Microalgae can be used to produce versatile high-value fuels, such as methane, biodiesel, ethanol, or hydrogen gas. One of the most important factors that influence the economics of microalgae cultivation is the primary production of biomass per unit area. This is determined by productivity rates during cultivation, which are influenced by the local climate conditions (solar irradiation, temperature). To compare locations in different climate regions for microalgae cultivation, a mathematical model for an idealized closed photobioreactor was developed. The applied growth kinetics were based on theoretical maximum photon-conversion efficiencies (for the conversion of solar energy to chemical energy in the form of biomass). Known or estimated temperature effects for different algal strains were incorporated. The model was used to calculate hourly average areal productivity rates as well as annual primary production values under local conditions at seven example locations. Here, hourly weather data (solar irradiance and air temperature) were taken into account. According to these model calculations, maximum annual yields were achieved ... mehrin regions with high irradiation and temperature patterns in or near the optimum range of the specific algal strain (here, desert and equatorial humid climates). The developed model can be used as a tool to assess and compare individual locations for microalgae cultivation.