Even within the simplest real solar cell model, the exact value of the fill factor (FF) is only computable by numerical calculations. Here, we perform approximations to the power–voltage curve given by the one-diode model with series and shunt resistance losses, obtaining explicit expressions for the voltage and current at the maximum power point, and thus an explicit approach for the FF. Over a broad range of possible solar cell parameters, including cells where the impact of shunt losses on the fill factor is not negligible, the approximate equations yield relative errors typically around 1%. The equations are applied to explore the dependence of FF on alternative buffer material thickness of organic solar cells, and to investigate the incidence of shunt and series resistance losses on the FF of Cu(In,Ga)Se2 solar cells under indoor illumination conditions. Copyright © 2012 John Wiley & Sons, Ltd.