In applications one must relate the probability constants α and β to differences of practical importance in the field of application. This paper states and proves a fundamental theorem which establishes this relationship and then derives elementary formulae for making power calculations in the most frequently encountered situations such as for main effects, interactions, regression coefficients and response surfaces. After an examination of the sensitivity of power calculations to ranges of α, β, and error degrees of freedom, modifications are made in the formulae which allow them to be used without reference to tables and charts: i.e., they are made portable.