Gera Tools

One-Compartment PK Parameter Calculator

Estimate Cmax, Cmin, AUC, t½, and Vd from two drug levels

Enter two timed drug concentrations plus dose and interval to derive one-compartment pharmacokinetic parameters — elimination rate, half-life, volume of distribution, clearance, extrapolated peak and trough, and AUC. For clinical pharmacokinetics. It runs free in your browser on Gera Tools, with nothing uploaded.

Last updated Source: Gera Tools

Which model does this calculator use?

It uses a one-compartment, first-order elimination model. This treats the body as a single well-mixed compartment from which drug is cleared at a rate proportional to its concentration — the standard model for vancomycin, aminoglycosides, and many therapeutic-drug-monitoring tasks.

When two drug levels are drawn during the elimination phase, a one-compartment model can recover the key pharmacokinetic parameters needed to individualise dosing. This calculator performs that derivation for both IV bolus and short-infusion regimens.

When to use this calculator

The one-compartment approach is the workhorse for therapeutic drug monitoring (TDM) of drugs that mix rapidly in the body, most notably vancomycin and aminoglycosides. You might reach for this when:

  • A pharmacist or clinical pharmacokineticist is adjusting a vancomycin dose using a peak-and-trough pair drawn at steady state.
  • A student wants to derive PK parameters from data in a clinical textbook case.
  • You are computing expected levels at alternative dosing intervals before the next dose.

The method assumes the drug obeys first-order elimination (a constant fraction removed per unit time) and that the body behaves as one well-mixed compartment — assumptions that hold reasonably well for many antibiotics in stable patients.

How it works

The elimination rate constant comes directly from the two levels, and every other parameter follows from it:

kₑ   = ln(C1 / C2) / (t2 − t1)
t½   = 0.693 / kₑ
Cmax = C1 × e^(kₑ × (t1 − t_inf))      (extrapolated to end of infusion)
Cmin = Cmax × e^(−kₑ × (τ − t_inf))    (extrapolated trough)
Vd   = Sawchuk-Zaske (infusion) or Dose / C0 (bolus)
CL   = kₑ × Vd
AUC  = Dose / CL                       (over the interval at steady state)

The Sawchuk-Zaske form for Vd accounts for the fact that elimination continues during the infusion itself, which a simple bolus formula would ignore.

Worked example

Consider a vancomycin infusion scenario (illustrative figures):

  • Dose: 1,500 mg infused over 1 hour, every 12 hours
  • Peak drawn 1 hour after infusion end: 30 mg/L (at time t1 = 2 h post-start)
  • Trough drawn 1 hour before next dose: 8 mg/L (at time t2 = 11 h post-start)

From these two levels:

  • kₑ = ln(30/8) / (11 − 2) = 1.322 / 9 ≈ 0.147 /h
  • t½ = 0.693 / 0.147 ≈ 4.7 hours
  • The extrapolated true peak and volume follow from the Sawchuk-Zaske equations.

These are clearly illustrative — real dosing decisions require verified assay timing and clinical judgement.

Common pitfalls

  • Distribution phase sampling: drawing the “peak” too early (within 1–2 h of a bolus) captures the distribution phase, not elimination. The kₑ will be overestimated.
  • Non-steady-state levels: if the patient has not reached steady state (typically 4–5 half-lives), the predicted Cmax and Cmin will not match the next dose’s observed levels.
  • Changing renal function: kₑ is only valid at the time of sampling; acute kidney injury between doses invalidates the extrapolation.