Pharmacokinetics
AUC Calculator
Works out the area under the concentration–time curve (AUC) from measured levels with the trapezoidal rule, or from dose and clearance.
Area under curve, to last sample
33.00mg·h/L
Moderate exposure – therapeutic range
Inputs
Labels the result. Enter concentrations in mg/L — nothing is converted.
Concentration–time data, in any order — points are sorted by time before calculating. At least two points.
Try an example profile (fills the trapezoidal method)
Working
Each trapezoid's area is the mean concentration × the time step.
| Interval (h) | Δt (h) | Mean C | Area |
|---|---|---|---|
| 0 → 1 | 1 | 4 | 4.00 |
| 1 → 2 | 1 | 7 | 7.00 |
| 2 → 4 | 2 | 5 | 10.00 |
| 4 → 8 | 4 | 3 | 12.00 |
| AUC₀→t (sum) | 33.00 | ||
Concentration–time profile
Concentration (mg/L) against time (h), sorted by time.
AUC₀→t = Σ (Cᵢ₋₁ + Cᵢ) / 2 × (tᵢ − tᵢ₋₁)
kₑ = ln(Cₙ₋₁ / Cₙ) / (tₙ − tₙ₋₁) AUC₀→∞ = AUC₀→t + Cₙ / kₑ
AUC = Dose × F / CL
The linear trapezoidal rule joins neighbouring samples with straight lines and adds up the trapezoids underneath. Cₙ is the last measured concentration and tₙ its time; kₑ is the elimination rate constant estimated from the last two points.
Sampling stops before the drug is gone, so the area after the last sample (Cₙ / kₑ) is added to give the total exposure AUC₀→∞. From dose and clearance, F is the bioavailable fraction (100% = 1) and CL the clearance in L/h, giving mg·h/L.
Keep learning
References
- Gibaldi M, Perrier D. Pharmacokinetics. 2nd ed. New York: Marcel Dekker; 1982.
- Ducharme MP, Shargel L, editors. Shargel and Yu's Applied Biopharmaceutics & Pharmacokinetics. 8th ed. New York: McGraw Hill; 2022.
Common questions
AUC₀→t is the area up to the last blood sample. AUC₀→∞ adds an estimate of the area after it, assuming the level keeps falling at the same first-order rate. Bioavailability and clearance calculations need AUC₀→∞.
Extrapolation needs at least three points, a last concentration above zero, and a last concentration lower than the one before. If the curve is still rising or flat at the end, no elimination rate can be fitted.
This tool uses the linear rule for every interval. On the falling part of a curve it slightly overestimates the area; many regulatory analyses switch to the log-linear rule once concentrations decline.
No. The selector only labels the answer. Enter concentrations in the matching unit (mg/L for mg·h/L). Note that 1 mg/L equals 1 μg/mL, but ng/mL values are 1000 times larger.
Prepared by the PharmaWallah student team. Verify results with your textbook or instructor. Report an error · Editorial policy