A model is presented to estimate the hourly total radiation received at the Earth's surface for cloudy atmosphere. Hourly total radiation values of the model applied for Istanbul (41.1-degrees-N, 29.0-degrees-E) are calculated based on total radiation for clear conditions, cloud cover and zenith angle. Results of the model are compared with measurements and with the other studies on the same subject. Statistical analyses of calculated and measured values are in good agreement with the mean correlation coefficients and the mean relative error are 0.956 and 13.3%, respectively. In addition, cloud transmittances are determined for different cloud types and zenith angles. The mean values of cloud transmittance are 0.25, 0.26 and 0.53 for low, middle and high cloud levels, respectively.