What is the h-index?

A h-index is a rough summary measure of a researcher’s productivity and impact. Productivity is quantified by the number of papers, and impact by the number of citations the researchers' publications have received. It can be useful for identifying the centrality of certain researchers as researchers with a higher h-index will, in general, have produced more work which is considered important by their peers.

A simple definition of the h-index

The h-index was originally defined by J. E. Hirsch in a Proceedings of the National Academy of Sciences article as the number of papers with citation number ≥ h. An h-index of 3 hence means that the author has published at least three articles, of which each has been cited at least three times.

The h-index can also simply be determined by charting the article's citation counts. The h-index is then determined by the interception of the chart's diagonal with the citation data. In this case there are 3 papers that are above the diagonal, and hence the h-index is 3.

Plotting citation count of papers to calculate the h-index
How to derive the h-index from a plot of papers ranked by their number of citations: The first n papers above (or on) the diagonal (red line) constitute the h-index. In this case the h-index is 3.

The definition of the h-index comes with quite few desirable features:

  • First, it is relatively unaffected by outliers. If e.g. the top ranked article had been cited 1,000 times, this would not change the h-index.
  • Second, the h-index will generally only increase if the researcher continues to produce good work. The h-index would increase to 4 if another paper was added with 4 citations, but would not increase if papers were added with fewer citations.
  • Third, the h-index will never be greater than the number of papers the author has published; to have an h-index of 20, the author must have published at least 20 articles which have each been cited at least 20 times.

A step-by-step outline how to calculate your h-index

  • Step 1: List all your published articles in a table.
  • Step 2: For each article gather the number it has been cited.
  • Step 3: Rank the papers by the number of times they have been cited.
  • Step 4: The h-index can now be inferred by finding the entry at which the rank in the list is greater than the number of citations.

Here is an example of a table where articles have been ranked by their citation count and the h-index has been inferred to be 3.

RankArticleTimes citedExplanation
1Article A11.
2Article B6.
3Article C4← h-index is 3
4Article D3← The citation number here is less than the article rank
5Article E3.
6Article F1.

Luckily, there are services like Scopus, Web of Science, and Google Scholar that can do the heavy lifting and automatically provide the citation count data and calculate the h-index.

Why it is important for your career to know about the h-index

The h-index is not something that needs to be calculated on a daily basis, but it's good to know where you are for several reasons. First, climbing the h-index ladder is something worth celebrating. If it's worth opening a bottle of champagne or just getting a cafe latte that's up to you, but seriously take your time to celebrate this achievement (there aren't that many in academia). But more importantly, the h-index is one of the measures funding agencies or the university's hiring committee calculate when you apply for a grant or a position. Given the often huge number of applications, the h-index is calculated in order to rank candidates and apply a pre-filter.

Of course, funding agencies and hiring committees do use tools for calculating the h-index, and so can you.

It is important to note that depending on the underlying data that these services have collected, your h-index might be different. Let's have a look at the h-index of the well known physicist Stephen W. Hawking to illustrate it:

ServiceHawking's h-index
Web of Science76
Google Scholar130

So, if you are aware of a number of citations of your work that are not listed in these databases, e.g. because they are in conference proceedings not indexed in these databases, then please state that in your application. It might give your h-index an extra boost.

Can all your academic achievements be summarized by a single number?

Definitely not! People are aware of this and there have been many attempts to address particular shortcomings of the h-index, but in the end it's just another number that is meant to emphasize or de-emphasize certain aspects of the h-index. Anyway, you have to know the rules in order to play the game, and you have to know the rules in order to change them. If you feel that your h-index does not properly reflect your academic achievements, then be pro-active and mention that in your application!