What is the half-life (t1/2) formula of a drug?

The half-life of a drug is an important pharmacokinetic parameter that indicates the time it takes for the concentration of the drug in the plasma to decrease by half. The correct formula for determining the half-life is derived from the relationship between the volume of distribution (Vd) and the clearance (CL) of the drug.

The formula is expressed as:

t1/2 = 0.693 x (Vd / CL).

In this case, it's important to note that the factor of 0.7 often used is a rounded version of 0.693, which is derived from the natural logarithm of 2 (ln(2)). Since clearance reflects the rate at which the drug is eliminated from the body, and the volume of distribution indicates the extent of drug distribution throughout the body’s compartments, this relationship clarifies how the two components interact to determine a drug's half-life.

In essence, the half-life is directly proportional to the volume of distribution—indicating that a larger Vd (which means the drug is widely distributed in body tissues) results in a longer half-life. Conversely, it is inversely proportional to clearance; a higher clearance means the drug is eliminated more quickly, resulting in a shorter half-life.