Accurate, explicit, and analytic expressions are derived for the dew point and frost point as functions of temperature and relative humidity. These are derived theoretically in terms of physical constants using the Rankine-Kirchhoff approximations, which assume an ideal gas, fixed heat capacities, and zero specific volume of condensates. Compared to modern laboratory measurements, the expressions are accurate to within a few hundredths of a degree over the full range of Earth-relevant temperatures, from 180 to 273 K for the frost point and 230 to 330 K for the dew point.