A solution of the laminar boundary-layer equations has been obtained for free convection from the outer surface of a vertical cylinder. The temperature of the cylinder surface was taken to be uniform. Heat-transfer results have been found for Prandtl numbers of 0.72 and 1 (i.e., for gases) and are presented on graphs. The Nusselt numbers for the cylinder were higher than those for the flat plate. Also, the deviation of the cylinder Nusselt numbers from those for the flat plate was greater for Prandtl number of 0.72 than for Prandtl number of 1. A quantitative criterion was established for determining the conditions under which the heat transfer from a cylinder could be calculated with sufficient accuracy using the flat-plate results. An analysis based on replacing the free-convection problem by a problem in pure conduction through a fictitious layer of stagnant fluid gave good agreement with the boundary-layer solution.