What is the h-index and how is it calculated?
The h-index is the largest number h such that a researcher has at least h papers cited at least h times each. Seven papers with 25, 18, 12, 9, 6, 4 and 2 citations give an h-index of 5: five papers have 5 or more citations, but there are not six with 6 or more. The physicist Jorge E. Hirsch proposed it in 2005.
Detail
Where it comes from
Hirsch published the proposal in PNAS in 2005 under the title "An index to quantify an individual's scientific research output". The idea was one number for both productivity and impact: publishing a lot without being cited does not raise it, and neither does a single very highly cited paper.
The i10-index
The i10-index is the number of papers with at least 10 citations. Google Scholar introduced it in July 2011 with Google Scholar Citations profiles. Its threshold is fixed at 10, while the threshold of the h-index grows with the researcher's output. Scopus and Web of Science do not show an i10-index; OpenAlex calculates one.
Why the number differs between databases
Scopus, Web of Science and Google Scholar index different sets of publications, so the same researcher can have three different h-indexes. An h-index quoted without the database and the date says little.
The author's own warning
In 2020 Hirsch wrote that he had come to believe the index can also fail spectacularly and have severe unintended negative consequences. It is a rough measure, not a verdict.