AUC Calculator (Trapezoidal Rule, Pharmacokinetics)
Calculate the area under the concentration–time curve (AUC₀–t and AUC₀–∞) by the linear or linear-up/log-down trapezoidal rule, with Cmax, Tmax, terminal half-life, CL/F and Vz/F.
How it works
linear trapezoid: ΔAUC = (C₁ + C₂) ÷ 2 × (t₂ − t₁) · log trapezoid (falling levels): ΔAUC = (C₁ − C₂) ÷ ln(C₁ ÷ C₂) × (t₂ − t₁) · λz = −slope of ln C vs t over the last points · AUC₀–∞ = AUC₀–t + C last ÷ λz · CL/F = dose ÷ AUC₀–∞ · Vz/F = CL/F ÷ λz
The area under the plasma concentration–time curve measures total drug exposure and is the basis of bioavailability, bioequivalence and clearance calculations. Non-compartmental analysis splits the curve into trapezoids between sampling times. The linear rule is accurate while levels rise, but overestimates the area when they fall exponentially, so the linear-up/log-down method (the default in Phoenix WinNonlin-style analysis and recommended in regulatory guidance) uses the logarithmic trapezoid for declining segments. The tail beyond the last sample is extrapolated from the terminal rate constant; regulators expect the extrapolated part to be under 20% of AUC₀–∞.
Worked example
Samples at 0, 0.5, 1, 2, 4, 6, 8 and 12 h of 0, 4.2, 6.8, 7.5, 5.6, 3.9, 2.7 and 1.3 mg/L, linear-up/log-down: AUC₀–t = 47.54 mg·h/L, Cmax 7.5 mg/L at 2 h. The last three points give λz = 0.1830 /h (half-life 3.79 h), so AUC₀–∞ = 47.54 + 1.3 ÷ 0.1830 = 54.65 mg·h/L (13.0% extrapolated). For a 100 mg dose CL/F = 1.830 L/h and Vz/F = 10.0 L.
Sources: Noe DA. Parameter estimation and reporting in noncompartmental analysis of clinical pharmacokinetic data. Clin Pharmacol Drug Dev 2020;9 Suppl 1:S5–S17 · FDA — Bioavailability Studies Submitted in NDAs or INDs, General Considerations (2022)
Frequently asked questions
What is the trapezoidal rule for AUC?
It approximates the area under the concentration–time curve as a series of trapezoids: for each interval, the average of the two concentrations times the time between them. Adding all intervals gives AUC₀–t.
When should I use the log trapezoidal method?
For the declining part of the curve, where concentrations fall exponentially. The linear rule overestimates those areas, especially with widely spaced samples; the linear-up/log-down combination is the usual standard.
What is the difference between AUC₀–t and AUC₀–∞?
AUC₀–t stops at the last measured concentration. AUC₀–∞ adds the extrapolated tail, C last ÷ λz, to estimate total exposure. If the extrapolated part is above about 20%, AUC₀–∞ is unreliable and sampling should be extended.
How is clearance calculated from AUC?
CL = F × dose ÷ AUC₀–∞. After an IV dose F = 1 and the result is true clearance; after an oral dose you get apparent clearance, CL/F.
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Educational pharmacokinetic estimate for health professionals only — not medical advice or a prescription. Population parameters vary widely between patients; base real dosing on the product label, measured drug levels, local protocols and a clinical pharmacist.