PK Half-Life & Dosing Interval Calculator (Educational)
Explore basic pharmacokinetics with a simple half-life and dosing interval calculator. Estimate half-life from k or from two time–concentration points, see how much drug remains after a given interval, and compute times to 90%, 95%, or 99% elimination in a one-compartment, first-order model.
First-Order Elimination Half-Life from k or Two Points
You dosed mice with a test compound at 10 mg/kg IV, drew plasma samples at 1 and 4 hours, and got concentrations of 8.2 and 2.1 µg/mL. How long does the drug stay in the system? A PK half-life calculator takes two plasma concentration–time points (or a known elimination rate constant) and returns the half-life — the time it takes for the plasma concentration to drop by half. That number drives everything downstream: dosing frequency, steady-state predictions, and washout period before the next experiment.
The most common mistake: using time points from the distribution phase instead of the elimination phase. After IV dosing, plasma levels drop in two stages — a fast initial decline as drug distributes into tissues (distribution, or α phase) followed by a slower decline as the body eliminates the drug (elimination, or β phase). If both your time points fall in the distribution phase, you calculate a falsely short half-life. Pick points on the terminal log-linear segment of the curve.
This calculator uses a one-compartment first-order model. It is educational and useful for planning preclinical PK studies. It is not a substitute for clinical pharmacokinetic modeling or dosing decisions, which require multi-compartment analysis, patient-specific parameters, and medical oversight.
% Drug Remaining After n Half-Lives
The relationship between half-lives elapsed and drug remaining follows a simple geometric progression: after 1 half-life, 50% remains; after 2, 25%; after 3, 12.5%; after 4, 6.25%; after 5, 3.125%. The rule of thumb is that a drug is essentially eliminated after 5 half-lives (<3.2% remaining), which is why washout periods in clinical studies are typically set at 5× the terminal half-life.
This relationship is exact only for first-order (linear) elimination, where the fraction eliminated per unit time is constant regardless of concentration. Most drugs follow first-order kinetics at therapeutic concentrations. A few (like ethanol and phenytoin at high doses) follow zero-order or saturable (Michaelis–Menten) elimination, where a constant amount (not fraction) is eliminated per unit time and the concept of a fixed half-life does not apply.
For study planning: if the half-life is 6 hours, full washout takes ~30 hours. If you need to re-dose before full washout (e.g., maintaining therapeutic levels), the residual drug from the previous dose adds to the new dose — this is accumulation, covered in the next section.
Dosing Interval and Steady-State Accumulation
When you give repeated doses at a fixed interval shorter than 5 half-lives, each dose adds to the residual drug from previous doses. The plasma concentration ratchets upward with each dose until the amount eliminated per interval equals the dose — this is steady state. The time to reach steady state is approximately 4–5 half-lives regardless of the dosing interval.
The accumulation factor (R) tells you how much higher the steady-state peak is compared to the first-dose peak: R = 1 / (1 − e⁻ᵏτ), where k is the elimination rate constant and τ is the dosing interval. If τ = t½ (dosing every half-life), R = 2 — steady-state peak is twice the first-dose peak. If τ = 2×t½, R = 1.33. If τ = 0.5×t½ (dosing every half of a half-life), R = 3.4.
For preclinical study design, pick a dosing interval that keeps trough levels above the efficacious concentration (e.g., above EC90 from your in vitro data) while keeping peak levels below the toxicity threshold. The calculator shows both peak and trough predictions at steady state.
Multi-Compartment Caveats (One-Compartment Limits)
The one-compartment model assumes the drug distributes instantaneously and uniformly throughout the body. In reality, most drugs have a distribution phase: after IV dosing, plasma levels drop rapidly as drug moves into tissues (fast compartment → slow compartment), then decline more slowly during true elimination. The terminal half-life (from the slow phase) is what most people mean by “the half-life,” but the distribution half-life matters too — it determines how quickly peak tissue levels are reached.
If your two plasma time points straddle the distribution-elimination boundary, a one-compartment fit will give you a half-life somewhere between the distribution and elimination half-lives — a meaningless hybrid. Plot at least 6–8 time points over the full PK profile, identify the log-linear terminal phase, and fit only those points for the elimination half-life.
Highly lipophilic drugs, drugs with tissue binding, or drugs with enterohepatic recycling can show multi-exponential decline that the one-compartment model cannot capture. For these compounds, use dedicated PK software (Phoenix WinNonlin, NONMEM, or similar) for proper multi-compartment modeling.
PK Half-Life Calibration Notes
My calculated half-life from two time points does not match the published value. What went wrong?
The published value was probably derived from a full PK profile with multi-compartment modeling. Your two-point estimate only captures one segment of the curve. Also check species — half-life in mice (fast metabolism) is often 5–10x shorter than in humans for the same compound.
The half-life from my oral PK study is longer than from the IV study. Is that possible?
Yes. After oral dosing, absorption continues while elimination is ongoing. If absorption is slow (flip-flop kinetics), the apparent terminal half-life reflects the absorption rate, not the elimination rate. The IV half-life is the true elimination half-life.
Can I use this calculator for biologics (antibodies, peptides)?
With caution. Antibodies have half-lives of days to weeks and follow target-mediated disposition, not simple first-order kinetics. Small peptides may have half-lives of minutes. The one-compartment model gives a rough estimate but does not capture FcRn recycling or target-mediated clearance.
Is this calculator suitable for clinical dosing decisions?
No. This is an educational tool for understanding PK concepts and planning preclinical experiments. Clinical dosing requires patient-specific factors (renal/hepatic function, drug interactions, body weight) and should be determined by a qualified clinician or clinical pharmacologist.
Elimination and Accumulation Equations
Five equations cover the one-compartment PK model:
Units note: k is in inverse time units (h⁻¹ if t is in hours). t½ and τ must use the same time unit. Concentrations can be in any unit (ng/mL, µg/mL) as long as C₁ and C₂ use the same one.
Drug at 8-Hour Intervals with t½ = 6 h Run
Scenario: You are planning a mouse PK study with repeated oral dosing. The compound has a half-life of 6 hours in mice (determined from IV PK). The Cmax after a single 50 mg/kg oral dose is 12 µg/mL. You want to dose every 8 hours and need to predict steady-state peak and trough levels.
Step 1 — Elimination rate constant.
k = 0.693 / 6 = 0.1155 h⁻¹.
Step 2 — Trough after first dose (at t = 8 h).
C(8) = 12 × e⁻₀⋅¹¹⁵⁵ ⨉ ⁸ = 12 × e⁻₀⋅⁹²⁴ = 12 × 0.397 = 4.76 µg/mL.
Step 3 — Accumulation factor.
R = 1 / (1 − e⁻₀⋅⁹²⁴) = 1 / (1 − 0.397) = 1 / 0.603 = 1.66.
Step 4 — Steady-state predictions.
Peak (Cmax,ss) ≈ 1.66 × 12 = 19.9 µg/mL.
Trough (Cmin,ss) ≈ 1.66 × 4.76 = 7.9 µg/mL.
Step 5 — Evaluate.
If the in vitro EC90 is 5 µg/mL and the toxicity threshold is 30 µg/mL, this dosing regimen keeps trough above EC90 (7.9 > 5) and peak below toxicity (19.9 < 30). Steady state is reached by ~5 half-lives = 30 hours (~4 doses). The regimen looks viable for a multi-day efficacy study.
Sources
NCBI — Pharmacokinetics (StatPearls): Overview of first-order elimination, half-life, and steady-state principles.
FDA — Population Pharmacokinetics Guidance: Regulatory framework for PK modeling and study design.
PharmPK — Clinical Pharmacokinetics Course: Educational resource for PK parameter estimation and dosing calculations.
Nature Reviews Drug Discovery — PK/PD Modeling: Review of pharmacokinetic modeling approaches in drug development.
Frequently Asked Questions
What does pharmacokinetic half-life mean in this tool?
Half-life (t½) is the time required for the amount or concentration of a substance to decrease to 50% of its initial value. In this simple one-compartment model, it assumes exponential decay where the elimination rate is proportional to the amount present (first-order kinetics). After one half-life, 50% remains; after two, 25%; after three, 12.5%, and so on. Understanding this helps you see how half-life quantifies drug elimination and why it's fundamental to pharmacokinetics.
How are half-life and elimination rate constant related?
The elimination rate constant (k) and half-life (t½) are mathematically related by: t½ = ln(2) / k, which is approximately 0.693 / k. If you know one, you can calculate the other. A larger k means faster elimination and a shorter half-life. For example, if k = 0.0866 per hour, then t½ ≈ 8 hours. Understanding this relationship helps you convert between half-life and elimination rate constant and see how they're inversely related.
What does the 'target fraction remaining' interval represent?
This is a purely theoretical calculation showing the dosing interval (τ) that would leave a specified fraction of the starting amount at the end of the interval. For example, if you set the target to 0.25 (25%), the tool calculates how many hours it would take to reach 25% of the initial level using τ = -ln(f)/k. This is for educational intuition only—it is NOT a clinical dosing recommendation. Understanding this helps you see how interval relates to fraction remaining and why theoretical intervals are for learning, not clinical use.
Can I use this calculator to choose a real dosing schedule?
No, absolutely not. This tool is for educational purposes only and uses a highly simplified model. Real drug dosing requires consideration of many factors including drug formulation, absorption characteristics, multi-compartment distribution, patient-specific factors (age, weight, renal/hepatic function), drug interactions, therapeutic windows, and clinical judgment. Always consult qualified healthcare professionals and use validated pharmacokinetic software for clinical decisions. Understanding this limitation helps you use the tool for learning while recognizing that clinical dosing requires validated procedures and professional judgment.
Why is this based on a one-compartment, first-order model?
The one-compartment, first-order model is the simplest pharmacokinetic model and serves as a foundation for understanding drug elimination. It assumes the body acts as a single, well-mixed compartment and that elimination is proportional to the amount present. While many real drugs follow more complex multi-compartment kinetics, this simple model provides useful intuition about half-life concepts and is commonly taught in introductory pharmacology courses. Understanding this helps you see why simplified models are used for education and when more complex models are needed.
What does estimating k from two time-concentration points assume?
When you provide two time-concentration data points, the tool assumes both measurements were taken during the elimination phase (after absorption and distribution are complete). It fits a simple log-linear decline (ln C vs time) to estimate the slope, which gives -k. If the points include absorption/distribution phases, or if concentrations increased rather than decreased, the estimate will be invalid. Understanding this helps you recognize when time-concentration points are appropriate for k estimation and why phase recognition is essential.
How long does it take to reach 90%, 95%, or 99% elimination?
In a simple first-order model: 90% elimination (10% remaining) takes about 3.3 half-lives; 95% elimination (5% remaining) takes about 4.3 half-lives; 99% elimination (1% remaining) takes about 6.6 half-lives. These are commonly cited milestones in pharmacokinetics education and drug washout period estimation. Understanding this helps you estimate elimination times for specific percentages and see why these milestones are useful for drug washout planning.
What is the relationship between dosing interval and drug accumulation?
If dosing intervals are short relative to half-life, drug levels can accumulate because less drug is eliminated between doses. If intervals are long compared to half-life, levels drop significantly between doses. The degree of accumulation depends on the fraction remaining after each interval: if fraction remaining is high (e.g., 0.9), accumulation is significant; if low (e.g., 0.1), accumulation is minimal. Understanding this helps you see how interval selection affects drug accumulation and why proper interval selection is important.
How accurate is the one-compartment model for real drugs?
The one-compartment model is a simplification that works well for educational purposes and some drugs that distribute rapidly and uniformly. However, many real drugs follow multi-compartment kinetics with distinct distribution and elimination phases. The model also ignores absorption, saturable clearance, protein binding, and patient variability. For accurate pharmacokinetic analysis of real drugs, multi-compartment models and patient-specific factors are typically needed. Understanding this helps you see when simplified models are appropriate and when more complex models are required.
Can I use this tool for therapeutic drug monitoring (TDM)?
No. This tool is strictly for educational purposes and does not provide therapeutic drug monitoring recommendations. TDM requires validated assays, patient-specific factors, therapeutic windows, clinical judgment, and integration with patient care. This tool uses simplified calculations that don't account for the many factors required in clinical TDM. Always consult qualified healthcare professionals and use validated TDM protocols for actual patient care. Understanding this limitation helps you use the tool for learning while recognizing that TDM requires validated procedures and clinical expertise.