Drug Half-Life from Clearance and Volume of Distribution

For a one-compartment drug the elimination half-life is not an independent property. It falls out of two things: how much space the drug is spread through, and how fast the body empties that space. A large volume of distribution with a slow clearance gives a long half-life, and $t_{1/2} = 0.693\,V_d / \mathrm{CL}$ is that statement written down. A drug with a 50 L volume and a clearance of 3 L/h has a half-life of $0.693 \ imes 50 / 3 = 11.6$ hours.

The 0.693 is $\ln 2$, and it comes from first-order kinetics: the fraction removed per unit time is constant, so the fall is exponential and the time to halve is $\ln 2$ divided by the rate constant $k = \mathrm{CL}/V_d$. This is why the classic mistake, treating a half-life as a fixed property of the molecule, misleads. Renal failure lowers clearance and lengthens the half-life without the drug changing at all, and fluid overload raises the volume of distribution and does the same.

The one-compartment assumption is the real limit. Many drugs distribute into a fast central compartment and a slow peripheral one, giving two or three half-lives rather than one, and a level drawn during the fast distribution phase will suggest a half-life far shorter than the elimination phase that actually governs accumulation. First-order kinetics also fail where an enzyme saturates: phenytoin and alcohol switch toward zero-order elimination at ordinary doses, at which point the whole idea of a half-life stops applying and small dose increases produce large level increases.