Pharmacokinetic Non-Compartmental Analysis (NCA): AUC, Half-life, and Clearance Online Calculator
Non-compartmental analysis (NCA) assumes no compartmental model and derives exposure and disposition parameters directly from concentration-time points. It is the default method for bioequivalence and toxicokinetic studies, and the approach most people implement by hand in Excel using the trapezoidal rule.
Formulas
AUC(0→t_last) = Σ (Ci + Ci+1)/2 × Δt Linear trapezoidal
AUC(t_last→∞) = C_last / λz Terminal extrapolation
AUMC(0→t_last) = Σ (ti·Ci + ti+1·Ci+1)/2 × Δt
AUMC(t_last→∞) = C_last·t_last/λz + C_last/λz²
λz = Negative slope of log-linear regression through several terminal points (minimum 3)
t½ = ln2 / λz
MRT = AUMC(0→∞) / AUC(0→∞)
CL = Dose / AUC(0→∞) Extravascular dosing yields CL/F
Vz = Dose / (λz × AUC(0→∞)) Extravascular dosing yields Vz/F
Vss = CL × MRT Valid for intravenous dosing only
The four area equations are from Gabrielsson & Weiner, Non-compartmental analysis, Methods Mol Biol 2012;929:377-89, equations (1)–(4).
Why not pure linear trapezoidal by default
The linear trapezoidal method connects adjacent points with straight lines, but the true elimination phase is a downward-concave exponential—the straight line always lies above the curve, so the descending segments are systematically overestimated; the ascending segments are similarly underestimated. This is not a minor error; the magnitude depends on how sparse your sampling is.
The default linear-up/log-down method uses straight-line interpolation only on ascending segments and switches to the log trapezoidal rule on descending segments:
Descending segment (Ci+1 < Ci): ΔAUC = (Ci − Ci+1) × Δt ÷ ln(Ci / Ci+1)
This expression is exact for a monoexponential segment, so the elimination phase is estimated far more accurately.
Verification example
Using monoexponential IV data C(t) = 100 × e^(−0.2t) (mg/L), dose 1000 mg, sampled at 0 / 1 / 2 / 4 / 8 / 12 / 24 h. Every entry has an analytical true value—not copied from any textbook:
| Parameter | Analytical true value | This tool (log-down) | Pure linear trapezoidal |
|---|---|---|---|
| AUC(0→24) | 495.8851 | 495.8152 (−0.014%) | 525.4450 (+5.96%) |
| λz | 0.2 | 0.200192 | same |
| t½ | 3.4657 | 3.4624 | same |
| AUC(0→∞) | 500 | 499.9113 | 529.5411 |
| AUMC(0→∞) | 2500 | 2498.4090 | — |
| MRT | 5 | 4.9977 | — |
| CL | 2 | 2.0004 L/h | 1.8884 |
| Vz | 10 | 9.9922 L | 9.4331 |
The tool loads with this dataset; you can verify it immediately. The right column is the cost of not switching methods: clearance is underestimated by 5.6%, and clearance is the parameter that drives dosing decisions.
The residual error under 0.1% comes from concentrations being entered to two decimal places, not from the method.
Scope and limitations
- The number of terminal points used for λz affects all downstream parameters. This tool defaults to the last 4 points; you can change it. Auto mode selects the point count that maximises adjusted R²—the standard approach, but the points it chooses may differ from what you would select by eye. The tool lists which points were used; check them.
- When the extrapolated fraction exceeds 20%, AUC(0→∞) is unreliable, and the tool will warn you. EMA and FDA bioequivalence guidelines require AUC(0→t) to cover at least 80% of AUC(0→∞). Exceeding this threshold means sampling was not long enough—no algorithm can fix it.
- For extravascular routes, CL and Vz carry bioavailability F, yielding CL/F and Vz/F. Using CL/F as CL systematically overestimates clearance by 1/F. The tool labels the output according to the route you select.
- Vss = CL × MRT is valid only for intravenous dosing. After oral dosing, MRT includes the mean absorption time (MAT), and the result is not a true steady-state volume of distribution.
- Multiple-dose accumulation, steady-state parameters (AUCτ, Cav, fluctuation), and statistical comparisons are not supported. One curve, one subject, one dose.
- How to handle concentrations below the lower limit of quantification (BLQ) depends on the study protocol and can materially affect results. This tool does not apply BLQ rules—enter the values you have decided to use. A value of 0 will cause that segment to fall back to the linear trapezoidal rule.
FAQ
Should I use the linear or log trapezoidal rule for AUC?
**Use the log trapezoidal rule for the elimination phase (linear-up/log-down)—this is the default and the standard practice.** The linear trapezoidal method connects adjacent points with a straight line, but the true elimination phase is a downward-concave exponential; the straight line always lies above the curve, so descending segments are systematically overestimated. Empirically: with sparse sampling of monoexponential data, the pure linear rule overestimates by **5.96%**, while log-down deviates only −0.014%—because the log trapezoidal formula is exact for a monoexponential segment. The consequence lands on clearance: CL = dose ÷ AUC, so a 6% overestimate of AUC means CL is underestimated by about 5.6%, and CL is the parameter that drives dosing decisions.
How many terminal points should I use for λz?
Guidelines require a minimum of 3; in practice 3–5 are commonly used. **This choice affects every downstream parameter** (t½, terminal extrapolation, AUC(0→∞), CL, and Vz all depend on λz), so it is not a minor detail. This tool defaults to the last 4 points and also offers an "Auto" mode that selects the point count maximising **adjusted R²**—adjusted rather than ordinary R² because the latter almost always selects the fewest possible points. In either mode, the tool lists the time points actually used; check that they fall in the elimination phase.
What do I do when the extrapolated fraction exceeds 20%?
**Collect additional samples at later time points—there is no other fix.** EMA and FDA bioequivalence guidelines generally require AUC(0→t) to cover at least 80% of AUC(0→∞), i.e., extrapolation not exceeding 20%. Exceeding this means the last sample was collected while concentrations were still high and the curve was far from complete; in that case more than one-fifth of AUC(0→∞) is extrapolated from C_last/λz, while λz itself is estimated from only a few terminal points—errors compound. Changing the calculation method or the number of fitting points cannot fix this; it is a sampling design issue.
What is the difference between CL and CL/F?
With oral or any extravascular route you do not know how much drug actually reached the systemic circulation, so the calculated value is **CL/F** (where F is bioavailability). True clearance CL = (CL/F) × F. Treating CL/F as CL **systematically overestimates clearance by 1/F**—a twofold error when F = 0.5. The same applies to Vz/F, which is not the true volume of distribution. Separating F requires a paired intravenous dose in the same subject. This tool labels the output according to the route you select and never conflates the two.
Why is Vss not reported for extravascular dosing?
Because Vss = CL × MRT is only valid for intravenous dosing. After oral administration, MRT includes the **mean absorption time** (MAT = MRT_oral − MRT_iv), and the result is neither a true steady-state volume of distribution nor a quantity with a clear physical meaning. Rather than report a number that will be misinterpreted, the tool omits it. Vz (or Vz/F) can still be calculated after oral dosing because it is defined through the terminal phase and does not rely on this assumption.
How should I handle BLQ concentrations?
**This tool does not apply BLQ rules on your behalf** because the handling varies by study protocol: set to 0, exclude entirely, or impute as LLOQ/2 are all used in practice, and the choice can materially affect AUC and λz. Apply your protocol's rule before entering the data. Note that entering 0 causes that interval to fall back automatically to the linear trapezoidal rule—the log trapezoidal formula is undefined when concentration is zero—and this is intentional.
Can this tool compute steady-state parameters for multiple dosing?
No. This tool handles **a single dose in a single subject**—one curve at a time. Steady-state parameters (AUCτ, Cav, Fluctuation, accumulation ratio Rac) require the dosing interval τ and a criterion for steady state, which is a separate algorithm. Statistical comparisons across subjects (geometric mean ratio, 90% confidence interval) are also outside scope—that is bioequivalence analysis; this site has a [t-test](../t-test/) and [sample size / confidence interval tools](../sample-size/) that can complement this calculator.
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