= Electropherogram peak area
{title2=$A_p$}
An \b[<electropherogram peak area>] is the time integral of detector <signal> above an assigned baseline over a specified peak interval:
$$
A_p=\int_{t_a}^{t_b}[s(t)-b(t)]\,dt.
$$
Its units are signal multiplied by time. It differs from peak height and from the amount of material unless a detector-response and transport model connects them. Broadening a peak can lower its height while preserving its area.
For an isolated <Gaussian distribution> of signal, $s-b=H\exp[-(t-t_m)^2/(2\sigma_t^2)]$, integration over the complete peak gives $A_p=H\sigma_t\sqrt{2\pi}$. An original peak with $H=2$ signal units and $\sigma_t=3$ s has area $15.04$ signal-seconds. Doubling the width at unchanged area halves the height. Integrating only a finite interval loses the corresponding tails; integrating overlapping peaks can include another species' response.
Why can migration time enter quantification? Suppose a concentration-sensitive detector gives $s-b=kc$ for a band moving at constant speed $v$ through a capillary of internal <area> $S$. The amount passing the detector is
$$
n=S\int c(t)v\,dt=\frac{Sv}{k}A_p.
$$
Since $v=L_d/t_m$, \b[$n\propto A_p/t_m$] at fixed $S$, $L_d$ and response coefficient $k$. A slow band spends longer in the detection window and can have more raw time-integrated signal for the same amount. This motivates <time-corrected electropherogram peak area>; the first-party software explicitly calculates it as raw area divided by migration time.<Processing Methods - CE data by Waters>[Procedure, Step 5, items 4–5]{ref}
For stipulated raw areas 120 and 180 signal-seconds at migration times 200 and 300 s, both corrected values are 0.60 signal units. Equal corrected values imply equal modeled amounts only if the relevant response coefficients and sampling conditions agree. Different species need not have equal detector responses, and a detector measuring a different physical observable requires its own model.
Baseline error has an especially simple consequence. If the estimated baseline exceeds the true one by $\delta b$ throughout a window of duration $T$, the area error is $-\delta bT$. A 0.01 signal-unit offset over 60 s subtracts 0.60 signal-seconds. Blank measurements, explicit integration limits and inspection of unresolved neighbors therefore matter even when the numerical integration itself is exact.
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