What this calculator works out
This calculator applies first-order elimination: the amount remaining after a given time, when a fixed proportion is removed in each half-life.
Most substances follow first-order kinetics at therapeutic concentrations, which is why half-life is the standard way of describing how long something persists. Alcohol is the well-known exception. This is a teaching and planning aid, not a casework tool.
Exponential elimination
Before you rely on the result
- Half-life is substance-specific and comes from published pharmacokinetic data. It also varies between individuals with age, liver and kidney function and other medication.
- The starting figure can be an amount or a concentration — the model is proportional, so the units cancel.
- First-order kinetics assume elimination is not saturated. At very high concentrations some substances shift to zero-order.
- Detection in a sample is not the same as an active effect. Metabolites frequently persist far longer than the parent substance.
Each half-life removes half of what remains, so after five half-lives about 3% is left and after seven about 1%. Five is the conventional point at which a substance is considered substantially eliminated, and the same arithmetic in reverse is why a repeated dose reaches steady state after roughly five half-lives.
How this calculator works
Exponential decay expressed in half-lives:
Remaining = starting value × 0.5(elapsed time ÷ half-life)
Percentage remaining = remaining ÷ starting value × 100Expressing the exponent as elapsed time divided by half-life means the calculation works for any consistent time unit. Three half-lives leave 12.5% whether each is six hours or six days.
Worked example: three half-lives
Using the default figures — a starting value of 100, a six hour half-life, after 18 hours:
- Half-lives elapsed: 18 ÷ 6 = 3
- Remaining: 100 × 0.5³ = 12.5
- That is 12.50% of the starting value
Extend to 30 hours, five half-lives, and 3.13% remains. Extend to 42 hours, seven half-lives, and 0.78% remains. The proportion falls quickly at first and then very slowly — which is why "how long does it stay in the system" has no single answer, and depends entirely on what concentration the question means.
Common mistakes
- Using a half-life from a different substance or population. It is highly specific.
- Assuming first-order kinetics at very high concentrations. Some substances saturate.
- Confusing the parent substance with its metabolites. Metabolites often persist much longer.
- Treating detection thresholds as fixed. They vary by method and matrix.
- Reading elimination as loss of effect. The two are related but not the same.
Frequently asked questions
What is the difference between first-order and zero-order elimination?
First-order removes a constant proportion per unit time, producing an exponential decline described by a half-life. Zero-order removes a constant amount per unit time regardless of concentration, producing a straight-line decline. Alcohol is the standard example of zero-order at typical concentrations, because the enzyme pathway is saturated.
Why do detection windows differ from half-lives?
Because detection depends on the assay's sensitivity and the sample type as well as the concentration. Urine typically detects substances for longer than blood; hair can retain evidence of use for months. Metabolites with longer half-lives than the parent substance extend the window further again.
Does half-life change between people?
Substantially, for many substances. Age, liver and kidney function, genetics affecting metabolising enzymes, other medication and pregnancy all shift it. Published figures are population means with ranges, and applying a mean to an individual carries the usual caveats.
What is steady state?
The point at which a repeated dose is being eliminated as fast as it is administered, so the concentration stops rising. It is reached after roughly five half-lives of regular dosing — the same arithmetic as elimination, run the other way. It is why some medicines take days to reach full effect.
Is what I enter stored?
No. Everything you enter is processed in your browser and is never transmitted or retained. Even so, treat any public website as an unsecured environment and do not enter identifiable case information.
Related tools
References
- National Institute for Health and Care Excellence — clinical guidance and the British National Formulary on drug pharmacokinetics
- GOV.UK — Forensic Science Regulator codes of practice for toxicology
Sources are checked at publication and can change — how I choose and check references.