My Easy Science
PK Quick Calculator
Two blood levels in, half-life out. Then clearance, volume, and the dose to reach a target level.
Inputs
Worked example
Half-life and k
Clearance, Vd and k
Enter any two and the third is worked out. CL = k × Vd.
Two points (IV bolus)
Clearance and volume
Loading and maintenance dose
Concentration against time
Model: one-compartment, first-order elimination.
| Time (h) | Concentration (mg/L) |
|---|
Half-life
— h
Half-life: how long it takes for the level to fall by half.
Checked against three hand-worked examples (see the page source comments).
Results are shown to 2 decimal places.
Enter the two levels, then tap Show half-life and clearance.
| Value | Result | Unit |
|---|---|---|
| Elimination constant (k) | — | /h |
| Half-life (t½) | — | h |
| Clearance (CL) | — | L/h |
| Volume of distribution (Vd) | — | L |
| Starting level (C₀) | — | mg/L |
| AUC₀₃₁ₕ | — | mg·h/L |
| Loading dose | — | mg |
| Maintenance rate | — | mg/h |
| Maintenance dose (per interval) | — | mg |
| Time to 90% eliminated | — | h |
| Time to 95% eliminated | — | h |
For learning only. Not for patient care decisions. Always check with a qualified professional and the product label.
How it works
After a single dose, most drugs fall in a straight line on a log scale: each half-life cuts the level in half. Two blood levels are enough to find that speed. Take 20 mg/L at 2 hours and 10 mg/L at 8 hours. The level halved in 6 hours, so the half-life is 6 hours, and k, the elimination constant, is 0.693 / 6 = 0.1155 per hour. Working back to time zero gives C₀ = 20 × e^(0.1155 × 2) = 25.2 mg/L, so a 1000 mg dose spread into a volume of 1000 / 25.2 = 39.7 L, and the area under the curve to infinity is 25.2 / 0.1155 = about 218 mg·h/L.
Clearance is k times the volume: 0.1155 × 40 = 4.62 L/h, the volume of blood fully cleared of drug each hour. The same numbers answer the dosing questions. To reach a target level of 10 mg/L at once, the loading dose is target × volume: 10 × 40 = 400 mg. To keep it there, the drip rate is target × clearance: 10 × 4.62 = 46.2 mg per hour, which is 554 mg every 12 hours. If the salt or the bioavailability is less than 1, divide by both: only the active, absorbed part counts.
Time to clear most of a dose follows the same k. Ninety percent is gone after 3.32 half-lives and 95 percent after 4.32, so a 6-hour half-life means about 20 hours to 90 percent gone. The graph draws the fall from your first level so you can see the half-life in the shape of the curve; switch to the semi-log view and the fall becomes a straight line.