Abstract Analytical and generalised derivations of the Angstrom equation as well as the Angstrom-Prescott equation are presented. These derivations explicitly relate all the coefficients in both equations to climatological variables. This opens up a possibility for evaluating the coefficients in the Angstrom and Angstrom-Prescott equations through calculations that do not involve the present ‘educated guess’ exercise used in choosing values for these coefficients. It is also shown that while the analytical form of the Angstrom equation is apparently exact, the analytical form of the Angstrom-Prescott equation is relatively more approximate. The latter equation is, in fact, derived from the former equation through some approximations/assumptions elaborated in this text.