Abstract A procedure is described for rapidly estimating the flow-rate and heat transfer for laminar free and mixed convection in inclined ducts. Solutions are given by closed-form expressions, suitable for routine use at spreadsheet level. The flow-rate is obtained by equating the sum of the pressure differences which drive the flow with that of those opposing it. Among the former, the contribution of free convection is represented by superposing a pressure difference equal to that due to buoyancy in a static column of fluid of the same height as the duct. In the initial development it is assumed that wall friction and heat transfer may be represented by expressions for forced convection, including entrance effects. The procedure is tested against CFD results for a vertical parallel-plate duct with heat flux at one wall only. Despite the severity of the case, agreement is found to be sufficiently good to validate the method for routine initial design and optimisation studies for most conditions of free and mixed convection. Discrepancies become noticeable only at high Grashof number, where the buoyancy component is high enough to produce substantial asymmetry in the velocity profile.