One-Compartment Oral Dose Model Calculator
Model plasma drug concentration after an oral dose, including peak concentration, time to peak, and the full absorption-elimination curve.
💊 What is the One-Compartment Oral Dose Model?
The one-compartment oral dose model describes how plasma drug concentration rises and then falls after a drug is swallowed, capturing both the absorption process (drug moving from the gut into the bloodstream) and elimination (drug being removed from the body) in a single equation: C(t) = (F Dose ka) / (Vd(ka - ke)) x (e^(-ke t) - e^(-ka t)).
Pharmaceutical formulators use this model to predict how quickly and how high a new oral formulation's concentration will peak, directly informing dosing frequency and formulation design (immediate-release versus extended-release). Clinical pharmacists use Cmax and Tmax, the model's two headline outputs, to time blood draws for therapeutic drug monitoring or to predict when a patient will feel a drug's peak effect. Pharmacokinetics students use this model as the natural next step after the IV bolus model, since it introduces competing absorption and elimination processes and the resulting characteristic rise-then-fall curve.
A common misconception is that the peak concentration occurs exactly when absorption finishes. It does not, Cmax occurs at the specific time (Tmax) when the instantaneous rate of absorption exactly equals the instantaneous rate of elimination, which is generally before absorption is fully complete.
This calculator computes concentration at any time you choose, automatically finds Cmax and Tmax, and plots the full absorption-then-elimination curve so you can see exactly how the peak relates to the entire concentration-time profile.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Fast Absorption, Full Bioavailability
Dose = 500 mg, F = 1, Vd = 50 L, ka = 1.5/hr, ke = 0.2/hr, t = 2 hr
Example 2 — Reduced Bioavailability
Dose = 300 mg, F = 0.8, Vd = 30 L, ka = 1.0/hr, ke = 0.15/hr, t = 3 hr
Example 3 — Slower Absorption, Larger Volume
Dose = 1000 mg, F = 0.6, Vd = 80 L, ka = 0.8/hr, ke = 0.1/hr, t = 5 hr
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for oral drug concentration over time?
C(t) = (F x Dose x ka) / (Vd x (ka - ke)) x (e^(-ke t) - e^(-ka t)), where F is bioavailability, ka is the absorption rate constant, ke is the elimination rate constant, and Vd is volume of distribution. This is the standard one-compartment oral absorption model.
How do you calculate Tmax, the time of peak concentration?
Tmax = ln(ka / ke) / (ka - ke). This is the time at which the rate of drug entering the blood (absorption) exactly equals the rate leaving (elimination), the mathematical peak of the concentration curve, found by setting the derivative of C(t) to zero.
How do you calculate Cmax, the peak concentration?
Substitute Tmax back into the concentration equation: Cmax = C(Tmax). There is no simpler closed-form shortcut, Tmax must be found first, then plugged into the main C(t) formula.
Why does oral concentration rise and then fall, unlike an IV bolus?
After an oral dose, drug must first be absorbed from the gut into the bloodstream (governed by ka) before elimination (governed by ke) can remove it. Early on, absorption dominates and concentration rises; once most of the dose is absorbed, elimination dominates and concentration falls.
What happens if the absorption rate constant equals the elimination rate constant?
The standard formula has a ka minus ke term in the denominator, so if they were exactly equal it would divide by zero. In that special (rare) case, a different limiting form of the equation applies (involving t x e^(-ke t) instead), which this calculator flags as an error rather than silently returning an incorrect result.
How does bioavailability (F) affect this model?
F directly scales the entire concentration curve, a drug with F = 0.5 (50% bioavailability) produces exactly half the concentration at every time point compared to the same dose with F = 1.0 (100% bioavailability), since only a fraction of the dose reaches systemic circulation.
What is the difference between this model and the IV bolus model?
The IV bolus model assumes the entire dose is instantly available (C0 = Dose/Vd right away), producing pure exponential decline from the start. This oral model adds a competing absorption process, so concentration must rise before it falls, producing the characteristic peaked curve seen after swallowing a pill.
Can this model be used for any oral dosage form?
It works best for immediate-release oral formulations that follow simple first-order absorption. Extended-release, delayed-release, and formulations with complex or multiple absorption phases need more advanced models beyond this single-ka approximation.
What units should I use for the rate constants?
Enter both ka (absorption) and ke (elimination) in per hour, dose in milligrams, and volume of distribution in liters, this combination yields concentration directly in mg/L and time results (Tmax) in hours.
How is this related to the AUC and bioavailability calculators on this site?
This model describes the instantaneous concentration at any moment, while AUC (computed by the AUC Calculator) is the total area under this entire curve. Bioavailability (F), found by the Bioavailability and Oral Dose Adjustment Calculator, is a direct input here that scales the whole curve up or down.