The Kardashian Index is a measure of the discrepancy between an academic's social media profile and publication record based on the direct comparison of numbers of citations and Twitter followers.
The Kardashian Index (K-index) can be calculated as follows:
K - index = F(a) / F(c)
F(a) is the actual number of Twitter followers of academic X. F(c) is the number academic X should have given their citations C; given a trend identified in the original paper, it is calculated as:
F = 43.3C0.32
The author of the index says that "a high K-index is a warning to the community that researcher X may have built their public profile on shaky foundations, while a very low K-index suggests that a scientist is being undervalued. ... those people whose K-index is greater than 5 can be considered 'Science Kardashians'.