An h-index is not a score somebody assigns you. It is a count, and you can do it by hand in about a minute if you have that researcher’s papers sorted by citations.
The part that catches people out is what the count is taken over. It is taken over one database’s idea of which papers exist and who has cited them, and no two databases agree on that. So a researcher does not have an h-index. They have one per place you looked, and a bare number with no source attached cannot be checked by anyone.
What an h-index counts
Hirsch introduced the index in 2005 with a definition that is worth reading slowly:
A scientist has index h if h of his or her Np papers have at least h citations each and the other (Np − h) papers have ≤ h citations each.
Google Scholar states the same rule more plainly for a publication: the h-index is the largest number h such that at least h articles were cited at least h times each. Their example is a publication with five articles cited 17, 9, 6, 3 and 2 times, which has an h-index of 3.
Check that against the definition. Three articles (17, 9 and 6) were cited at least three times each. A fourth would need at least four citations, and the fourth article has three. So the count stops at 3.
Two consequences fall straight out of the arithmetic, before any argument about whether the index is a good idea:
- The h-index can never exceed the number of papers. Someone with six papers cannot have an h-index above 6, however often those six are cited.
- It can never go down. Citations only accumulate, so the count only ever moves one way.
Count it yourself in one minute
You need one thing: that researcher’s papers with a citation count each, sorted from most cited to least. Then walk down the list.
Suppose the sorted counts are 41, 22, 9, 7, 5, 3 and 1. Number the rows as you go, and compare each row’s position with its citation count:
| Position | Citations | Is citations ≥ position? |
|---|---|---|
| 1 | 41 | yes |
| 2 | 22 | yes |
| 3 | 9 | yes |
| 4 | 7 | yes |
| 5 | 5 | yes |
| 6 | 3 | no |
The last row where the answer is still yes gives you the index. Here it is position 5, so the h-index is 5. You can stop reading the list at the first “no” — nothing further down can change the answer.
Why the same researcher has more than one h-index
Now the part that makes a bare number useless.
The count depends entirely on the paper set you counted over, and no two databases hold the same set. Martín-Martín and colleagues compared citation coverage across 252 subject categories and found Google Scholar located 93–96% of citations in every area, against 35–77% for Scopus and 27–73% for Web of Science. Those missing citations are not spread evenly — each one that is absent can drop a row below the line and take a point off the index.
The vendors document the mechanism themselves. Clarivate states that the aggregate metrics on a Web of Science researcher profile are derived from citations to that author’s Core Collection papers only, so a paper that Web of Science indexes in another of its databases can carry citations that never reach the profile total. Elsevier notes that Scopus is still adding pre-1996 cited references going back to 1970, and says plainly that “the h-index might increase over time” as a result — the same author, the same papers, a larger number next year.
You do not even have to compare two vendors. Google Scholar reports two h-indexes for the same person on the same screen: it computes, in its own words, “two versions, All and Recent, of three metrics - h-index, i10-index and the total number of citations”. Both are that researcher’s h-index. They are different numbers.
So the useful form is never “her h-index is 34”. It is “her h-index is 34 in X, as of date”, which is a claim a reader can go and check.
What the h-index cannot tell you
Four limits are worth holding on to, and none of them are reasons to throw the number away. Three of them are in Hirsch’s original paper.
It is capped by career length. Because h can never exceed the paper count, an outstanding researcher four years in is structurally unable to reach the h-index of a mediocre one thirty years in. Hirsch saw this immediately and proposed dividing by the years since the first publication: the parameter m, the slope of h against time, which he offers as a “yardstick to compare scientists of different seniority”. He measures n “from the time elapsed since their first published paper till the present”, and suggests m ≈ 1 as the mark of a successful scientist and m ≈ 2 as the mark of an outstanding one.
It is field-dependent. Hirsch expected this and said why: typical h values differ between fields according to “the average number of references in a paper in the field, the average number of papers produced by each scientist in the field, and the size (number of scientists) of the field”. Timing is a fourth axis. We measured that one across 26 fields, and the time to citation varies by a factor of 2.7 — so the same h-index at the same career stage is not the same achievement in mathematics as in cell biology. Comparing across fields without saying so is the most common misuse of the number.
It rewards large collaborations. In Hirsch’s own words, “a scientist with a high h achieved mostly through papers with many coauthors would be treated overly kindly by his or her h”, and subfields that work in big teams show larger h values for that reason alone.
It says nothing about any one paper. The index is deliberately insensitive to the tail. A single field-defining paper and a single ignored paper move it by the same amount, which is usually zero — Hirsch notes that for an author with a few seminal papers and extraordinarily high citation counts, “the h index will not fully reflect that scientist’s accomplishments”.
Hirsch put the summary better than any of his critics did: “a single number can never give more than a rough approximation to an individual’s multifaceted profile, and many other factors should be considered in combination in evaluating an individual.”
Getting the sorted list without a subscription
Everything above needs the same input: that researcher’s papers, each with a citation count, sorted. That is the part that is annoying to assemble by hand, because the papers are spread across databases and several of the tidy ones are behind an institutional licence.
Litlas publishes an author page for researchers in its index, readable without an account. It lists that researcher’s papers with the citation count on each one, and a Most cited sort that puts the list straight into the order the count needs. From there you walk down the rows exactly as in the table above. The same page gives you the venue and year on each paper, so you can see at a glance whether the list is drawing on conference proceedings or journals alone.
The papers themselves come from one search across 16 scholarly sources (OpenAlex, Crossref, DataCite, OpenCitations, ROR/ORCID, arXiv, DBLP, OpenReview, ACL Anthology, PubMed, PMC Open Access, DOAJ, CORE, OpenAIRE Graph, Unpaywall and Common Crawl), and opening the citation graph on any of them shows what it cited and who has cited it since. Papers you keep go into a board with your own notes and tags, and export as BibTeX, RIS or CSL-JSON.
The free plan needs no card and works right away.
For formal evaluation exercises, use whichever database your institution has committed to, so that everyone being compared is counted in the same place.
Three things to remember
- The h-index is the largest h where h papers each have at least h citations. Sort by citations, walk down, stop at the first row whose count is below its position.
- Always write the database and the date next to the number. Google Scholar alone gives the same researcher two of them.
- It is capped by the number of papers, so it measures seniority as much as impact. That is what Hirsch’s m parameter was for.
Bibliography
- Clarivate. “Web of Science Researcher Profile: Metrics Sidebar.” https://webofscience.zendesk.com/hc/en-us/articles/25549893703313-Web-of-Science-Researcher-Profile-Metrics-Sidebar. Accessed 22 August 2026.
- Elsevier. “How can I use an h-graph?” Scopus support. https://www.elsevier.support/scopus/answer/how-can-i-use-an-hgraph. Accessed 22 August 2026.
- Google Scholar. “Google Scholar Citations.” https://scholar.google.com/intl/en/scholar/citations.html. Accessed 22 August 2026.
- Google Scholar. “Google Scholar Metrics.” https://scholar.google.com/intl/en/scholar/metrics.html. Accessed 22 August 2026.
- Hirsch, J. E. “An Index to Quantify an Individual’s Scientific Research Output.” Proceedings of the National Academy of Sciences 102, no. 46 (2005): 16569–16572. https://doi.org/10.1073/pnas.0507655102
- Martín-Martín, Alberto, Enrique Orduna-Malea, Mike Thelwall, and Emilio Delgado López-Cózar. “Google Scholar, Web of Science, and Scopus: A Systematic Comparison of Citations in 252 Subject Categories.” Journal of Informetrics 12, no. 4 (2018): 1160–1177. https://doi.org/10.1016/j.joi.2018.09.002