Calculate the Shannon-Wiener diversity index and evenness for ecological communities. Enter species abundances to measure biodiversity, compare communities, and understand ecological health.
The Shannon-Wiener Diversity Index (H') is the most widely used measure of biodiversity in ecology. Originally developed by Claude Shannon for information theory (1948) and applied to ecology by Robert MacArthur, it quantifies the uncertainty in predicting the species identity of a randomly chosen individual from a community. Higher uncertainty means more diversity—a community with many equally common species has high H', while one dominated by a single species has low H'.
The formula is elegantly simple: H' = −Σ(pᵢ × ln pᵢ), where pᵢ is the proportion of individuals belonging to species i. Values typically range from 0 (monoculture) to about 4.5 (extremely diverse tropical community), with most temperate ecosystems falling between 1.5 and 3.5. The companion metric, Pielou's evenness (J = H'/H'max), measures how equally individuals are distributed among species, ranging from 0 (completely dominated) to 1 (perfectly even).
This calculator computes the Shannon Index, evenness, Simpson's Index, and species richness from your species abundance data. Enter up to 20 species with their individual counts to get a comprehensive diversity assessment.
Biodiversity measurement is fundamental to ecology, conservation, and environmental monitoring. The Shannon Index provides a single, interpretable number that captures both species richness and abundance distribution—making it the default metric in ecological assessment worldwide. Keep these notes focused on your operational context. Tie the context to the calculator’s intended domain. Use this clarification to avoid ambiguous interpretation.
Shannon Index: H' = −Σ(pᵢ × ln pᵢ), where pᵢ = nᵢ/N. Maximum diversity: H'max = ln(S), where S = species richness. Pielou's Evenness: J = H'/H'max (range 0-1). Simpson's Index: D = 1 − Σ(pᵢ²). Effective Species Number: exp(H'). N = total individuals, S = number of species.
Result: H' = 1.51, J = 0.94, S = 5
Total N = 150. Proportions: Oak 0.30, Maple 0.253, Birch 0.213, Pine 0.167, Hickory 0.067. H' = −(0.30×ln0.30 + 0.253×ln0.253 + 0.213×ln0.213 + 0.167×ln0.167 + 0.067×ln0.067) = 1.51. H'max = ln(5) = 1.61. Evenness J = 1.51/1.61 = 0.94. This is a moderately diverse community with high evenness.
The Shannon Index captures two components of diversity: species richness (how many species) and evenness (how equally individuals are distributed). A community of 100 individuals split perfectly as 20×5 species (H'=1.61) is more diverse than 100 individuals split 96+1+1+1+1 among 5 species (H'=0.28), despite having identical species richness (S=5).
The effective number of species—calculated as exp(H')—translates the abstract index into an intuitive quantity: "this community behaves as if it had X equally common species." This conversion helps communicate results to non-specialists. An H' of 2.3 corresponds to about 10 effective species; H' of 3.5 corresponds to about 33 effective species.
Conservation biologists use the Shannon Index to: (1) Monitor ecosystem health over time (declining H' signals habitat degradation), (2) Compare habitats for conservation priority (higher H' areas are typically higher priority), (3) Assess restoration success (H' should increase as restoration proceeds), and (4) Evaluate environmental impact (comparing H' before and after development).
However, H' alone is insufficient for conservation decisions. It doesn't capture: functional diversity (the range of ecological roles), phylogenetic diversity (evolutionary distinctiveness), endemism (uniqueness to a location), or beta diversity (variation between habitats). A comprehensive biodiversity assessment uses H' alongside these complementary metrics.
The Shannon Index belongs to a family of diversity measures called Rényi entropies, parameterized by order q. At q=0, you get species richness (S); at q→1, the Shannon entropy; at q=2, a function of Simpson's Index. Higher-order indices give more weight to common species. The "diversity profile" plotting effective species number against q order provides a complete picture—if one community's profile is entirely above another's, it is unambiguously more diverse at all scales.
There's no universal "good" value—it depends on the ecosystem type. Typical ranges: coral reefs 3.0-4.5, tropical forests 3.5-5.0, temperate forests 1.5-3.5, grasslands 1.0-3.0, agricultural fields 0.3-1.0, heavily polluted water 0.0-0.5. A declining H' over time indicates biodiversity loss, which is more diagnostically useful than any single threshold.
H' combines species richness and evenness into one number. Two communities can have identical H' but very different structures: one might have 5 equally common species, another 10 species with one dominant and 9 rare ones. Evenness (J) separates these cases. J near 1.0 means individuals are evenly distributed; J near 0 means one species dominates.
The choice of logarithm base is conventional and doesn't affect comparisons within the same base. Natural log (ln, base e) is standard in ecology and gives values in "nats." Log base 2 gives values in "bits" (information theory convention). Log base 10 gives values in "decits." Always specify which base you use when reporting H' values, or comparisons are meaningless.
Both measure diversity but weigh species differently. Shannon is more sensitive to rare species (every species contributes to H' via its proportion). Simpson's Index (D = 1 − Σpᵢ²) is more sensitive to dominant species—it measures the probability that two randomly chosen individuals are different species. For fully characterized communities, they usually agree on which is more diverse.
Absolutely. It's used in: genomics (diversity of gene sequences), linguistics (vocabulary diversity), economics (market concentration), sociology (cultural diversity), and information theory (data compression). Any system describable as a collection of distinct types with frequencies can be measured with Shannon entropy.
H' is sensitive to sample size—undersampling systematically underestimates diversity because rare species are missed. A general guideline: sample at least 200 individuals for communities with <20 species, or use rarefaction to standardize comparisons across unequal sample sizes. The accumulation curve (H' vs. sample size) should plateau before you trust the estimate.