We extend the pioneering work of J.E. Hirsch, the inventor of the h-index, by proposing a simple and seemingly robust approach for comparing the scientific productivity and visibility of institutions. Our main findings are that i) while the h-index is a sensible criterion for comparing scientists within a given field, it does not directly extend to rank institutions of disparate sizes and journals, ii) however, the h-index, which always increases with paper population, has an universal growth rate for large numbers of papers; iii) thus the h-index of a large population of papers can be decomposed into the product of an impact index and a factor depending on the population size, iv) as a complement to the h-index, this new impact index provides an interesting way to compare the scientific production of institutions (universities, laboratories or journals).
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