Potential evapotranspiration PE is calculated for Nigeria by a simple energy balance method and compared with the methods of Thornthwaite, Gamier and Penman. Solar radiation is obtained from twelve monthly linear regressions using measurements of sunshine n and radiation at Benin and Kano (Nigeria), Accra(Ghana), Fort Lamy (Tchad) and Niamey (Niger) and values of extraterrestrial radiation So and possible sunshine N obtained from tables. Daytime net radiation is calculated from a linear regression upon solar radiation which is shown to be appropriate for various stations throughout the world. It is assumed that in the PE model nearly all of the net radiation is used to provide the energy for evaporation and the water equivalent of the net radiation (potential water loss ER) can be equated with PE. The equation is ER=PE=.017 {.617 So (a+b n/N)–24} where a and b are the appropriate monthly intercept and coefficient in a linear regression between solar radiation and sunshine. Measurements of PE and pan evaporation during the wet season, when ‘oasis’ effects are small and net radiation is the most important source of energy for evaporation, are in good agreement with ER. ER is a better approximation of the measurements than those obtained from the Thornthwaite, Gamier and Penman formulas. The difference between rainfall p and PE defines areas of dry season deficit and wet season surplus. The index P-PE is used to delimit the broad vegetation zones which have been mapped by Keay. For the forest-savanna boundary P-PE=O.