One-Compartment IV Bolus Model Calculator
Model plasma drug concentration after an IV bolus dose using the classic one-compartment first-order elimination equation.
💉 What is the One-Compartment IV Bolus Model?
The one-compartment IV bolus model is the foundational pharmacokinetic equation describing how plasma drug concentration declines after an instantaneous intravenous dose. It treats the entire body as a single, uniformly-mixed compartment, with concentration following the exponential decay function C(t) = C0 x e^(-ke t), where C0 = Dose / Vd is the theoretical concentration immediately after the dose.
Pharmacology students use this model as the starting point for understanding every more advanced pharmacokinetic concept, since half-life, clearance, and volume of distribution are all embedded directly in its two parameters (C0 and ke). Clinical pharmacists use it to predict plasma levels at any point after an IV dose, useful for timing follow-up blood draws or estimating when a level will fall to a safe range. Researchers use the model's semi-log linearity as a diagnostic tool, if measured concentration-time data plots as a straight line on a log-concentration axis, the drug follows one-compartment, first-order kinetics.
A common misconception is that this model applies to any route of drug administration. It specifically describes an instantaneous IV bolus, oral doses need an added absorption term (handled by the One-Compartment Oral Dose Model), and continuous infusions need a different equation entirely (handled by the One-Compartment IV Infusion Model), both available elsewhere in this collection.
This calculator computes C0 and the concentration at any time you specify, reports the implied half-life, and plots the full decay curve so you can see the shape of the entire concentration-time relationship at a glance.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Moderate Elimination
Dose = 500 mg, Vd = 50 L, ke = 0.15/hr, t = 6 hr
Example 2 — Faster Elimination
Dose = 1000 mg, Vd = 40 L, ke = 0.2/hr, t = 5 hr
Example 3 — Slow Elimination, Longer Evaluation
Dose = 300 mg, Vd = 30 L, ke = 0.1/hr, t = 10 hr
❓ Frequently Asked Questions
🔗 Related Calculators
What is the one-compartment IV bolus model?
It is the simplest pharmacokinetic model, treating the entire body as a single well-mixed compartment that a drug distributes into instantly after an IV bolus dose, then leaves via first-order elimination. Concentration follows C(t) = C0 x e^(-ke t), where C0 = Dose / Vd.
How do you calculate C0 after an IV bolus?
C0, the concentration immediately after the dose, equals Dose divided by the volume of distribution: C0 = Dose / Vd. This represents the theoretical concentration if the entire dose instantly and completely mixed throughout the volume it distributes into.
How do you find concentration at any time after an IV bolus?
Use C(t) = C0 x e^(-ke x t), where C0 is the initial concentration, ke is the elimination rate constant, and t is the elapsed time. This exponential decay formula is the defining equation of first-order, one-compartment pharmacokinetics.
When is the one-compartment model a good approximation?
It works well for drugs that distribute into tissue quickly relative to how fast they're eliminated, so that a clear, separate initial distribution phase isn't visible on the concentration-time curve. Drugs with a slow, distinct distribution phase are better described by a two-compartment model.
What does the elimination rate constant represent in this model?
ke is the fractional rate at which concentration declines per unit time once elimination is the dominant process. It is related to half-life by t1/2 = ln(2)/ke, and can be derived from clearance and volume of distribution via ke = CL/Vd.
How is this different from the elimination rate constant and half-life calculators on this site?
Those calculators find ke and half-life from raw data or convert between them. This calculator uses an already-known ke (plus dose and Vd) to build the full concentration-time function and evaluate it at any specific time you choose, showing the entire decay curve.
Can this model be used for infusions or oral doses?
No, this specific formula assumes an instantaneous IV bolus. Continuous IV infusions follow a different equation with a rising then falling phase, and oral doses require an absorption term, both handled by the dedicated One-Compartment IV Infusion and One-Compartment Oral Dose Model Calculators on this site.
Why does the concentration curve look like a straight line on some pharmacokinetic charts?
When plotted with concentration on a logarithmic axis and time on a linear axis, C(t) = C0 x e^(-ke t) becomes a straight line, since taking the natural log of both sides gives ln(C) = ln(C0) - ke*t, a linear equation. This semi-log plot is the standard way pharmacokineticists visually confirm first-order elimination.
What happens to concentration as time approaches infinity?
Concentration approaches zero but mathematically never reaches exactly zero in this idealized exponential model, in practice, a drug is considered clinically eliminated after about 4 to 5 half-lives, when concentration falls to roughly 3% to 6% of C0.
What units should I use for the inputs?
Enter dose in milligrams and volume of distribution in liters to get concentration directly in mg/L. Enter the elimination rate constant in per hour and time in hours, since the exponential term requires ke and t to use matching time units.