Grid computing has gained considerable attention in research and industry. High expectations are associated with the approach. However, so far only few papers have been published about the costs caused by Grid computing. In this article we pursue two main goals: to analyze the different types of costs and to determine the total costs of a resource provider. Our approach is based on the discussion of general cost categories that have to be taken into account. We give concrete numbers for the different categories and use these numbers to estimate the costs in two real life Grids: the EGEE project and the Grid of the pharmaceutical company Novartis. A summarizing discussion concludes the paper.