An index to quantify an individual’s scientific research output

F the few scientists who earn a Nobel prize, the impact and relevance of their research is unquestionable. Among the rest of us, how does one quantify the cumulative impact and relevance of an individual’s scientific research output? In a world of limited resources, such quantification (even if potentially distasteful) is often needed for evaluation and comparison purposes (e.g., for university faculty recruitment and advancement, award of grants, etc.). The publication record of an individual and the citation record clearly are data that contain useful information. That information includes the number (Np) of papers published over n years, the number of citations (Nc j ) for each paper (j), the journals where the papers were published, their impact parameter, etc. This large amount of information will be evaluated with different criteria by different people. Here, I would like to propose a single number, the ‘‘h index,’’ as a particularly simple and useful way to characterize the scientific output of a researcher. A scientist has index h if h of his or her Np papers have at least h citations each and the other (Np h) papers have h citations each. The research reported here concentrated on physicists; however, I suggest that the h index should be useful for other scientific disciplines as well. (At the end of the paper I discuss some observations for the h index in biological sciences.) The highest h among physicists appears to be E. Witten’s h, which is 110. That is, Witten has written 110 papers with at least 110 citations each. That gives a lower bound on the total number of citations to Witten’s papers at h2 12,100. Of course, the total number of citations (Nc,tot) will usually be much larger than h2, because h2 both underestimates the total number of citations of the h most-cited papers and ignores the papers with h citations. The relation between Nc,tot and h will depend on the detailed form of the particular distribution (1), and it is useful to define the proportionality constant a as