What this generator produces
This generator tabulates first-order elimination at a chosen step interval across a total period, so the shape of the decline is visible rather than implied by a single figure.
The same argument applies as for the body cooling curve: a table shows the diminishing rate of change in a way that one calculated value cannot. This is a teaching and planning aid, not a casework tool.
Curve settings
Before you read the table
- The half-life must be appropriate to the substance and, ideally, to the individual.
- Step interval controls the resolution. A step equal to the half-life shows the halving clearly; a smaller step shows the curve.
- The generator caps the total period at 240 hours to keep the table usable.
- Modelled values below any assay's detection threshold are arithmetic rather than anything measurable.
Find any two rows where the value has halved, and the interval between them is the half-life — anywhere on the curve. That constancy is what defines first-order elimination, and it is the clearest way to see the difference from the straight-line decline of a zero-order process.
How this calculator works
The decay equation evaluated at each step:
For each time x from 0 to the total, in steps:
value = starting value × 0.5(x ÷ half-life)Because the proportion removed is constant, the absolute amount removed falls with each step. The first step removes the most and every subsequent step removes less, which is the opposite of a zero-order process.
Worked example: 30 hours in 3 hour steps
Using the default figures — a starting value of 100, a six hour half-life, 30 hours in 3 hour steps:
- Hour 0: 100.00 · Hour 6: 50.00 · Hour 12: 25.00
- Hour 18: 12.50 · Hour 24: 6.25 · Hour 30: 3.13
The first six hours remove 50 units. The last six remove 3.12. Same proportion, entirely different absolute amount — and the intermediate rows at 3, 9, 15 hours and so on show the curve between the halvings. Reading down the column is the fastest way to understand why elimination questions need a stated threshold to have an answer.
Common mistakes
- Reading the tail as meaningful. Values below detection thresholds are arithmetic only.
- Using a step much larger than the half-life. The curve disappears between rows.
- Applying it to a zero-order substance. Alcohol declines in a straight line.
- Assuming the modelled curve matches an individual. Half-lives vary between people.
- Forgetting metabolites. They follow their own curves and often persist longer.
Frequently asked questions
Why tabulate rather than give a single figure?
Because the shape carries information a point value does not. Seeing that the first interval removes fifty units and the last removes three makes the diminishing rate obvious immediately, and it explains why detection windows depend so heavily on the sensitivity of the assay.
What step size should I use?
Something noticeably smaller than the half-life — a third to a half of it shows the curve well. A step equal to the half-life produces a clean halving sequence, which is useful for demonstrating the principle but hides the shape between points.
How does this relate to detection windows?
A detection window ends when the concentration falls below the assay's threshold. Since the curve flattens, small differences in threshold produce large differences in window. This is why the same substance has different quoted detection times for blood, urine and hair, and why quoted windows vary between sources.
Can this be used for anything other than drugs?
Yes — first-order decay describes radioactive decay, some chemical reactions and any process removing a constant proportion per unit time. The arithmetic is identical; only the interpretation of the units changes.
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 pharmacokinetic guidance
- GOV.UK — Forensic Science Regulator codes of practice for toxicology
Sources are checked at publication and can change — how I choose and check references.