Health & Medicine · Pharmacokinetics
Drug Half-Life Calculator
Calculates the remaining drug concentration in the body after a given number of half-lives, and estimates the time for complete elimination.
Calculator
Formula
C(t) is the drug concentration remaining at time t. C_0 is the initial drug concentration or dose. t is the elapsed time since the dose was administered. t_{1/2} is the half-life of the drug — the time it takes for the concentration to fall to half its current value. The exponent t / t_{1/2} represents the number of half-lives that have elapsed. Each additional half-life reduces the remaining concentration by 50%. Full elimination is conventionally considered to occur after 4–5 half-lives, at which point less than 3–6% of the original dose remains.
Source: Rowland M, Tozer TN. Clinical Pharmacokinetics and Pharmacodynamics: Concepts and Applications. 4th ed. Lippincott Williams & Wilkins, 2010.
How it works
Every drug is eliminated from the body at a characteristic rate described by its half-life (t½) — the time required for the plasma concentration to fall to exactly half its current value. For most drugs, this follows first-order kinetics, meaning the rate of elimination is proportional to the current concentration. This results in an exponential decay curve rather than a linear one. The concept of half-life is foundational to pharmacokinetics and directly determines dosing frequency, accumulation with repeated doses, and washout times.
The governing formula is C(t) = C₀ × (1/2)^(t / t½), where C₀ is the initial dose or peak concentration, t is elapsed time, and t½ is the half-life. Each complete half-life that passes reduces the remaining amount by 50%. After one half-life, 50% remains; after two, 25%; after three, 12.5%; after four, 6.25%; and after five half-lives, only about 3.1% of the original dose persists. Clinicians conventionally regard 4–5 half-lives as the time required for a drug to be effectively eliminated — and also the time required for a drug given at regular intervals to reach steady-state plasma concentrations.
Practical applications of the half-life calculation are widespread in clinical medicine. Anesthesiologists calculate drug clearance before procedures. Psychiatrists time medication switches based on washout periods — for example, the long half-life of fluoxetine (1–6 days) means a 5-week washout before starting an MAOI. Emergency physicians estimate when analgesics or sedatives will wear off. Pharmacists counsel patients on timing interactions between drugs. Regulatory agencies and researchers use half-life data to establish dosing regimens in clinical trials and product labeling.
Worked example
Consider a patient who received a single oral dose of 200 mg of a drug with a half-life of 8 hours. A clinician wants to know how much of the drug remains after 24 hours.
Step 1 — Identify inputs: C₀ = 200 mg, t½ = 8 hours, t = 24 hours.
Step 2 — Calculate half-lives elapsed: t / t½ = 24 / 8 = 3 half-lives.
Step 3 — Apply the formula: C(24) = 200 × (0.5)³ = 200 × 0.125 = 25 mg remaining.
Step 4 — Percent remaining: 25 / 200 × 100 = 12.5% of the original dose is still present in the body.
Step 5 — Estimate full elimination: Five half-lives = 5 × 8 = 40 hours after dosing, at which point approximately 3.1% (about 6.25 mg) remains — conventionally considered negligible for clinical purposes.
This information helps the clinician determine whether a second dose is safe to give, whether therapeutic levels are still active, or whether a drug-drug interaction window has passed.
Limitations & notes
This calculator assumes simple one-compartment, first-order elimination kinetics. Many drugs do not follow this simple model — drugs with two-compartment or multi-compartment distribution (such as digoxin or amiodarone) have a complex biphasic elimination curve, and a single half-life value is insufficient to describe their behavior. Additionally, the effective half-life of a drug can vary significantly between individuals due to age, renal function, hepatic function, genetic polymorphisms in metabolizing enzymes (e.g., CYP2D6, CYP3A4), body composition, and drug-drug interactions that inhibit or induce metabolic pathways. This tool is intended for educational purposes only and should not replace individualized clinical pharmacokinetic monitoring, therapeutic drug monitoring (TDM), or professional medical advice. Patients should never adjust medication timing based solely on half-life calculations without consulting a qualified healthcare provider.
Frequently asked questions
What does a drug's half-life actually mean?
A drug's half-life is the time it takes for the concentration of the drug in the bloodstream to fall to half of its previous value. For example, if a drug has a half-life of 6 hours and you start with 100 mg in your system, after 6 hours 50 mg remains, after 12 hours 25 mg remains, and so on. It is one of the most important pharmacokinetic parameters used to determine dosing frequency and predict drug behavior over time.
How many half-lives does it take to completely eliminate a drug?
Clinically, a drug is considered effectively eliminated after 4 to 5 half-lives, at which point only 6.25% to 3.1% of the original dose remains. While technically the concentration never reaches exactly zero in a mathematical sense, the remaining amount after 5 half-lives is generally considered clinically insignificant. For drugs with very narrow therapeutic windows, monitoring may be extended beyond this period.
Why does the half-life matter for steady-state drug levels?
When a drug is taken at regular intervals, it accumulates in the body until the rate of elimination equals the rate of administration — this is called steady state. Steady state is reached after approximately 4 to 5 half-lives of repeated dosing, regardless of the dose size. This is why drugs with long half-lives like fluoxetine (1–4 days) take several weeks to reach stable therapeutic levels, while short-acting drugs like ibuprofen (2 hours) reach steady state within a day.
Can kidney or liver disease affect drug half-life?
Yes, significantly. Most drugs are eliminated by the kidneys (renal excretion) or the liver (hepatic metabolism), and impairment of either organ can dramatically prolong a drug's half-life. For example, the antibiotic vancomycin has a half-life of about 4–8 hours in patients with normal renal function, but this can extend to over 200 hours in patients with end-stage renal disease. Dose adjustments and therapeutic drug monitoring are critical in these populations to prevent toxicity.
Is the drug half-life the same as the washout period?
The washout period — the time required to clear a drug sufficiently before starting another medication or procedure — is typically defined as 4 to 5 half-lives. However, in some clinical contexts, particularly when switching between psychiatric medications or preparing for surgery, longer washout periods may be required based on active metabolites, receptor occupancy, or specific drug interaction risks. Always consult a pharmacist or physician for guidance on specific drug washout requirements.
Last updated: 2025-01-15 · Formula verified against primary sources.