Shannon Diversity Index Calculator

Shannon Diversity Index Calculator

Calculate the Shannon-Wiener diversity index (H), species richness (k), and Pielou evenness (E) from population counts in an ecological community. Enter species names and individual counts to measure how diverse and evenly distributed the community is.

Shannon diversity index formula

The Shannon-Wiener diversity index is defined as:

$$H = -\sum_{i=1}^{k} p_i \ln(p_i)$$

Where $p_i = n_i / N$ is the proportion of individuals belonging to species $i$, $n_i$ is the count for that species, $N$ is the total number of individuals, and $k$ is species richness (the number of species present).

Evenness and related metrics

Pielou's evenness compares observed diversity to the maximum possible for $k$ species:

$$E = \frac{H}{\ln(k)}$$

Evenness ranges from 0 to 1, where values closer to 1 indicate more equal abundance across species. The average population size is simply $N / k$.

Choosing a logarithm base

The natural logarithm (base $e$) is standard in ecology and produces values in nats. Base 2 gives bits (common in information theory), and base 10 gives dits. The relative ranking of communities is unchanged; only the numeric scale differs.

Example calculation

A rainforest survey finds 5 scarlet macaws, 12 blue morpho butterflies, 2 capybaras, 5 three-toed sloths, and 1 jaguar ($N = 25$, $k = 5$):

$$H = -(0.2 \ln 0.2 + 0.48 \ln 0.48 + 0.08 \ln 0.08 + 0.2 \ln 0.2 + 0.04 \ln 0.04) \approx 1.33$$

$$E = \frac{1.33}{\ln 5} \approx 0.83$$

For related ecology tools, see the Carrying Capacity Calculator or the Lotka-Volterra Calculator.