear response at the concentration extremes.
Can I extrapolate beyond the calibration range?
Extrapolation is unreliable because the linear relationship may not hold outside the calibrated range. Dilute samples that read above your highest standard, or prepare additional standards.
Ready to run the numbers?
Open Calibration Curve Calculator