Repeated exponential decay with an optional missed intervalLive current inputs
Health & Fitness
Medication Interval Estimate Calculator
Explore a generic first-order pharmacokinetic model using half-life, entered dose interval, bioavailability, and clearance-change scenarios while keeping the prescription as the governing schedule.
Scenario half-life—
Elimination-rate constant—
Single-dose residual at interval—
Idealized accumulation factor—
Approx. time to 90% steady state—
Idealized peak-to-trough ratio—
Time to entered residual threshold—
Model boundary—
FIRST-ORDER EXPOSURE MODEL
Repeated exponential decay with an optional missed interval
Separate dose pulses accumulate into an idealized envelope; the missed-dose scenario is visible without suggesting a catch-up action.
INTERVAL LEDGER
Idealized peak and pre-dose residual by administration
Each row applies the same mathematical interval and records the optional omission.
| Dose event | Clock time | Administered? | Post-dose amount | Pre-next-dose amount | Residual fraction |
|---|
MODEL SETUP
Use the prescription and label as the factual anchor
- Enter a documented half-life only for educational modeling.
- Keep the prescribed interval unchanged in real use.
- Use the clearance factor as a scenario, not a patient-specific adjustment.
- Never use the missed-interval curve to invent a catch-up dose.
WHY HALF-LIFE IS NOT A PRESCRIPTION
Exposure timing depends on more than one terminal number
Half-life governs exponential decline in this simplified model, but absorption, multiple compartments, active metabolites, therapeutic window, formulation, and patient factors can change real exposure.
The accumulation factor describes a mathematical steady-state ratio under consistent dosing. It is not a therapeutic target or safety guarantee.
PHARMACOKINETIC MODEL
Translate half-life into decay and repeated-dose accumulation
The model assumes linear one-compartment first-order elimination and instantaneous input. Real medicines may violate each assumption.
Detailed calculation process and general formulas
k = ln(2) / t_halfA(t) = Dose × F × e^(-kt)Residual(τ) = e^(-kτ)R_acc = 1 / (1 - e^(-kτ))t_threshold = -ln(thresholdFraction) / kSymbols, meanings, and units
- k
- first-order elimination-rate constant1/hour
- t_half
- scenario elimination half-lifehours
- τ
- entered dose intervalhours
- F
- entered bioavailability fractiondecimal
- R_acc
- idealized accumulation factorratio
MODEL DIAGNOSTICS
What changes when the interval meets the half-life
The page exposes three distinct effects.
Within-interval decline
—Residual fraction shows the modeled amount left before the next dose.
Repeated accumulation
—The geometric-series limit is reported separately.
Missed event
—The curve leaves a visible gap without recommending compensation.
Decision takeaway: Use this model to understand exponential timing, never to override the medication label or prescriber.
Applied decisions
Questions the generic model can illustrate
Interval longer than half-life
The entered interval exceeds the scenario half-life.
What the result clarifies: The curve shows greater modeled decline between events.
Clearance scenario decreases
The clearance factor is reduced while the reference half-life stays fixed.
What the result clarifies: The effective half-life lengthens and the idealized envelope accumulates more.
Worked default scenario
Current-input substitution and reconciliation
Method references
Evidence used to frame this specific model
Scope and limitations
Educational pharmacokinetic illustration only. Do not use it to select a drug, dose, interval, missed-dose response, or treatment plan. Follow the product label and prescribing clinician.
Medication Interval Estimate Calculator | First-Order Half-Life Model FAQ
Can I calculate my dosing interval from half-life?
No. Actual intervals depend on drug-specific efficacy, safety, formulation, patient factors, and labeling.
What does the clearance factor do?
It scales the reference half-life inversely as a hypothetical sensitivity scenario.
Does the accumulation factor predict blood concentration?
No. It is a dimensionless result from a simplified instantaneous-input model.
What should I do after a missed dose?
Follow the medication-specific label or contact the prescribing team; this calculator does not advise catch-up actions.