Estimates of the downward global solar and long-wave radiations are commonly made using simple models. We have tested the estimates produced by a number of these simple models against the values predicted by the radiative transfer model used in a climate model in order to determine their suitability for global applications. For clear sky, two simple models were comparable, but under cloudy conditions a combination of a clear-sky model based on the Angstrom-Prescott equation (which deals with the downwelling solar radiation) with a cloud transmissivity utilising total cloud fraction proved best. The lowest root mean square errors were 27 W m−2 for clear-sky global solar radiation and 90 W m−2 for cloudy conditions. For downward long-wave radiation in clear-sky conditions, the model of Garratt (1992) performed best with a root mean square error of 24 W m−2. However, in cloudy conditions the model of Idso & Jackson (1969) performed best with a root mean square error of 22 W m−2, and, as it performs nearly as well as that of Garratt (1992) in clear-sky conditions, it is probably the best choice.