An exact solution of the laminar boundary-layer equations for free convection from a vertical cylinder haying uniform surface heat flux has been obtained. Numerical results have been given for Prandtl number of 1, that is, for gas. It is showed that when average Nusselt numbers are calculated for a cylinder with uniform surface heat flux using the temperature difference halfway along the height, the results are close to those for a uniform surface temperature cylinder. In addition, an analysis based on pure heat conduction through on equivalent stagnant layer of fluid has been made and the results have been extended to other Prandtl numbers for which the boundary-layer solution is not available. A criterion for the condition under which the flatplate results are sufficiently accurate for calculating the heat transfer from a cylinder has been established for practical purposes.