Pharmacokinetics simulator: one- and two-compartment concentration-time curves, repeated administration and steady-state accumulation

See what a regimen does to an invented drug: one- or two-compartment model, IV bolus, IV infusion or oral absorption, repeated at an interval. Draws the concentration-time curve and gives Cmax and Cmin at steady state, the average level, the accumulation ratio and the half-lives. A teaching tool: it never works out an amount to give.

Keep it one tap away for everyday use.

Drug
Regimen
Curve
Steady st.

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For study and teaching, not medical advice. Check with a qualified professional.

Invented drug

Start from a made-up drug

Model Clearance CL (L/h) Volume V (L)

Regimen to try

Route Amount each time (mg) Interval τ (h) Number of administrations Absorption rate ka (1/h) Fraction absorbed F (0 to 1)

CL is the volume of plasma cleared of drug per hour; V links the amount in the body to the concentration. With two compartments, drug also moves into and out of a peripheral compartment (tissues) at the rate Q. ka sets how fast an oral dose is absorbed and F how much of it reaches the blood. This page only shows what the regimen you type does to an invented drug; it never works out an amount to give.

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What it does

This page is a teaching simulator. You describe an invented drug with a few pharmacokinetic numbers, type a regimen (how much, how often, by which route, how many times), and it draws the concentration in plasma over time. It shows how levels build up with each administration until they settle into a repeating pattern, the steady state, and gives the peak and trough there, the average level and the accumulation ratio.

It is for study and teaching, not medical advice. It only goes one way, from a regimen you enter to the curve it produces for a made-up drug. It has no feature that works out an amount to give, and it must not be used for real patients.

How to use it

Start from one of three made-up drugs, or type your own numbers.
Choose the model. In a one-compartment model the body is one well-mixed space: the level falls with a single half-life, ln 2 × V / CL. In a two-compartment model the drug also spreads into tissues (the peripheral compartment, volume V2) at the rate Q, so the curve falls fast at first (α phase, distribution) and then more slowly (β phase, elimination).
Set clearance CL (litres of plasma cleared per hour) and volume V (or the central volume V1).
Choose the route. An IV bolus puts the whole amount in at once. An IV infusion runs at a steady rate for the duration you set (at most the interval). By mouth uses first-order absorption with rate constant ka, and F is the fraction that reaches the blood.
Set the amount each time, the interval τ and the number of administrations. The curve, the numbers and the dashed steady-state lines update as you type. Switch to a log axis to see the phases as straight lines.

What the numbers mean

Cmax and Cmin at steady state: the highest and lowest level in one interval once the regimen has run long enough. They come from the exact steady-state formula, not from the last interval drawn.
Average at steady state = AUCτ / τ, where AUCτ = F × amount / CL.
Accumulation ratio = AUC over an interval at steady state ÷ AUC over the first interval. For an IV bolus in one compartment it equals 1 / (1 − e^(−kτ)). The peak ratio compares the peaks instead.
Fluctuation = (Cmax − Cmin) ÷ average, as a percentage.
90 % of steady state is reached after ln 10 / λ (about 3.3 half-lives of the slowest phase), whatever the interval.

Worked example

Drug A (made up) has CL 5 L/h, V 50 L, ka 1 /h and F 0.8; the regimen is 250 mg by mouth every 12 h, 10 times. Its half-life is 6.93 h. The first administration peaks at 3.097 mg/L after 2.56 h. At steady state the page shows Cmax 4.612 mg/L (2.16 h after each administration) and Cmin 1.916 mg/L, an average of 3.333 mg/L (AUCτ 40 mg·h/L), an accumulation ratio of 1.503, a peak ratio of 1.489 and a fluctuation of 80.9 %. Ninety per cent of steady state is reached after 23 h, about 1.9 intervals.

Tips

Halve the interval and the amount together: the average stays the same, but the fluctuation shrinks.
Lengthen the half-life (raise V or lower CL) and watch accumulation and the time to steady state grow.
In Drug B, switch the axis to log to see the two straight phases of a two-compartment drug.

FAQ

Can it tell me what dose to give? No. It is deliberately one-way: it shows what an entered regimen does to an invented drug, for learning how the curves behave.

Why is steady state not the last interval drawn? With few administrations the curve may still be climbing; the steady-state values are what the pattern settles to.

Is anything sent anywhere? No. Everything is calculated in this page.

Where the numbers come from

Models and closed forms: M. Gibaldi and D. Perrier, Pharmacokinetics (2nd ed., Marcel Dekker 1982): one- and two-compartment models, the Bateman function for first-order absorption, superposition and steady state by geometric series; M. Rowland and T. N. Tozer, Clinical Pharmacokinetics and Pharmacodynamics (Lippincott Williams and Wilkins): accumulation ratio and time to steady state. Formulas only; no tables copied.
Calculations written by fibub. Checked in the tests against SciPy solve_ivp (LSODA) on 24 random regimens (agreement to 3 × 10⁻¹¹), against 30-half-life ODE runs for steady state (10⁻⁹), and against the closed forms for one-compartment oral, bolus and infusion and two-compartment bolus steady state.
The three drugs are invented; their numbers are made up for teaching.

Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.

Last updated 2026-11-09.