What this calculator does
First-order elimination means a fixed proportion clears per unit time, not a fixed amount. That produces the familiar halving pattern: half gone after one half-life, three quarters after two, and so on.
The five half-life convention follows directly. After five half-lives 3.13 per cent remains, so 96.9 per cent has been eliminated, which is where the rule of thumb that a drug is essentially cleared after five half-lives comes from.
The formula
Divide elapsed time by the half-life to get the number of half-lives, then raise 0.5 to that power. The result is the fraction remaining, and one minus it is the fraction eliminated.
| Term | Meaning |
|---|---|
| Half-life | The time for the amount present to fall by half. |
| First-order elimination | Clearance proportional to the amount present, which produces exponential decay. |
| Five half-lives | The convention for practical elimination, leaving about 3 per cent. |
The inputs explained
| Field | What to enter |
|---|---|
| Half-life (hours) | The half-life of the substance, in hours. |
| Elapsed time (hours) | Elapsed time since the dose, in the same units. |
When to use it
Understanding how long something lasts
The half-life alone does not answer it; the number of half-lives elapsed does.
Estimating when a steady state is reached
Repeated dosing reaches steady state after about the same five half-lives.
Learning pharmacokinetics
The exponential pattern is the foundation of how drug levels are reasoned about.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much clears with each half-life?
The same substance at four points after dosing.
| Elapsed time | Fraction remaining | Half-lives elapsed |
|---|---|---|
| 0 hours | 100.0% | 0.00 |
| 6 hours | 50.0% | 1.00 |
| 12 hours | 25.0% | 2.00 |
| 30 hours | 3.13% | 5.00 |
Questions
Why five half-lives rather than four or six?
It is a convention rather than a threshold. Four leaves 6.25 per cent and six leaves 1.6 per cent. Five was chosen as the point where the remaining amount is generally too small to matter clinically.
Does this apply to all drugs?
To most, but not all. A few follow zero-order kinetics, where a fixed amount clears per unit time regardless of concentration, and alcohol is the familiar example. Those do not halve and this calculation does not describe them.
Is this dosing guidance?
No. It is generic arithmetic on an exponential curve. Real clearance varies with kidney and liver function, age, other medicines and genetics, and dosing decisions belong with a prescriber or pharmacist.
How does this relate to steady state?
The same five half-lives applies in reverse. With regular dosing, levels accumulate toward a plateau and reach roughly 97 per cent of it after five half-lives, which is why loading doses exist for drugs with long ones.
For radioactive decay by the same mathematics, see the half-life calculator. For estimated kidney clearance, see the creatinine clearance calculator.