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Pharmacokinetics Calculator · Bioequivalence & Trial PK

AUC Calculator: Trapezoidal Pharmacokinetic Exposure

Estimate observed drug exposure from concentration-time pairs using the linear trapezoidal rule. Reports AUC0-t, Cmax, Tmax, sample count, terminal concentration, and interval breakdown — built for clinical pharmacologists, CRO analysts, and formulation teams planning BE and Phase 1 PK studies.

Quick Answer

AUC (area under the concentration–time curve) quantifies total systemic drug exposure in noncompartmental pharmacokinetics. This free calculator applies the linear trapezoidal rule to paste-in time–concentration pairs and reports observed AUC (AUC0-t), Cmax, Tmax, and interval breakdown. Pharma teams use AUC for bioequivalence study planning, exposure–response analysis, and clearance estimates — with links to half-life, clearance, and bioavailability calculators in the NovaPharmaNews PK hub.

Linear Trapezoidal Rule
AUC = ∑ ((C1 + C2) / 2) × (t2 - t1)
C = concentration; t = time; each adjacent pair forms one trapezoid. Regulatory NCA often uses linear-up/log-down hybrid — see Evidence section.

Calculate AUC

Paste time-concentration pairs and select units. The calculator sums trapezoids between adjacent points for observed exposure.

Concentration-time data

Enter one pair per line. Accepted separators: comma, tab, or space. Do not include units in the rows.

AUC is reported as concentration × time using your selected units.

Input example

Use rows such as 1, 8.7 or 2 6.1. The calculator treats the first value as time and the second as concentration.

Observed AUC

-

concentration x time

Cmax
-
concentration
Tmax
-
time
Data points
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points
Terminal concentration
-
concentration
Trapezoid intervals used in the AUC calculation
Interval Time span Average concentration Partial AUC

How to Use This AUC Calculator

1
Paste time-concentration pairs with one observation per line. The first number is time and the second is concentration.
2
Keep units consistent. If time is in hours and concentration is in mg/L, AUC is reported as mg/L × hours.
3
Check that time values increase from top to bottom and that concentrations are zero or positive.
4
Review observed AUC (AUC0-t), Cmax, Tmax, point count, terminal concentration, and the interval audit table.
5
Chain to the Clearance Calculator (CL = D/AUC), Half-Life Calculator (washout and steady state), or Bioavailability Calculator (dose-normalized F) for downstream PK analysis.

Linear, Log, and Hybrid Trapezoidal Methods

Noncompartmental AUC integration assumes a shape between consecutive samples. The linear trapezoidal rule used here connects points with straight lines — appropriate for quick checks and educational use. On declining concentration profiles, linear interpolation can sit above the true exponential decay and slightly overestimate AUC during elimination.

Log-trapezoidal interpolation applies when concentrations fall, using the formula (t2 − t1)(C1 − C2) / ln(C1 / C2). Linear-up/log-down hybrid uses linear interpolation when concentration rises and log-trapezoidal when it falls — the approach FDA and EMA NCA guidance commonly expects for bioequivalence submissions. Validated NCA software (WinNonlin, Phoenix, R PKNCA) applies the hybrid by default; this browser tool uses linear trapezoidal for transparent, paste-in arithmetic.

AUC0-t vs AUC0-inf

This calculator reports observed AUC through the last entered time point (AUC0-t / AUClast). It does not estimate terminal slope (λz) or add extrapolated area for AUC0-inf. If the first point is time zero, the result is commonly interpreted as AUC0-t. Regulatory BE datasets require both AUClast and AUC0-inf from validated NCA with adequate terminal-phase sampling.

Pharma & Bioequivalence Trial Context

AUC is a co-primary endpoint in most bioequivalence studies alongside Cmax. Sponsors compare test and reference products under crossover or replicate designs, log-transform AUC and Cmax, and apply two-one-sided-tests (TOST) with 90% confidence intervals against the 80–125% acceptance limits. Food-effect, formulation-bridge, and renal/hepatic impairment studies also rely on exposure metrics derived from concentration–time profiles.

Phase 1 first-in-human and dose-escalation studies use AUC to characterize dose proportionality, support maximum tolerated dose selection, and feed population PK models. Exposure–response analyses link AUC (and Cmax, Cmin) to efficacy biomarkers, QTc, or adverse event rates — but the model and thresholds must come from validated trial data, not a single-subject calculator output.

After calculating observed AUC, use the Clearance Calculator for CL = Dose/AUC, the Half-Life Calculator for washout and steady-state timing, the Bioavailability Calculator for absolute or relative F from dose-normalized AUC ratios, and the Loading Dose Calculator when rapid target concentration is needed for long half-life drugs.

Worked Example

Example calculation

Points: (0, 0), (1, 8), (2, 6), (4, 2) using hours and mg/L.

Interval 0 to 1: ((0 + 8) / 2) × (1 − 0) = 4 mg/L × hours.

Interval 1 to 2: ((8 + 6) / 2) × (2 − 1) = 7 mg/L × hours.

Interval 2 to 4: ((6 + 2) / 2) × (4 − 2) = 8 mg/L × hours.

Total observed AUC: 19 mg/L × hours. Cmax = 8 mg/L at Tmax = 1 h.

Evidence & sources

Frequently Asked Questions

AUC, or area under the concentration-time curve, estimates total systemic drug exposure over a measured sampling interval. Higher AUC generally means greater exposure, although clinical interpretation depends on dose, route, clearance, target concentration range, and safety margin. AUC is a primary endpoint in bioequivalence studies and a core input for clearance (CL = Dose / AUC) and exposure–response modeling.
The linear trapezoidal rule connects adjacent concentrations with straight lines and sums trapezoid areas — simple but can overestimate AUC on declining curves. Log-trapezoidal uses logarithmic interpolation during elimination and is more accurate when concentrations decline exponentially. Linear-up/log-down hybrid applies linear interpolation when concentration rises and log-trapezoidal when it falls; FDA and EMA NCA guidance commonly treats this hybrid as the default for regulatory submissions. This calculator uses linear trapezoidal only; validated NCA software applies the hybrid for BE analysis.
The linear trapezoidal rule divides the concentration-time profile into adjacent intervals and sums each trapezoid: ((C1 + C2) / 2) × (t2 − t1). It is a noncompartmental approximation for observed exposure between the first and last measured sample. Each interval contribution is shown in the results table so you can audit the arithmetic step by step.
This calculator reports observed AUC over the entered interval — commonly described as AUC0-t or AUClast when the first time point is zero and the last point is the final measurable concentration. It does not estimate terminal elimination rate (λz), extrapolated residual area, or AUC0-inf. Regulatory bioequivalence studies typically report both AUClast and AUC0-inf from validated NCA software.
AUC0-inf is total exposure from time zero extrapolated to infinity: AUC0-inf = AUClast + Clast / λz, where λz is the terminal elimination rate constant from log-linear regression of the terminal phase. If more than about 20–25% of AUC0-inf is extrapolated beyond the last measurable concentration, regulators may question whether sampling captured adequate terminal phase. This calculator does not perform λz regression or infinity extrapolation.
Bioequivalence assessments compare rate and extent of exposure between a test and reference product. AUC reflects extent of exposure (how much drug reaches systemic circulation), while Cmax reflects peak exposure. FDA and EMA require log-transformed AUC and Cmax with 90% confidence intervals for generic and many formulation-change submissions. This calculator helps trialists sanity-check observed exposure arithmetic; formal BE conclusions require validated study conduct and statistical analysis.
Under standard two-one-sided-tests (TOST) analysis, the 90% confidence interval for the geometric mean ratio of test to reference must fall entirely within 80% to 125% for both AUC and Cmax to conclude bioequivalence. This corresponds to ±20% on the log scale. Narrow therapeutic index drugs may use tighter limits (90–111% for some products per FDA guidance). A point estimate from this calculator alone cannot demonstrate BE — confidence intervals from the full crossover dataset are required.
At minimum, two points define one trapezoid, but reliable NCA requires rich sampling: pre-dose, frequent samples during absorption (around Tmax), and sufficient terminal-phase samples (often 3–5 points spanning at least two half-lives) to characterize λz for AUC0-inf. Sparse sampling designs in Phase 1 or population PK use model-based methods rather than trapezoidal AUC alone. For this calculator, enter all available observed pairs in strictly increasing time order.
Clearance links dose to exposure: CL = Dose / AUC (for IV) or CL/F = Dose / AUC (for extravascular routes). Half-life reflects elimination rate but does not alone determine AUC — dose, bioavailability, and clearance together define exposure. After calculating AUC here, use the Clearance Calculator for CL = D/AUC, the Half-Life Calculator for elimination and washout timing, and the Bioavailability Calculator when comparing oral and IV exposure.
AUC can support exposure–response analysis because it summarizes total exposure over the sampling window. The relationship may link to efficacy, adverse events, or therapeutic drug monitoring targets, but the exposure–response model and clinical threshold must come from validated evidence. AUC is necessary but not sufficient — Cmax, Cmin, time above threshold, and pharmacodynamic endpoints often matter equally.
You need at least two observed concentration-time pairs with times in strictly increasing order and non-negative concentrations. Use consistent time and concentration units across all points. Paste one pair per line with comma, tab, or space separators. Do not include units in the data rows — select time unit and enter concentration unit in the form fields instead.
No. Regulatory bioequivalence and clinical pharmacology submissions require validated NCA software (e.g., WinNonlin, Phoenix, R packages with audit trails) that applies FDA/EMA-preferred linear-up/log-down integration, λz selection rules, outlier handling, and subject-level datasets under GLP/GCP. This browser tool is a transparent educational and development-stage arithmetic aid for observed linear trapezoidal AUC — not a substitute for submission-ready NCA.

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t½ Half-Life Calculator CL Clearance Calculator F Bioavailability Calculator Vd Volume of Distribution LD Loading Dose Calculator

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