Calculator explanation
This single-dose tracker estimates how a medication’s remaining amount declines over time using the concept of half-life. You enter a medication name (for labeling), an initial dose in milligrams, a half-life in hours, and a therapeutic window (minimum and maximum). The calculator then generates a timeline and highlights when the estimated amount is Above maximum, Therapeutic, or Below minimum.
The results section also reports two practical milestones: the first time the estimated amount enters your therapeutic range, and the first time it drops below your minimum threshold. Finally, you can download a CSV file so you can keep a record, compare scenarios, or graph the curve in a spreadsheet.
Important: This tool is for education and planning only. It does not provide medical advice and it does not replace guidance from a clinician or pharmacist. Real drug levels depend on absorption, distribution, metabolism, elimination, formulation (immediate vs extended release), interactions, organ function, and individual variability.
What this tool is (and is not)
This page models a single dose that begins at time 0 and then decays exponentially. It is useful for understanding how half-life affects timing: how quickly a drug declines, how long it stays within a target window, and how sensitive the curve is to changes in half-life or thresholds.
It is not a full pharmacokinetic simulator. It does not model multiple doses, accumulation to steady state, delayed absorption, changing clearance, active metabolites, or concentration units like mg/L. The output is best interpreted as “mg remaining relative to the initial dose,” which is a simplified proxy for concentration.
How the math works
The calculator uses exponential decay based on half-life. If D is the initial dose (mg), t is time (hours), and H is half-life (hours), the estimated remaining amount is:
Remaining(t) = D × 0.5^(t / H)
The timeline is computed every 0.5 hours from 0 up to your “Track for (hours)” value. For readability, the on-page table shows whole hours (0, 1, 2, …), while the CSV export includes every 0.5-hour step.
Inputs and assumptions (plain language)
- Medication Name is used only for labeling the results and the CSV export.
- Initial Dose (mg) is treated as the starting amount at time 0. The model assumes immediate availability.
- Half-Life (hours) is assumed constant over the tracking period. In reality, half-life can vary by person and context.
- Therapeutic Minimum/Maximum (mg) define the target window for the remaining amount. The calculator flags values above the maximum as “Above maximum (toxic)” to emphasize risk, but the label is generic and not drug-specific.
- Track for (hours) controls how far into the future the timeline is generated (up to 240 hours).
How to interpret the results
The timeline table is a quick visual summary. Each row corresponds to a time point and includes a status label:
- Above maximum (toxic): the estimated remaining amount is at or above your maximum threshold.
- Therapeutic: the estimated remaining amount is between your minimum and maximum thresholds (inclusive).
- Below minimum: the estimated remaining amount is below your minimum threshold.
The two milestone fields are computed as follows. Time to Therapeutic Level is the first time point where the estimated amount is within your window. Time Below Minimum Threshold is the first time point after time 0 where the estimated amount drops below your minimum.
If the calculator reports “Never reaches therapeutic range,” it means that, given your thresholds, the curve never falls into the window during the tracked period. This can happen if the initial dose starts below the minimum, if the minimum is set too high, or if the maximum is set too low. If it reports “Never falls below minimum during tracked period,” it means the curve stays at or above your minimum for the entire tracked window.
Worked examples and scenario ideas
Examples help you sanity-check your inputs and understand what the curve is doing. The numbers below are illustrative and are not dosing recommendations.
Example 1: basic half-life milestones
Suppose you take a 100 mg dose of a medication with a 6-hour half-life. Using the formula:
- At 6 hours: 100 × 0.5^(6/6) = 100 × 0.5 = 50 mg
- At 12 hours: 100 × 0.5^(12/6) = 100 × 0.25 = 25 mg
- At 18 hours: 100 × 0.5^(18/6) = 100 × 0.125 = 12.5 mg
- At 24 hours: 100 × 0.5^(24/6) = 100 × 0.0625 = 6.25 mg
Notice the pattern: every additional half-life multiplies the remaining amount by 0.5. This is why half-life is such a useful “rule of thumb” for timing.
Example 2: therapeutic window timing
Using the same 100 mg dose and 6-hour half-life, imagine your therapeutic window is 20–60 mg. The curve starts at 100 mg (above maximum), then enters the window when it drops to 60 mg, and later leaves the window when it drops below 20 mg.
The calculator’s milestone “Time to Therapeutic Level” is the first time point where the amount is between 20 and 60 mg. Because the timeline is sampled every 0.5 hours, the reported time is an estimate at that resolution.
Example 3: sensitivity to half-life
Half-life strongly affects how long a medication stays above a threshold. If you keep the dose and thresholds the same but change the half-life from 6 hours to 3 hours, the curve declines twice as fast. If you change it from 6 hours to 12 hours, the curve declines half as fast. This is a helpful way to explore “best case vs worst case” scenarios when you only have an approximate half-life.
Scenario checklist (to avoid common input mistakes)
- Confirm units: half-life must be in hours. If you have minutes, divide by 60. If you have days, multiply by 24.
- Check the window: the minimum must be less than the maximum. If you reverse them, the calculator will stop and prompt you.
- Start with realistic thresholds: if your maximum is below your initial dose, the curve will begin “Above maximum.” That may be expected, but it’s worth confirming.
- Track long enough: if you only track 8 hours for a drug with a 40-hour half-life, you may not see it fall below the minimum.
- Remember this is single-dose: if you take repeated doses, real levels can accumulate and the curve will not match this single-dose decay.
Why the table shows whole hours but the CSV is more detailed
The on-page table is designed to be readable at a glance, so it shows whole hours only. Internally, the calculator computes values every 0.5 hours to provide smoother milestone detection and a more detailed export. If you need finer detail for charting, use the CSV download and plot the curve in a spreadsheet.
Limitations (important)
This model assumes immediate distribution and a constant half-life. Many medications have a separate absorption phase, and some have multi-compartment behavior where the “effective half-life” changes over time. Additionally, “therapeutic range” is typically defined in concentration units (like ng/mL) rather than mg remaining. Use this tool to understand decay behavior and relative timing, not to make clinical decisions.
FAQ
Does the calculator show blood concentration?
Not directly. The calculator outputs an estimated remaining amount (mg) based on half-life decay. In real pharmacokinetics, concentration depends on volume of distribution and other factors. If you need concentration, you typically need additional parameters and lab-based reference ranges.
Why does it say “Peak concentration at 0 hours”?
The current model assumes the dose is fully available at time 0, so the maximum value occurs immediately. Many real medications peak later due to absorption time; that behavior is outside the scope of this simplified tracker.
How should I choose a half-life value?
Use a reputable reference (prescribing information, clinical pharmacology resources, or a pharmacist). If you see a range (for example, 4–6 hours), you can run two scenarios: one with the shorter half-life (faster decline) and one with the longer half-life (slower decline). Comparing the two helps you understand uncertainty.
Can I use this for multiple doses or repeated dosing schedules?
This page is designed for a single dose. Repeated dosing can lead to accumulation and a different curve shape. You can still use this tool for intuition (for example, “how much remains after X hours?”), but it will not represent steady-state behavior.
What does “Never reaches therapeutic range” mean?
It means that, within the tracked time window, the estimated amount never falls between your minimum and maximum thresholds. Common causes include a therapeutic window that does not overlap the curve (for example, minimum too high), or tracking for too short a period.
Privacy
The calculator runs in your browser. The values you enter are used to compute the timeline and generate the CSV locally. If you are entering sensitive information, consider using a generic medication label (for example, “Medication A”) and avoid including personal identifiers.
Reviewed by: Stephanie Ben-Joseph