Which equation expresses the relationship between half-life (t1/2), Vd, and Cl?

• A. t1/2 = 0.693 × Vd / Cl
• B. t1/2 = 0.693 × Cl / Vd
• C. t1/2 = Dose / Cl
• D. t1/2 = Vd / Dose

Answer: (A)

In first-order elimination, half-life reflects how long it takes the body to clear half of the drug, which depends on how widely the drug distributes (Vd) and how quickly it is cleared (Cl). The elimination rate constant is k = Cl / Vd. Since t1/2 = 0.693 / k, substituting k gives t1/2 = 0.693 × Vd / Cl. This shows that drugs with a large distribution volume take longer to reach half-life because they reside in tissues longer, while higher clearance speeds up elimination and shortens the half-life.

The other forms don’t match the biology. Dose relates to how much drug is given, not how fast it’s eliminated, so Dose/Cl isn’t a time-based measure. Expressions like Vd/Dose or Cl/Vd don’t represent the time constant for a concentration to fall by half.