What is the Shannon Diversity Index?
The Shannon diversity index (often written H or H′) is a widely used measure of biodiversity in ecology. It combines two components of a community: species richness (how many different species are present) and evenness (how equally individuals are distributed among those species). A community with many species in balanced proportions scores high; one dominated by a single species scores low.
How to use this calculator
Enter the number of individuals counted for each species, separated by commas — for example 40, 30, 20, 10. The calculator finds the total number of individuals, converts each count into a proportion, and applies the Shannon formula. It also reports the number of species (\(S\)), the total count (\(N\)), and Pielou's evenness (\(J\)), which scales \(H\) between 0 and 1.
The formula explained
For each species \(i\), the proportion is \(p_i = n_i / N\), where \(n_i\) is that species' count and \(N\) is the grand total. The index is then:
$$H = -\sum_{i=1}^{S} p_i \ln p_i$$
This calculator uses the natural logarithm (\(\ln\)), so \(H\) is expressed in "nats." Evenness is \(J = H / \ln(S)\).
Worked example
Suppose you count four species: 40, 30, 20, and 10 individuals (\(N = 100\)). The proportions are 0.4, 0.3, 0.2, 0.1. Then $$H = -(0.4\cdot\ln 0.4 + 0.3\cdot\ln 0.3 + 0.2\cdot\ln 0.2 + 0.1\cdot\ln 0.1) \approx 1.2799.$$ With \(S = 4\), \(\ln(4) = 1.3863\), so evenness \(J \approx 0.923\) — a fairly even community.
FAQ
What is a "good" H value? \(H\) usually ranges from about 1.5 to 3.5 in real ecosystems; values above 3 indicate very high diversity. There is no fixed maximum because it depends on richness.
Should I use ln or log10? Both are used in the literature. This tool uses the natural log (\(\ln\)), the most common convention. Results in different log bases differ by a constant factor.
What does evenness tell me? Pielou's evenness \(J\) ranges from 0 to 1. A value near 1 means individuals are spread almost equally across species; a low value signals dominance by a few species.
