6.25
mg/L
6.3
%
4
0.1155
1/hour
93.8
%
19.93
hours
6.25
mg/L
6.3
%
4
0.1155
1/hour
93.8
%
19.93
hours
The Drug Half-Life Calculator computes the remaining concentration of a drug after a given period using first-order elimination kinetics. Understanding drug half-life is fundamental to pharmacology, clinical dosing, drug testing, and understanding how medications work in the body.
The half-life (t½) is defined as the time required for the plasma concentration of a drug to decrease by exactly 50%. This concept, rooted in exponential decay mathematics, is one of the most important pharmacokinetic parameters because it determines dosing frequency, time to reach steady state, and washout time after discontinuation.
Most drugs follow first-order kinetics, meaning a constant fraction (not a constant amount) of the drug is eliminated per unit time. This produces an exponential decay curve where the rate of elimination is proportional to the amount of drug present. Mathematically, the concentration at any time equals the initial concentration multiplied by 0.5 raised to the power of (elapsed time divided by half-life).
Key clinical applications of half-life include: Dosing interval selection — most drugs are dosed every 1-2 half-lives to maintain therapeutic levels. Steady state prediction — it takes approximately 4-5 half-lives of continuous dosing to reach steady state (>93.75% of final level). Washout calculation — after stopping a drug, it takes 4-5 half-lives for >93.75% to be eliminated. Drug testing windows — detection times depend on the drug's half-life and assay sensitivity.
Half-lives vary enormously across medications: remifentanil has a half-life of only 3-10 minutes (used in anesthesia for rapid offset), acetaminophen is 2-3 hours, metformin is 4-8 hours, fluoxetine (Prozac) is 1-3 days, and amiodarone has a half-life of 40-55 days, meaning it takes months to fully clear from the body.
This calculator also computes the time to reach a target concentration, which is useful for drug testing, determining when it is safe to switch medications, and calculating washout periods for clinical trials. The exponential decay formula provides precise predictions when first-order kinetics apply.
The calculator uses the exponential decay formula for first-order kinetics:
The time-to-target formula is derived by solving the decay equation for time, using logarithms to invert the exponential function. This calculation assumes first-order elimination without ongoing drug input.
The Remaining Concentration shows the predicted drug level after the elapsed time. After 1 half-life, 50% remains; after 2 half-lives, 25%; after 3, 12.5%; after 4, 6.25%; after 5, 3.125%. The Time to Target tells you when the concentration will drop to a specific level — useful for drug switching, testing, or safety. Values assume no additional doses are taken. In clinical practice, consult drug-specific guidelines as some drugs have active metabolites with their own half-lives.
Inputs
Results
After 24 hours (4 half-lives), only 6.25% (6.25 mg/L) of a drug with t½=6h remains. The target of 10 mg/L is reached at ~20 hours.
Inputs
Results
After 96 hours (2 half-lives), 25% remains (50 mg/L). Reaching 5 mg/L takes about 263 hours (~11 days).
Drug half-life (t½) is the time required for the plasma concentration to decrease by 50%. It reflects how quickly the body eliminates a drug through metabolism (primarily liver) and excretion (primarily kidneys). Shorter half-lives require more frequent dosing.
After 5 half-lives, approximately 96.875% of the drug is eliminated, which is generally considered 'cleared.' After 7 half-lives, 99.2% is gone. For practical purposes, most guidelines use 5 half-lives as the washout period.
Half-life is affected by liver function (metabolism), kidney function (excretion), age (neonates and elderly have longer half-lives), body composition (fat-soluble drugs last longer in obese patients), drug interactions, and genetic variations in metabolizing enzymes.
Steady state occurs when the rate of drug administration equals the rate of elimination, resulting in consistent plasma levels. It takes 4-5 half-lives to reach steady state. For a drug with a 12-hour half-life, steady state is reached in 2-2.5 days.
Yes, some drugs have active metabolites with different (often longer) half-lives. Fluoxetine (t½ ~2 days) has an active metabolite norfluoxetine (t½ ~7 days), meaning clinical effects persist long after the parent drug is eliminated.
Most drugs are dosed every 1-2 half-lives. A drug with a 12-hour half-life is typically dosed every 12 hours (BID). Extended-release formulations artificially extend the effective half-life, allowing less frequent dosing (e.g., once daily).
First-order: a constant fraction is eliminated per unit time (most drugs). Zero-order: a constant amount is eliminated per unit time, regardless of concentration (e.g., alcohol at ~10 g/hr, high-dose phenytoin). This calculator assumes first-order kinetics.
Drug detection windows depend on the half-life and test sensitivity. Cannabis metabolites (t½ ~5 days in heavy users) can be detected for weeks. Cocaine (t½ ~1 hour) clears quickly but metabolites (t½ ~6 hours) persist longer. Detection = 5-7 half-lives beyond the detectable threshold.
A loading dose is a larger initial dose that rapidly achieves therapeutic concentrations instead of waiting 4-5 half-lives. It is especially important for drugs with long half-lives. Loading dose = Target concentration × Volume of distribution.
Yes, half-life can change due to disease progression (worsening liver/kidney function), drug interactions (enzyme inducers shorten it, inhibitors prolong it), age-related changes, and changes in hydration or nutritional status.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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