elimination rate constant

Think of a leaky bucket where the hole lets out a fixed percentage of whatever water remains each minute. The elimination rate constant, written k, is that percentage expressed as a fraction. It tells you what fraction of the drug present in the body is removed per unit of time.

Because it is a fraction per time, its units are 'per hour' or 'per minute', not an amount. In first-order kinetics k is constant: even though the actual amount eliminated falls as the concentration falls, the proportion stays the same. The constant k is the slope of the line you get when you plot the logarithm of concentration against time.

The rate constant and the half-life are two ways of saying the same thing. They are linked by the half-life equalling the natural log of 2 (about 0.693) divided by k. A larger k means faster elimination and a shorter half-life. k also equals total body clearance divided by the volume of distribution, tying it back to the underlying physiology.