Shannon Diversity Index Calculator

The Shannon diversity index (H'), also called the Shannon-Wiener index, is a measure of species diversity in a community that accounts for both species richness (how many species) and evenness (how evenly individuals are distributed among species). It is calculated as H' = -sum(pi * ln(pi)), where pi is the proportion of individuals belonging to species i.

Divide each species' count by the total number of individuals to get its proportion pi, multiply each pi by its natural log, sum all those products, and negate the result. For counts of 45, 30, 15, and 10 (100 total), H' works out to approximately 1.235.

Species richness (S) is simply the number of different species present, it ignores how many individuals belong to each. H' incorporates both richness and the relative abundance of each species, so two samples with identical richness can have very different H' if one is dominated by a single species.

Evenness, also called Pielou's evenness (J = H' / ln(S)), rescales H' to a 0-1 range by dividing by the maximum possible diversity for that many species. A J close to 1 means individuals are spread almost equally across species, a low J means one or a few species dominate the community.

There is no universal threshold, H' depends heavily on the ecosystem type and sampling method. In practice, most communities score between 1.5 and 3.5, values are best compared relatively, between sites, seasons, or before-and-after a disturbance, rather than against a fixed benchmark.

The Shannon index was adapted from Claude Shannon's information entropy formula, which conventionally uses natural log (or log base 2 for bits). Ecology has standardized on natural log for H', though the choice of log base only rescales the index by a constant factor and does not change its interpretation.

No. H' is always between 0 (only one species present) and ln(S) (all species perfectly equally abundant), since each term -pi*ln(pi) is non-negative for 0 < pi <= 1, and the sum is maximized exactly when all proportions are equal.

There is no fixed rule, but small samples tend to underestimate true diversity because rare species are more likely to be missed entirely. Ecologists often use rarefaction curves alongside H' to check whether sampling effort was sufficient to capture the community's real diversity.

H' is widely used to compare biodiversity across sites, track changes in a community over time (for example, before and after habitat restoration or pollution), and assess ecosystem health, since higher, more stable diversity often correlates with a more resilient ecosystem.

The Simpson index measures the probability that two randomly selected individuals belong to different species, and is more heavily weighted toward the most abundant species. The Shannon index gives relatively more weight to rare species, making it more sensitive to species richness than Simpson's index.

Yes. The Shannon formula works on any set of mutually exclusive categories with counts, genera, habitat types, or land-use classes can all be substituted for species without changing the math, the interpretation simply shifts to diversity of that category instead.