A method is presented to calculate accurate approximations to the half-life values of elimination systems modelled by one compartment. The major advantage of this method is that only algebraic mathematical operations are required. The results will be of value not only to students beginning the study of elimination kinetics, but also to professionals in the natural and engineering sciences who need quick, accurate estimates of the half-life of some physical system with regard to the flow of a material through it. We illustrate the method by applying it to several examples.