---
title: "h-index: formula, variables and example"
description: "h-index explained: variables, a worked example, related methods and assumptions. The largest h such that h of a researcher's (or journal's) papers have at least h citations each."
url: https://scholar4ai.com/equations/h-index
markdown_url: https://scholar4ai.com/equations/h-index.md
license: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/)
share_text: "h-index explained: variables, a worked example, related methods and assumptions. The largest h such that h of a researcher's (or journal's) papers have at least h citations each. (as of 2026-11-05)"
data_url: https://scholar4ai.com/data/rankings.json
updated: 2026-11-05T06:02:37+09:00
window: 2026-10-07 to 2026-11-05
source: OpenAlex (CC0)
---

# h-index

$$
h = \max\{\, i : c_{(i)} \ge i \,\}
$$

The largest h such that h of a researcher's (or journal's) papers have at least h citations each.

- area: Bibliometrics
- 0 papers in the last 7 days
- Names searched for: Hirsch index, h-index, h index

Back to the ranking: https://scholar4ai.com/rankings/equations.md

## Variables and notation

c_(i) is the ith largest citation count; h is the largest rank i whose paper has at least i citations.

## Worked example

For sorted citations (10,8,5,3,1), the third paper has at least 3 citations but the fourth fewer than 4, so h=3.

## Related methods and when to use them

h-index combines output and citation thresholds; total citations are more sensitive to highly cited outliers. It depends on database coverage, field and time since publication and is not a per-paper quality score.

## Sources and further reading

- [An index to quantify an individual scientific research output](https://arxiv.org/abs/physics/0508025)

Examples use illustrative inputs, not observed research results. Logarithms are natural unless stated otherwise. Guide updated 2026-11-05. Prepared by Scholar4AI. [Editorial and verification policy](/editorial-policy).

## Key findings

- No paper of the tracked journals mentioned h-index in the last 30 days (2026-10-07 to 2026-11-05).
- From Nov 2023 to Oct 2026, 95 archived papers mentioned h-index in their title, abstract, keywords or full text, most of them in Mar 2026 (7).
- From 2017 to 2026 (so far), h-index was mentioned in 340 papers in the tracked journals, most of them in higher education and research (255), management (21) and AI (18).
- 26 of them were published in 2025, against 31 in 2017.
- Since 2023, the institutions with the most of these papers were Nanjing University (5), Shifa Tameer-e-Millat University (5) and HUN-REN Research Centre for Natural Sciences (3).
- The journals publishing most of them were Scientometrics (45), Journal of Informetrics (16) and Future Business Journal (7).
- The most-cited of them is “A bibliometric-based survey on AHP and TOPSIS techniques” (Expert Systems with Applications, 2017), with 491 citations.

## Mentions over 36 months

*Papers mentioning it by publication month, Nov 2023 to Oct 2026 (titles, abstracts, keywords and full texts)*

| Trend | Nov 23–Oct 24 | Nov 24–Oct 25 | Nov 25–Oct 26 | 36 months |
|---|---:|---:|---:|---:|
|  | 25 | 32 | 38 | 95 |

## Papers per year

*Papers per publication year and category*

| Category | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 | 2025 | 2026 (so far) |
|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|
| [Higher Education and Research](https://scholar4ai.com/categories/higher-education-and-research.md) | 23 | 33 | 43 | 36 | 31 | 22 | 20 | 11 | 14 | 22 |
| [Management](https://scholar4ai.com/categories/management.md) | 1 | 0 | 1 | 0 | 1 | 1 | 2 | 6 | 5 | 4 |
| [AI](https://scholar4ai.com/categories/ai.md) | 3 | 0 | 1 | 0 | 1 | 1 | 2 | 3 | 2 | 5 |
| [Health Economics and Policy](https://scholar4ai.com/categories/health-economics-and-policy.md) | 4 | 2 | 2 | 1 | 2 | 1 | 0 | 0 | 0 | 1 |
| [Economics](https://scholar4ai.com/categories/economics.md) | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 3 | 2 | 1 |
| [Information Systems](https://scholar4ai.com/categories/information-systems.md) | 0 | 2 | 1 | 2 | 0 | 0 | 2 | 0 | 0 | 1 |
| [Operations Research](https://scholar4ai.com/categories/operations-research.md) | 0 | 2 | 0 | 1 | 1 | 0 | 0 | 2 | 0 | 0 |
| [Statistics](https://scholar4ai.com/categories/statistics.md) | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 2 | 3 |
| [Finance](https://scholar4ai.com/categories/finance.md) | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
| [Tourism and Hospitality](https://scholar4ai.com/categories/tourism-and-hospitality.md) | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
| [Marketing](https://scholar4ai.com/categories/marketing.md) | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| All categories | 31 | 39 | 50 | 42 | 37 | 25 | 27 | 26 | 26 | 37 |

## Where the papers come from

*Journals with the most papers, since 2023*

| # | Journal | Papers |
|---:|---|---:|
| 1 | [Scientometrics](https://scholar4ai.com/journals/scientometrics.md) | 45 |
| 2 | [Journal of Informetrics](https://scholar4ai.com/journals/journal-of-informetrics.md) | 16 |
| 3 | [Future Business Journal](https://scholar4ai.com/journals/future-business-journal.md) | 7 |
| 4 | [Quality & Quantity](https://scholar4ai.com/journals/quality-quantity.md) | 5 |
| 5 | [The Journal of Academic Librarianship](https://scholar4ai.com/journals/the-journal-of-academic-librarianship.md) | 3 |
| 6 | [Journal of Business and Psychology](https://scholar4ai.com/journals/journal-of-business-and-psychology.md) | 3 |
| 7 | [Journal Of Big Data](https://scholar4ai.com/journals/journal-of-big-data.md) | 3 |
| 8 | [Knowledge and Information Systems](https://scholar4ai.com/journals/knowledge-and-information-systems.md) | 2 |
| 9 | [International Journal of Approximate Reasoning](https://scholar4ai.com/journals/international-journal-of-approximate-reasoning.md) | 2 |
| 10 | [Journal of the Knowledge Economy](https://scholar4ai.com/journals/journal-of-the-knowledge-economy.md) | 2 |

*Institutions with the most papers, since 2023*

| # | Institution | Papers |
|---:|---|---:|
| 1 | [Nanjing University](https://scholar4ai.com/institutions/nanjing-university.md) | 5 |
| 2 | Shifa Tameer-e-Millat University | 5 |
| 3 | HUN-REN Research Centre for Natural Sciences | 3 |
| 4 | Mahidol University | 3 |
| 5 | [Universidad de Granada](https://scholar4ai.com/institutions/universidad-de-granada.md) | 3 |
| 6 | [University of Technology Sydney](https://scholar4ai.com/institutions/university-of-technology-sydney.md) | 3 |
| 7 | Amrita Vishwa Vidyapeetham | 2 |
| 8 | [Centre National de la Recherche Scientifique](https://scholar4ai.com/institutions/centre-national-de-la-recherche-scientifique.md) | 2 |
| 9 | Children's Medical Center | 2 |
| 10 | [Dalian University of Technology](https://scholar4ai.com/institutions/dalian-university-of-technology.md) | 2 |

*Countries with the most papers, since 2023*

| # | Country | Papers |
|---:|---|---:|
| 1 | China | 19 |
| 2 | United States | 14 |
| 3 | Germany | 12 |
| 4 | Spain | 11 |
| 5 | Italy | 10 |
| 6 | India | 9 |
| 7 | United Kingdom | 8 |
| 8 | Hungary | 8 |
| 9 | Pakistan | 8 |
| 10 | Australia | 6 |

*Keywords with the most papers, since 2023*

| # | Keyword | Papers |
|---:|---|---:|
| 1 | h-index | 72 |
| 2 | bibliometric indicators | 15 |
| 3 | citation analysis | 15 |
| 4 | research evaluation | 14 |
| 5 | [research trends](https://scholar4ai.com/keywords/research-trends.md) | 14 |
| 6 | research productivity | 13 |
| 7 | citation impact | 10 |
| 8 | citation metrics | 9 |
| 9 | citation counts | 8 |
| 10 | co-authorship | 6 |

## Most-cited papers

*Most-cited papers since 2017*

| # | Citations | Per month | Title | Journal | Published | Authors |
|---:|---:|---:|---|---|---|---|
| 1 | 491 | 4.2 | [A bibliometric-based survey on AHP and TOPSIS techniques](https://doi.org/10.1016/j.eswa.2017.02.016) | [Expert Systems with Applications](https://scholar4ai.com/journals/expert-systems-with-applications.md) | 2017-02-09 | Shaher H. Zyoud, Daniela Fuchs-Hanusch |
| 2 | 437 | 4.1 | [Some bibliometric procedures for analyzing and evaluating research fields](https://doi.org/10.1007/s10489-017-1105-y) | [Applied Intelligence](https://scholar4ai.com/journals/applied-intelligence.md) | 2017-12-13 | María Gutiérrez-Salcedo, M. Ángeles Martínez, José A. Moral-Muñoz et al. |
| 3 | 368 | 3.5 | [Emerging trends and new developments in information science: a document co-citation analysis (2009–2016)](https://doi.org/10.1007/s11192-018-2695-9) | [Scientometrics](https://scholar4ai.com/journals/scientometrics.md) | 2018-03-07 | Jianhua Hou, Xiucai Yang, Chaomei Chen |
| 4 | 204 | 1.8 | [A theoretical model of the relationship between the h-index and other simple citation indicators](https://doi.org/10.1007/s11192-017-2351-9) | [Scientometrics](https://scholar4ai.com/journals/scientometrics.md) | 2017-03-20 | Lucio Bertoli Barsotti, Tommaso Lando |
| 5 | 201 | 2.3 | [Software survey: ScientoPy, a scientometric tool for topics trend analysis in scientific publications](https://doi.org/10.1007/s11192-019-03213-w) | [Scientometrics](https://scholar4ai.com/journals/scientometrics.md) | 2019-08-30 | Juan Ruiz-Rosero, Gustavo Ramírez-González, Jesus Viveros-Delgado |
| 6 | 144 | 1.9 | [Bibliometric mapping of mobile learning](https://doi.org/10.1016/j.tele.2020.101491) | [Telematics and Informatics](https://scholar4ai.com/journals/telematics-and-informatics.md) | 2020-08-26 | İdris Göksu |
| 7 | 137 | 1.2 | [A bibliometric analysis of leading universities in innovation research](https://doi.org/10.1016/j.jik.2017.03.006) | [Journal of Innovation & Knowledge](https://scholar4ai.com/journals/journal-of-innovation-knowledge.md) | 2017-06-22 | Christian A. Cancino, José M. Merigó, Freddy Coronado |
| 8 | 123 | 3.9 | [Artificial intelligence and multimodal data fusion for smart healthcare: topic modeling and bibliometrics](https://doi.org/10.1007/s10462-024-10712-7) | [Artificial Intelligence Review](https://scholar4ai.com/journals/artificial-intelligence-review.md) | 2024-03-15 | Xieling Chen, Haoran Xie, Xiaohui Tao et al. |
| 9 | 117 | 1.3 | [Predicting citation counts based on deep neural network learning techniques](https://doi.org/10.1016/j.joi.2019.02.011) | [Journal of Informetrics](https://scholar4ai.com/journals/journal-of-informetrics.md) | 2019-03-11 | Ali Abrishami, Sadegh Aliakbary |
| 10 | 97 | 1.1 | [Methods to account for citation inflation in research evaluation](https://doi.org/10.1016/j.respol.2019.04.009) | [Research Policy](https://scholar4ai.com/journals/research-policy.md) | 2019-04-30 | Alexander Michael Petersen, Raj Kumar Pan, Fabio Pammolli A et al. |

Archive counts by publication year: a paper counts when its title, abstract or keywords name the equation, or when OpenAlex's full-text search finds it there (searched for the last 30 days' papers and, by a pass over the past years, for older ones). Names added to the list later are looked for in older papers as the archive is read again.

*Papers mentioning h-index, newest first.*

| Date | Title | Journal | Authors | Affiliations |
|---|---|---|---|---|

## Cite this page

Scholar4AI. (2026). h-index. Journal and Conference Research Rankings. Retrieved November 5, 2026, from https://scholar4ai.com/equations/h-index

```bibtex
@misc{scholar4ai-equations-h-index,
  author = {{Scholar4AI}},
  title = {h-index},
  year = {2026},
  howpublished = {\url{https://scholar4ai.com/equations/h-index}},
  urldate = {2026-11-05},
  note = {Journal and Conference Research Rankings; data from OpenAlex (CC0); licensed CC BY-NC 4.0}
}
```

License: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/).