PHARM/PCS V5 · Procedure 25 Drug Decay and Binding
Area Under a Curve: Trapezoidal and Simpson's Rules
Compute the area under a curve from tabulated points by the trapezoidal rule, and by Simpson's rule when the spacing allows it.
What it computes
Computes the area under a curve from tabulated (x, y) data using both the trapezoidal rule and (when intervals are equal and even-numbered) Simpson's rule.
Inputs and outputs
You provide
- Paired x and y values, one pair per line
PHARM/PCS reports
- Area by the trapezoidal rule
- Area by Simpson's rule, when the intervals are equal and even in number
- A plot of the curve with the area shaded
When to use it
Whenever you need an AUC from discrete points without assuming a model, most often plasma-concentration AUC for bioavailability and clearance work, where it feeds Procedures 29 and 30.
Reading the results
The trapezoidal rule slightly overestimates area under a convex-declining curve but works with any spacing; Simpson's rule is more accurate but needs equal, even-numbered intervals, so if yours aren't, trust the trapezoidal value. Neither captures the tail beyond your last point, so extrapolate the terminal phase separately when total AUC matters.
It picks the rule your data supports
When every x interval is equal and the number of subintervals is even, both rules are reported. Otherwise only the trapezoidal value appears, because Simpson's rule does not apply. Neither method sees past your last point, so extrapolate the terminal phase separately when total AUC is what you need.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.