h-index

The h-index is computed from a citation list by sorting papers by citation count in descending order and finding the largest h where the h-th paper has at least h citations. It conflates productivity and impact in a single integer. The metric is field-dependent (citation cultures and densities differ widely), time-dependent (it can only grow), database-dependent (Google Scholar, Scopus and Web of Science return different values), and insensitive to highly cited outliers above the threshold. Responsible-assessment frameworks (DORA, Leiden Manifesto, CoARA, Hong Kong Principles) explicitly caution against using h-index for hiring, promotion or funding decisions.

How to calculate the h-index, step by step

1. Pull a complete list of a researcher’s publications together with each paper’s total citation count, from a single database (Google Scholar, Scopus, or Web of Science — do not mix sources, since they index different content and will produce different h values for the same person).
2. Sort the papers by citation count, highest to lowest.
3. Rank the sorted list 1, 2, 3…n.
4. Walk down the ranked list and find the largest rank position h at which the citation count is still greater than or equal to h. That number is the h-index.

Equivalently: a researcher has an h-index of h if h of their papers have each been cited at least h times, and the rest have been cited fewer than h times each. Plotting citation count (y-axis) against papers ranked by citation count (x-axis) and reading off where the descending citation curve crosses the diagonal line y = x is the same calculation in graphical form — the h-index is the coordinate of that crossing point.

Worked example

Suppose a researcher has published six papers with these citation counts, already sorted highest to lowest: 42, 23, 19, 8, 5, 1.

Rank	Citations	Citations ≥ rank?
1	42	Yes (42 ≥ 1)
2	23	Yes (23 ≥ 2)
3	19	Yes (19 ≥ 3)
4	8	Yes (8 ≥ 4)
5	5	Yes (5 ≥ 5)
6	1	No (1 < 6)

The largest rank at which the condition still holds is rank 5 (5 citations ≥ rank 5), and rank 6 fails it (1 citation < rank 6). This researcher’s h-index is therefore 5: five of their papers have at least five citations each, and the sixth paper’s single citation doesn’t count toward a sixth.

This worked example is illustrative — a generic numeric case constructed to show the mechanics, not a real researcher’s actual publication record.

Note what the calculation ignores: it doesn’t matter that the top paper has 42 citations rather than, say, 6 — once a paper clears the rank-h bar, additional citations above that bar don’t raise the h-index any further. That insensitivity to high-end outliers is one of the metric’s known limitations, addressed on this page’s companion entry on what counts as a good h-index for a given field and career stage.

References

• Hirsch JE, PNAS 102(46):16569-16572, 2005. Bornmann L & Daniel HD ‘The state of h index research’, 2009.