The H-index is an author-level indicator, an easily computable index giving an estimate of the significance and broad impact of a researcher's cumulative scientific contributions. Citation counts for authors is also an author-level indicator.
But note that publication and citation data can be influenced by many factors such as a researcher's age, career stage or discipline. It can be difficult to "measure" the impact of an individual researcher or a research group in a discipline or society, and comparing citation counts of different authors may only be done with care within the same, focused (i.e., narrow) subject area and at approximately the same career point.
Make sure that your profile in the database is correct and up-to-date, so your publications are identified as yours and your author-level indicators can be as correct as possible. Sign up and use your ORCID ID to allow publishers and databases to distinguish you from other researchers. See Create and connect your ORCID ID in Haris.
The H-index is a quantitative bibliometric indicator for authors. An author′s h-index is the number of publications (h) by the author which have been cited at least h number of times. For example, if an author has published 53 articles, of which 15 have been cited 15 or more times, that author′s h-index is 15.
The index was suggested in 2005 by Jorge E. Hirsch, a physicist at UC San Diego, and is thus also called the Hirsch index or Hirsch number (Hirsch, J. E.. 2005, "An index to quantify an individual's scientific research output," Proceedings of the National Academy of Sciences of the United States of America, vol. 102, no. 46, pp. 16569-16572, https://doi.org/10.1073/pnas.0507655102).
H-index is not normalized by field and should not be used to compare different disciplines. It also disadvantages early career researchers. It can only be used to compare researchers with the same career length and within the same discipline.
Choosing "Author search" in Web of Science and Scopus, or searching on an author's name in Google Scholar, you can find the author's H-index as well as citation count for the author.
See Web of Science instructions: how to create citation report with h-index by the University of Helsinki.
See also Evaluation based on scientific publishing: H-index by the University of Oulu.
Choosing "Author search" in Web of Science and Scopus, or searching on an author's name in Google Scholar, you will find the citation count for the author.
In Scopus, for example, you find "Tiotal citations" under "Author details" page:
By clicking "View citation overview" in Scopus, you can remove self-citations from the count.