h-index Calculator: h-index, i10, g-index, e-index and m-quotient from Citation Counts

How it works

h = largest h such that h papers have ≥ h citations each · i10 = papers with ≥ 10 citations · g = largest g such that the top g papers have ≥ g² citations in total · e = √(citations in the h-core − h²) · m-quotient = h ÷ years since first paper · Citations to reach h = t: Σ max(0, t − cᵢ) over the top t papers

The h-index, proposed by physicist Jorge Hirsch in 2005, combines productivity and impact in one number: a researcher has index h if h of their papers have each been cited at least h times. Sort the citation counts from high to low and find the last rank where the count is still at least the rank. One blockbuster paper cannot inflate it, and neither can many uncited papers. The i10-index, shown on Google Scholar profiles, simply counts papers with ten or more citations. Leo Egghe’s g-index gives credit for very highly cited work: it is the largest g for which the top g papers together have at least g² citations, so it is always at least h. Zhang’s e-index measures the citations in the h-core beyond the h² needed to qualify, which separates two people with the same h. Hirsch’s m-quotient divides h by career length: he suggested that after 20 years an h of about 20 (m ≈ 1) marks a successful scientist, 40 (m ≈ 2) an outstanding one and 60 (m ≈ 3) a truly unique one. All of these depend on the database (Google Scholar runs higher than Scopus or Web of Science), the field, co-authorship and self-citation, so use them as one input among many.

Worked example

A researcher with 25 papers, sorted 145, 98, 67, 51, 44, 39, 31, 28, 22, 19, 17, 15, 12, 11, 9, … The 12th paper has 15 citations (≥ 12) but the 13th has 12 (< 13), so h = 12. Fourteen papers have 10 or more citations, so i10 = 14. All 25 papers together hold 638 citations, at least 25² = 625, so g = 25. The top 12 papers hold 576 citations, so e = √(576 − 144) = 20.78. Over 12 years the m-quotient is 12 ÷ 12 = 1.00. To reach h = 13, papers 12 and 13 need 0 and 1 more citation, so just 1 citation spread over 1 paper.

Sources: Wikipedia: h-index (definition, Hirsch’s benchmarks, field values, criticisms) · Harzing, Publish or Perish: definitions of h, g, e, hc, hI and AWCR · Google Scholar Metrics: h-index and h5-index definitions

Frequently asked questions