Two ways to turn a signal into a concentration. Build a calibration curve from external standards and read the unknown off the line — fast, but it trusts that your sample behaves like the standards. Or use standard addition: spike the sample itself and extrapolate back to the x-intercept. Add a matrix effect and watch the external-standard answer drift off while standard addition still lands on the truth — the whole reason the method exists.
Yellow line = least-squares fit. Green marks the true value / x-intercept.
Recovered conc.—
True conc.—
Error—
R²—
When the matrix meddles, standard addition still tells the truth. An external-standard curve is built from clean standards, so if the real sample suppresses or enhances the signal — a matrix effect — the recovered concentration is biased by roughly that same percentage. Standard addition sidesteps it: because every measurement is made in the sample itself, the sample's own sensitivity cancels when you extrapolate to the x-intercept. Turn the matrix effect to +30% here and compare the error in each mode — external drifts, standard addition holds.
How It Works
Fit a line to knowns, then either read off it or extrapolate through it.
1
External standard
Measure the signal of standards at known concentrations, fit a least-squares line S = m·c + b, and read the unknown as c = (S − b)/m. The R² readout shows how tightly the standards define the line; measurement noise loosens it. This is the everyday calibration curve — quick and accurate when the sample matches the standards.
2
Standard addition
Switch modes and instead spike the sample with known additions, plotting signal versus amount added. The line now sits on top of the sample's own signal, and extrapolating it back to the baseline gives an x-intercept of −(original concentration). No separate standards, no assumption about the matrix — the answer is read straight off the extrapolation.
3
The matrix effect
Slide Matrix effect away from zero to make the sample more or less sensitive than the standards. In external mode the recovered value drifts by about that percentage — a systematic error you couldn't spot from R² alone. In standard-addition mode the slope changes but the x-intercept doesn't, so the recovered concentration stays put. That contrast is the practical lesson.
What is the standard addition method?
You spike the sample itself with known amounts of analyte and plot signal against the amount added. Because every point is measured in the real matrix, extrapolating the fitted line back to the baseline gives an x-intercept = −(original concentration), so the result is read as −(x-intercept). It's the go-to method when the matrix changes the analyte's sensitivity.
External standard vs standard addition — which should I use?
External standards (a calibration curve from separate solutions) are quick and accurate when the sample and standards respond identically: c = (signal − intercept)/slope. Standard addition adds analyte to the sample and extrapolates, correcting for matrix effects because the sample's own sensitivity cancels. Use external standards for clean, well-characterised matrices; standard addition when the matrix is uncertain or interfering.
What is a matrix effect?
Any influence of the sample's other components on the analyte signal — enhancing or suppressing sensitivity versus clean standards. It biases an external-standard result (built on clean standards) but not a standard-addition result (built in the sample). Slide the matrix-effect control and watch the external error grow while standard addition stays accurate.
How do you read concentration from a calibration curve?
Fit a least-squares line to standards to get the slope (sensitivity) and intercept (blank), check it with R², then solve c = (signal − intercept)/slope for the unknown. R² near 1 means a well-defined line; scatter in the standards widens the uncertainty. The linear range is set by Beer's law, and the best precision by the photometric error.
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