H-Index Estimator Formula

Understand the math behind the h-index estimator. Each variable explained with a worked example.

Use the H-Index Estimator

Formulas Used

Estimated H-Index

h_index_est = floor(sqrt(total_citations))

Average Citations per Paper

avg_cites = avg_citations

Total Publications

total_pubs = total_publications

Variables

VariableDescriptionDefault
total_publicationsTotal Publications50
total_citationsTotal Citations800
avg_citationsDerived value= total_citations / total_publicationscalculated

How It Works

How the H-Index Works

A researcher has an h-index of h if h of their papers have each been cited at least h times.

Estimation

An approximate h-index can be estimated as:

h ≈ floor(sqrt(Total Citations))

This approximation (Hirsch's original heuristic) works well for typical citation distributions. The exact h-index requires sorting papers by citation count.

Context

  • Early career: h = 5-10
  • Mid career: h = 15-30
  • Senior researcher: h = 30-60
  • Field leaders: h = 60+

    • Worked Example

    A researcher has 50 publications with 800 total citations.

    total_publications = 50total_citations = 800
    1. 01Average citations: 800 / 50 = 16.0 per paper
    2. 02H-index estimate: floor(sqrt(800)) = floor(28.3) = 28

    Frequently Asked Questions

    Why is this an estimate?

    The exact h-index requires the full list of citations for each paper, sorted in descending order. This formula gives a useful approximation.

    Can the h-index decrease?

    In theory no, since it only counts papers that have reached the threshold. In practice, corrections or retractions could lower it.

    How does h-index compare across fields?

    Citation rates vary enormously by field. An h-index of 20 in mathematics may be equivalent to 50 in biomedical sciences.

    Ready to run the numbers?

    Open H-Index Estimator