Half-Life and Drug Levels
The amount of a drug in the body halves after a fixed time, called the half-life. See on a made-up drug’s graph how repeated doses pile up and where the level levels off.
Dose (hollow = left out, double ring = doubled) Dotted: steady-state peak and trough
Now: 48.0 h (12.0 half-lives passed)
Level: 26.7 ● inside the working range
The model repeats the same amount at the same spacing. This only shows how the shape of the graph changes in a model. It does not say what anyone should actually do.
The numbers
Steady state (it stops piling up and the swings settle)
r = 0.5^(8 / 4) = 0.250
peak = 20 / (1 - r) = 26.7 ● inside the working range
trough = 20 x r / (1 - r) = 6.7 ● inside the working range
Highest and lowest after 5 half-lives (the case selected)
highest 26.7 ● inside the working range
lowest 6.6 ● inside the working range
How close the peaks get to the steady state
1 t½: 50.0% / 2 t½: 75.0% / 3 t½: 87.5% / 4 t½: 93.8% / 5 t½: 96.9%
It depends on the half-life alone, not on the size of one dose. “4 to 5 half-lives” is a rounded rule of thumb.
What to do about a missed dose or a different dose depends on the medicine. Ask the doctor or pharmacist who prescribed it. This graph is not advice on what to do.
Levels are made-up “scale units”: one dose adds 20, and the working range is 5 up to 30. These are not numbers of any real drug.
Model: everything enters the body at once, then falls by a fixed share per unit time, the simplest case. In reality absorption takes time, and some drugs clear differently at higher amounts.
How to play
Press Auto and the graph grows as time passes. Move the half-life and spacing sliders to see how peaks, dips and the time to level off change. The buttons compare, in the model, a case where one dose is left out and one where it is doubled. Every name and number is made up, and none of it is advice on how to take a medicine.
Learn more
After a drug enters the body it spreads to different parts, is changed into other substances mainly in the liver, and leaves mainly through the kidneys into urine. These are typical examples of how a drug level falls. The time for the level to halve is the elimination half-life; when it falls by a fixed share, 50% is gone after one half-life, 75% after two, 87.5% after three, 93.75% after four and about 97% after five. With repeated doses at a fixed spacing, the level is taught to approach a steady state in about 4 to 5 half-lives. The time to get there depends on the half-life alone, while the height of the plateau depends on the dose, the spacing and how readily the body clears the drug. Levels have a lower line where an effect begins and an upper line where unwanted effects begin, and the range between them is the therapeutic window. Those lines differ from person to person. Some drugs clear differently at larger amounts, so not every drug follows this simple model.