Plasma Concentration-Time Calculator
After an intravenous bolus dose, plasma drug concentration declines exponentially over time in the one-compartment model. The equation is: C(t) = C0 x e^(-ke x t), where C0 is the initial plasma concentration (mg/L), ke is the first-order elimination rate constant (hr-1), and t is the time elapsed (hr). This fundamental pharmacokinetic model is used to predict when concentrations will fall below a minimum effective concentration (MEC) and to design dosing intervals. Enter C0, ke, and the elapsed time to calculate the predicted concentration at that time point.
Plasma concentration-time formula
C(t) = C0 x e^(-ke x t)
C0 = initial concentration (mg/L); ke = elimination rate constant (hr-1); t = time elapsed (hr). The fraction remaining at time t = e^(-ke x t). Half-life t1/2 = 0.693 / ke. At time t1/2, exactly 50% of C0 remains.
Using the concentration-time profile
- The area under the C-t curve (AUC) = C0 / ke, and represents total drug exposure.
- Dosing interval is chosen so that the trough concentration remains above the minimum effective concentration (MEC) for the desired duration.
- For concentration-dependent antibiotics (e.g., aminoglycosides), peak concentration above MIC is the key PK/PD target.
- For time-dependent antibiotics (e.g., beta-lactams), the percentage of time above MIC (T greater than MIC) drives efficacy.
- Multiple-dose accumulation shifts the entire C-t curve upward; at steady state the trough equals C0 x e^(-ke x tau) / (1 - e^(-ke x tau)).
Plasma concentration-time: frequently asked questions
What is the one-compartment plasma concentration-time model?
The one-compartment model assumes the body behaves as a single well-mixed compartment. After an IV bolus, drug concentrations decline exponentially: C(t) = C0 x e^(-ke x t), where C0 is the initial concentration, ke is the elimination rate constant, and t is time. This model describes the elimination phase after the distribution phase is complete.
What is the initial concentration C0?
C0 is the theoretical plasma concentration immediately after an IV bolus dose (at time zero before any elimination). It is calculated as C0 = Dose / Vd. In practice, the earliest measurable concentration after a short infusion approximates C0 after correcting for any rapid distribution.
What is the elimination rate constant ke?
The elimination rate constant ke (units: hr-1) is the fraction of drug eliminated per hour. It is related to half-life by ke = 0.693 / t1/2. A larger ke means faster elimination and a shorter half-life.
When does the one-compartment model apply?
The one-compartment model applies when drug distribution equilibrates rapidly relative to elimination, so the decline in plasma concentration is dominated by a single exponential. Many drugs follow this pattern in the elimination phase. For drugs with prolonged distribution (alpha phase), a two-compartment model may be more accurate.
Can this calculator predict clinical drug levels for patient management?
This tool is for educational and illustrative purposes only. Clinical drug level prediction requires patient-specific pharmacokinetic data, validated Bayesian software, and professional interpretation. Never use this calculator to make clinical dosing decisions.
Official sources
- U.S. Food and Drug Administration: FDA Pharmacokinetics Guidance.
- NIH National Library of Medicine: Pharmacokinetics (StatPearls).
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.