Drug Half-Life Calculator
Find a drug's plasma half-life and elimination rate constant from two concentration measurements taken at different times.
⏳ What is Drug Half-Life?
Drug half-life (t1/2) is the time required for a drug's concentration in the bloodstream to fall by exactly half, once it is being eliminated from the body through metabolism and excretion. It is the single most useful number in pharmacokinetics for predicting how long a drug stays active, how often it needs to be dosed, and how long it takes to clear the body after the last dose.
Clinicians use half-life to set safe dosing intervals so a drug neither builds up to toxic levels nor drops below its effective level between doses. Pharmacists use it to counsel patients on how long a drug remains detectable or active after stopping. Pharmacology students and researchers use it to compare drugs, since a short half-life (a few hours, like many antibiotics) behaves very differently in the body than a long half-life (days, like some psychiatric medications).
A common misconception is that a drug is "completely gone" after one half-life. It is not, one half-life only removes 50% of the drug; roughly 4 to 5 half-lives are needed before a drug is considered clinically eliminated (94% to 97% gone). Another misconception is that half-life is a fixed physical constant like an element's atomic weight, in reality it can shift meaningfully with age, kidney function, liver function, and drug interactions.
This calculator derives half-life directly from two real concentration measurements rather than relying on a textbook average value, which matters because individual patients can metabolize the same drug at noticeably different rates.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Exactly One Half-Life Apart
C1 = 100 mg/L, C2 = 50 mg/L, Δt = 4 hr
Example 2 — Two Half-Lives Apart
C1 = 80 mg/L, C2 = 20 mg/L, Δt = 6 hr
Example 3 — Three Half-Lives Apart
C1 = 64 mg/L, C2 = 8 mg/L, Δt = 15 hr
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate a drug's half-life from two blood levels?
Take the elimination rate constant ke = ln(C1/C2) / delta t, where C1 and C2 are plasma concentrations at two times separated by delta t hours, then half-life t(1/2) = ln(2) / ke, approximately 0.693 / ke. This works because first-order elimination follows an exponential decay curve.
What is the difference between half-life and elimination rate constant?
The elimination rate constant (ke) describes the fractional rate of drug removal per hour, while half-life (t1/2) is the time needed for the concentration to fall by exactly half. They are directly related by t1/2 = ln(2)/ke, so either one can be derived from the other.
Why does the formula use natural log (ln) instead of log base 10?
First-order elimination is modeled as continuous exponential decay, C(t) = C0 * e^(-ke*t), and the natural logarithm is the correct inverse function for an exponential with base e. Using log base 10 would require an extra conversion factor.
How many half-lives until a drug is fully out of the body?
There is no exact zero point mathematically, but by convention a drug is considered clinically eliminated after about 4 to 5 half-lives, which leaves roughly 6% to 3% of the peak concentration remaining, a negligible amount for most purposes.
Does this calculator work for any two concentration readings?
It works for any two readings taken during the same first-order elimination phase, meaning after distribution into tissues is complete and absorption has stopped. Using a reading taken too early (during absorption or distribution) will produce an inaccurate half-life.
What units should I use for concentration and time?
Any consistent concentration unit works (mg/L, mcg/mL, ng/mL) since the units cancel out in the ratio C1/C2. Time should be entered in hours to match the elimination rate constant's typical /hr units, though the math scales to any consistent time unit.
Why must the second concentration be lower than the first?
Elimination removes drug from the plasma over time, so a valid pair of same-phase readings must show a decline. If your second value is equal to or higher than the first, the samples were likely taken during absorption or an infusion, not during elimination.
How does half-life affect dosing frequency?
Drugs with a short half-life (a few hours) typically need multiple daily doses to maintain a therapeutic level, while drugs with a long half-life (a day or more) can often be dosed once daily. Half-life is also the main driver of how long it takes a drug to reach steady state with repeated dosing.
Is elimination half-life the same as biological half-life?
In pharmacokinetics they are typically used interchangeably to mean the time for plasma concentration to fall by half. The broader term 'biological half-life' can also apply to other quantities such as radioactive tracers bound to tissue, but the calculation method is the same exponential-decay math.
Can a drug have more than one half-life value reported?
Yes. Drugs that follow two-compartment kinetics have a fast initial (alpha) distribution half-life and a slower terminal (beta) elimination half-life. The single half-life this calculator computes describes simple one-compartment, first-order elimination.