# H-index

The **h-index** is an author-level bibliometric indicator defined by Jorge E. Hirsch, a physicist at the [University of California, San Diego](https://www.edgepedia.org/university-of-california-san-diego), as the number of papers by a researcher that have each received at least that number of citations: a scientist has index h if h of their N_p papers have at least h citations each and the remaining N_p − h papers have at most h citations each.<sup>[1](https://pmc.ncbi.nlm.nih.gov/articles/PMC1283832/)</sup> It combines two things a raw citation count cannot separate: how much a researcher has published and how much attention that work has received.<sup>[2](https://jkms.org/pdf/10.3346/jkms.2018.33.e139)</sup> Hirsch proposed it in a 2005 paper in the *Proceedings of the National Academy of Sciences* as a single, simple number for characterizing scientific output in contexts such as faculty recruitment, advancement, and grant award.<sup>[1](https://pmc.ncbi.nlm.nih.gov/articles/PMC1283832/)</sup>

| Key fact | Detail |
|---|---|
| Definition | A researcher has index h if h of their papers have at least h citations each and the other papers have at most h citations each<sup>[1](https://pmc.ncbi.nlm.nih.gov/articles/PMC1283832/)</sup> |
| Origin | Proposed by J. E. Hirsch (Department of Physics, UC San Diego); received 15 August 2005, published *PNAS* 102(46):16569–16572, November 2005<sup>[1](https://pmc.ncbi.nlm.nih.gov/articles/PMC1283832/)</sup> |
| Reception | Nature and Science both reported on the preprint shortly after it appeared on arXiv in August 2005<sup>[3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2613214/)</sup> |
| Where it is shown | Displayed automatically on author profiles in Scopus and Web of Science; Google Scholar and Vidwan also compute it, with Google Scholar values typically higher than Scopus or Web of Science<sup>[2](https://jkms.org/pdf/10.3346/jkms.2018.33.e139)</sup><sup> • </sup><sup>[4](https://pmc.ncbi.nlm.nih.gov/articles/PMC10771139/)</sup> |
| Key property | By definition the h-index cannot decrease, and it is only weakly sensitive to further citations received<sup>[3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2613214/)</sup> |
| Main criticisms | Field-dependence, sensitivity to self-citations and co-authorship, disadvantage to early-career researchers, and dependence on the coverage of the citation database used<sup>[3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2613214/)</sup><sup> • </sup><sup>[4](https://pmc.ncbi.nlm.nih.gov/articles/PMC10771139/)</sup> |

## Calculation

The index is the largest number h such that a researcher has at least h papers with at least h citations each.<sup>[5](https://bibliometrics-quick-notes.github.io/Bibliometrics-Quick-Notes.pdf)</sup><sup> • </sup><sup>[18](https://guides.lib.uiowa.edu/measuring-impact/author)</sup> With citation counts of 10, 8, 3, and 1, the h-index is 3, because three papers have at least three citations each. A lower bound on the total citations of the h most-cited papers is \( h^{2} \); total citations are usually larger, and Hirsch related them through a proportionality constant \( a \) in \( N_{c,\mathrm{tot}} \approx a \cdot h^{2} \), which he established empirically to vary between 3 and 5.<sup>[1](https://pmc.ncbi.nlm.nih.gov/articles/PMC1283832/)</sup><sup> • </sup><sup>[6](https://pmc.ncbi.nlm.nih.gov/articles/PMC2669244/)</sup>

Hirsch developed the index from a study of physicists, but suggested it should be useful in other scientific disciplines as well.<sup>[1](https://pmc.ncbi.nlm.nih.gov/articles/PMC1283832/)</sup> In his 2005 data, the highest h among the physicists examined belonged to E. Witten, at 110, meaning 110 papers with at least 110 citations each.<sup>[1](https://pmc.ncbi.nlm.nih.gov/articles/PMC1283832/)</sup>

## Spread and adoption

The proposal circulated quickly. Hirsch submitted the paper to the arXiv preprint server in August 2005, and both *[Nature](https://www.edgepedia.org/nature-journal)* and *[Science](https://www.edgepedia.org/science-journal)* reported on it shortly afterward; at the initiative of Manuel Cardona, emeritus professor at the Max Planck Institute for Solid State Research in [Stuttgart](https://www.edgepedia.org/stuttgart) and a member of the US National Academy of Sciences, a revised version appeared in *PNAS* a few weeks later.<sup>[3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2613214/)</sup> The h index was put forward as an alternative to other bibliometric measures, including publication counts, mean citation counts, and total citations.<sup>[3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2613214/)</sup>

Today the h-index is one of the most widely used research metrics. It is easy to calculate and understandable for non-experts, and it is displayed automatically on author profiles in citation databases such as Scopus and [Web of Science](https://www.edgepedia.org/web-of-science).<sup>[2](https://jkms.org/pdf/10.3346/jkms.2018.33.e139)</sup> Recruiting agencies and grant-approving bodies use it as one indication of a researcher's output, which makes it practical for authors to know how their own value is computed.<sup>[4](https://pmc.ncbi.nlm.nih.gov/articles/PMC10771139/)</sup>

## Database dependence

The same researcher has different h-index values in different databases. [Google Scholar](https://www.edgepedia.org/google-scholar), Scopus, Web of Science, and Vidwan each index a different set of documents and count citations differently, and one's h-index is usually higher in Google Scholar than in Scopus or Web of Science.<sup>[4](https://pmc.ncbi.nlm.nih.gov/articles/PMC10771139/)</sup> Mixing citation counts pulled from different sources into one list produces a number that corresponds to no real database's h-index, so comparisons should use a single source consistently.<sup>[7](https://www.casrai.org/guides/how-to-calculate-h-index)</sup> The metric is also affected by the accuracy of the citation database used for its calculation, and databases may not include all relevant citations.<sup>[8](https://www.ajnr.org/content/ajnr/31/5/783.full.pdf)</sup><sup> • </sup><sup>[4](https://pmc.ncbi.nlm.nih.gov/articles/PMC10771139/)</sup>

## Criticisms

Bibliometricians have identified several systematic limitations:<sup>[3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2613214/)</sup>

- Field dependence. Like most pure citation measures, the h-index is field-dependent, because citation practices differ between fields and subfields, which can make comparisons across disciplines unfair.<sup>[3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2613214/)</sup><sup> • </sup><sup>[4](https://pmc.ncbi.nlm.nih.gov/articles/PMC10771139/)</sup>
- Self-citations and co-authors. Citations to a researcher's own work are included and can inflate the index, and the number of co-authors can influence the number of citations received.<sup>[3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2613214/)</sup><sup> • </sup><sup>[4](https://pmc.ncbi.nlm.nih.gov/articles/PMC10771139/)</sup> The h-index does not take into account the number of authors in each publication, so each author takes full credit for a multi-authored paper's citations.<sup>[9](https://link.springer.com/article/10.1007/s11192-022-04323-8)</sup>
- Career stage. In its original setting the index puts newcomers at a disadvantage, since both publication output and observed citation rates are relatively low early in a career.<sup>[3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2613214/)</sup>
- Insensitivity. The h-index can never decrease and is only weakly sensitive to the number of citations received, so it cannot register changes in performance.<sup>[3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2613214/)</sup> It is heavily driven by earlier papers and can penalize researchers who took a career break or spent time teaching or in industry even when their current record is strong.<sup>[10](https://library-guides.ucl.ac.uk/research-metrics/h-index)</sup>
- What it ignores. It concentrates on overall citations and neglects single important contributions, does not consider the context of citations, and does not capture contributions to teaching and service.<sup>[8](https://www.ajnr.org/content/ajnr/31/5/783.full.pdf)</sup><sup> • </sup><sup>[4](https://pmc.ncbi.nlm.nih.gov/articles/PMC10771139/)</sup> An author with one or a few foundational papers is not rewarded by the calculation, whereas scientists with many moderately cited publications are favored.<sup>[11](https://direct.mit.edu/qss/article/4/3/756/115876/The-ha-index-The-average-citation-h-index)</sup>

Because of these limits, commentators recommend using the h-index together with other metrics and qualitative evaluation rather than as a single measure of productivity and impact.<sup>[4](https://pmc.ncbi.nlm.nih.gov/articles/PMC10771139/)</sup> The DORA (San Francisco Declaration on Research Assessment) guidance on responsible metric use, published in 2024, sets out five principles for any indicator, including the h-index: be clear, be transparent, be specific, be contextual, and be fair.<sup>[12](https://sfdora.org/resource/guidance-on-the-responsible-use-of-quantitative-indicators-in-research-assessment/)</sup> The Leiden Manifesto likewise cautions against inappropriate indicator use and recommends that quantitative assessment supplement, not replace, expert judgment.<sup>[13](https://link.springer.com/article/10.1007/s11192-026-05552-x)</sup><sup> • </sup><sup>[14](https://www.datocms-assets.com/22590/1619993143-mapping-of-the-literature.pdf)</sup>

## Variants

The limitations have produced numerous h-index variants.<sup>[3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2613214/)</sup> The **m quotient**, computed by dividing the h-index by the number of years active since the first published paper, avoids the bias toward senior scientists with longer careers and more publications.<sup>[3](https://pmc.ncbi.nlm.nih.gov/articles/PMC2613214/)</sup> The **g-index**, proposed by Leo Egghe, is defined like the h-index but gives more weight to highly cited articles by assuming the top g articles have received at least g² citations in total.<sup>[15](https://bmjopen.bmj.com/content/9/3/e025320.full.pdf)</sup> The **contemporary h-index** weights recent articles more heavily, and the **AW-index** adjusts for the age of each individual paper.<sup>[8](https://www.ajnr.org/content/ajnr/31/5/783.full.pdf)</sup> To account for shared authorship, the **multi-authored h-index** modifies the original metric, the fractional **h_i-index** distributes each publication's citations among its authors, and the **hm-index** applies fractional credit based on document-level authorship counts.<sup>[8](https://www.ajnr.org/content/ajnr/31/5/783.full.pdf)</sup><sup> • </sup><sup>[9](https://link.springer.com/article/10.1007/s11192-022-04323-8)</sup><sup> • </sup><sup>[16](https://www.frontiersin.org/journals/research-metrics-and-analytics/articles/10.3389/frma.2026.1793664/pdf)</sup> A review of h-index variants also documents the **c-index** family, which adds bonus points reflecting an author's position in the authorship list of the papers in the h-core.<sup>[17](https://pmc.ncbi.nlm.nih.gov/articles/PMC6044490/)</sup>

## References

1. [J. E. Hirsch (2005). An index to quantify an individual's scientific research output. *PNAS* 102(46):16569–16572.](https://pmc.ncbi.nlm.nih.gov/articles/PMC1283832/)
2. [Gasparyan, A. Y. et al. (2018). Researcher and Author Impact Metrics. *Journal of Korean Medical Science* 33:e139.](https://jkms.org/pdf/10.3346/jkms.2018.33.e139)
3. [Bornmann, L. et al. (2008). The state of h index research. Is the h index the ideal way to measure research performance?](https://pmc.ncbi.nlm.nih.gov/articles/PMC2613214/)
4. [Mondal, H. et al. (2023). The h-Index: Understanding its predictors, significance, and criticism. *Journal of Education and Health Promotion* 12:2531.](https://pmc.ncbi.nlm.nih.gov/articles/PMC10771139/)
5. [Bibliometrics Quick Notes: the Hirsch index.](https://bibliometrics-quick-notes.github.io/Bibliometrics-Quick-Notes.pdf)
6. [van Rooij, J. M. et al. (2008). The Hirsch-index: a simple, new tool for the assessment of scientific output of individual scientists.](https://pmc.ncbi.nlm.nih.gov/articles/PMC2669244/)
7. [How to Calculate the h-Index (Step-by-Step), CASRAI Guides.](https://www.casrai.org/guides/how-to-calculate-h-index)
8. [Perspectives, *AJNR* 31(5):783 (2010).](https://www.ajnr.org/content/ajnr/31/5/783.full.pdf)
9. [Bi, H. H. (2022). Four problems of the h-index for assessing the research productivity and impact of individual authors. *Scientometrics* 128:2677–2691.](https://link.springer.com/article/10.1007/s11192-022-04323-8)
10. [The h-index, Research metrics guide, UCL Library Services.](https://library-guides.ucl.ac.uk/research-metrics/h-index)
11. [The ha-index: The average citation h-index. *Quantitative Science Studies* 4(3):756 (2023).](https://direct.mit.edu/qss/article/4/3/756/115876/The-ha-index-The-average-citation-h-index)
12. [Guidance on the responsible use of quantitative indicators in research assessment, DORA (2024).](https://sfdora.org/resource/guidance-on-the-responsible-use-of-quantitative-indicators-in-research-assessment/)
13. [Thelwall, M. (2026). Large language models and responsible research evaluation: an extension of the Leiden Manifesto. *Scientometrics*.](https://link.springer.com/article/10.1007/s11192-026-05552-x)
14. [Mapping of the literature on research assessment reform.](https://www.datocms-assets.com/22590/1619993143-mapping-of-the-literature.pdf)
15. [Modified versions of the h-index, *BMJ Open* 9:e025320 (2019).](https://bmjopen.bmj.com/content/9/3/e025320.full.pdf)
16. [Beyond cumulative impact: the he-index and a volume-normalized efficiency metric for research evaluation. *Frontiers in Research Metrics and Analytics* (2026).](https://www.frontiersin.org/journals/research-metrics-and-analytics/articles/10.3389/frma.2026.1793664/pdf)
17. [c-index and Subindices of the h-index: New Variants of the h-index to Account for Variations in Author Contribution.](https://pmc.ncbi.nlm.nih.gov/articles/PMC6044490/)
18. [University Libraries, The University of Iowa](https://guides.lib.uiowa.edu/measuring-impact/author)

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*Topic: Encyclopedia › Society and history › Broadcasting and journalism › Periodicals and publishing › Publishing and publishing houses › Scholarly publishing and journals infrastructure › Peer review, metrics, and publication ethics › Bibliometrics and citation analysis*

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