My Easy Science
Multiple Dose Simulator
Give the same dose again and again and watch the level climb to steady state. Drag the interval and see the peak and trough move.
Drag the slider. A shorter interval means more build-up.
Model: one-compartment, first-order elimination.
Set the dose and interval, then tap Show steady-state levels.
Accumulation factor (R)
— ×
Accumulation factor: how many times higher the steady-state peak is than the first-dose peak.
For learning only. Not for patient care decisions. Always check with a qualified professional and the product label.
Results
| Value | Result | Unit |
|---|---|---|
| Elimination constant (k) | — | /h |
| Half-life (t½) | — | h |
| Peak at steady state (Cmax,ss) | — | mg/L |
| Trough at steady state (Cmin,ss) | — | mg/L |
| Accumulation factor (R) | — | × |
| Average level at steady state (Css,av) | — | mg/L |
| Fluctuation ((Cmax − Cmin) / Css,av) | — | × |
| Time to 90% of steady state | — | h |
| Time to 95% of steady state | — | h |
| AUC per interval at steady state | — | mg·h/L |
| Time in therapeutic window (steady state) | — | % |
Curve data
| Time (h) | Concentration (mg/L) |
|---|
How it works
One dose peaks and then falls. Give the next dose before the first has fully gone, and the second peak lands higher than the first, because some drug is still there. Each dose adds a little less than the one before, and after about four to five half-lives the peaks stop climbing: what goes in each interval equals what leaves, and that is steady state. Take 500 mg every 8 hours, with a half-life of 8 hours and a volume of 50 L. The first dose peaks at 10 mg/L; half is still there when the next dose arrives, so the peaks double at steady state: 20 mg/L at the peak and 10 mg/L at the trough.
The maths is one number: e^(−k×interval). Here k is 0.0866 per hour, so e^(−0.0866×8) = 0.5, and the accumulation factor is 1 / (1 − 0.5) = 2.0. Clearance is k × Vd = 4.33 L/h, so the average level at steady state is 500 / (4.33 × 8) = 14.4 mg/L. Ninety percent of steady state takes 3.32 half-lives, 26.6 hours, and 95 percent takes 4.32 half-lives, 34.6 hours. Shorten the interval and the peaks and troughs squeeze together; stretch it past ten half-lives and each dose is effectively alone, with no build-up at all.
By mouth the same build-up happens, but each dose first has to be absorbed, so the peak comes later and lower. A loading dose sized to the steady-state peak gets you there with the first dose instead of the fourth or fifth. The green band is the therapeutic window: time spent inside it at steady state is the number that matters most in practice.
Checked against a hand-worked example (see the page source comments).
Results are shown to 2 decimal places.
Check the numbers
Worked example: dose 500 mg, Vd 50 L, t½ 8 h, interval 8 h, IV bolus. k = 0.693 / 8 = 0.0866 /h; e^(−k×τ) = e^(−0.693) = 0.5; R = 1 / (1 − 0.5) = 2.0; Cmax,ss = (500 / 50) × 2 = 20 mg/L; Cmin,ss = 20 × 0.5 = 10 mg/L; CL = 0.0866 × 50 = 4.33 L/h; Css,av = 500 / (4.33 × 8) = 14.4 mg/L; time to 90% of steady state = 3.32 × 8 = 26.6 h; to 95% = 4.32 × 8 = 34.6 h. Tap Worked example to load these numbers and check the results table matches.