This paper describes a radiative transfer method for calculating radiances in all-sky conditions and performing an integration over the view hemisphere of an arbitrary plane to calculate tilted irradiance. The advantage of this method is the combination of cloud parameters inside the radiative transfer model with a tilt procedure. For selected locations this method is applied with cloud, ozone, water vapour and aerosol input data to determine tilted irradiance, horizontal irradiance and optimal tilt angle. A validation is performed for horizontal and tilted irradiance against high-quality pyranometer data. For 27 sites around the world, the annual horizontal irradiation predicted by our model had a mean bias difference of +0.56% and a root-mean-squared difference of 6.69% compared to ground measurements. The difference between the annual irradiation estimates from our model and the measurements from one site that provides tilted irradiance were within +/- 6% for all orientations except the north-facing vertical plane. For European and African sites included in the validation, the optimal tilt from our model is typically a few degrees steeper than predictions from the popular PVGIS online tool. Our model is generally applicable to any location on the earth's surface as the satellite cloud and atmosphere data and aerosol climatology data are available globally. Furthermore, all of the input data are standard variables in climate models and so this method can be used to predict tilted irradiance in future climate experiments. (C) 2015 Elsevier Ltd. All rights reserved.