Mental calculation is a complex cognitive operation that is composed of a set of distinct functional processes. Using functional magnetic resonance imaging (fMRI), we mapped brain activity in healthy subjects performing arithmetical tasks and control tasks evoking a comparable load on visuo-constructive, linguistic, attentional and mnemonic functions. During calculation, as well as non-mathematical tasks, similar cortical networks consisting of bilateral prefrontal, premotor and parietal regions were activated, suggesting that most of these cortical areas do not exclusively represent modules for calculation but support more general cognitive operations that are instrumental but not specific to mental arithmetic. Significant differences between calculation and the non-mathematical tasks were found in parietal sub-regions, where non-arithmetic number or letter substitution tasks preferentially activated the superior parietal lobules whereas calculation predominantly elicited activation of the left dorsal angular gyrus and the medial parietal cortices. We interpret the latter activations to reflect sub-processes of mental calculation that are related to the processing of numerical representations during exact calculation and to arithmetical fact retrieval. Finally, we found that more complex calculation tasks involving the application of calculation rules increased activity in left inferior frontal areas that are known to subserve linguistic and working memory functions. Taken together, these findings help to embed the specific cognitive operation of calculation into a neural framework that provides the required set of instrumental components. This result may further inform the cognitive modeling of calculation and adds to the understanding of neuropsychological deficit patterns in patients.