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.

How is the elimination rate calculated from two levels?

The elimination rate constant kₑ equals the natural log of the ratio of the two concentrations divided by the time between them: ln(C1/C2) / (t2 − t1). Half-life is then 0.693 divided by kₑ. Both levels must be on the falling elimination phase.

Why must the two levels be decreasing?

The kₑ formula assumes both samples lie on the elimination phase, where concentration falls exponentially. If the second level is higher than the first, drug is still being absorbed or infused, the assumption breaks, and the tool will not compute a result.

How is volume of distribution estimated?

For an infusion the tool uses the Sawchuk-Zaske relationship, which derives Vd from the infusion rate, the elimination rate, and the extrapolated peak and trough. For an IV bolus (infusion time zero) it uses dose divided by the concentration back-extrapolated to time zero.

Can I use these values to set a new dose?

The parameters are a starting point for dose individualisation, but this tool is for education and estimation. Always confirm with a validated clinical pharmacokinetics service and consider assay timing, renal function, and the drug's therapeutic range before changing a dose.

One-Compartment PK Parameter Calculator

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.

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.

Example and notes

Levels of 30 mg/L at 1 h and 8 mg/L at 6 h give kₑ ≈ 0.264/h and a half-life of about 2.6 hours. Both samples must sit on the falling elimination phase: a peak drawn too early during distribution or absorption will overestimate kₑ. Treat the output as an estimate to be confirmed by a validated dosing service, with attention to assay timing, renal function, and the drug’s target range.