Shannon Diversity Index Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/6/2026
The Shannon index is calculated with H' = −Σ(pᵢ × ln(pᵢ)), where pᵢ is the proportion of each species in the total sample. For 4 species with perfectly equal counts, the index reaches its maximum possible value for that number of species, with an evenness of 1.
Explanation
The Shannon diversity index (also called the Shannon-Wiener index) is a classic ecology measure for quantifying a community's biodiversity from a sample: how many different species are present, and how evenly individuals are distributed among them. The index increases both with the number of species (species richness) and with the uniformity of their distribution (evenness): a community of 4 species with equal counts scores higher than a community of 4 species where one heavily dominates the other three, even though the number of species recorded is identical in both cases. This calculator also gives Pielou's evenness (J' = H' divided by the logarithm of the number of species), which expresses the share of the theoretical maximum diversity actually observed, on a scale from 0 (a single species totally dominates) to 1 (all species are equally represented). In field practice, this index is used to compare biodiversity across several sampling sites, or to track how a single site changes over time (before/after a disturbance, ecological restoration, or a change in agricultural practice). It complements other population-genetics tools on the site, such as our Hardy-Weinberg calculator (genetic diversity within a single species) or our population growth rate calculator (a population's dynamics over time): Shannon diversity, meanwhile, measures diversity across different species at a given moment.
Example: a community dominated by one species (90, 5, 3, 2 individuals)
Inputs
Counts: species 1 = 90, species 2 = 5, species 3 = 3, species 4 = 2 (total N = 100).
Calculation
Proportions: p₁=0.90, p₂=0.05, p₃=0.03, p₄=0.02. H' = −(0.90×ln(0.90) + 0.05×ln(0.05) + 0.03×ln(0.03) + 0.02×ln(0.02)) ≈ 0.428. Evenness J' = 0.428 ÷ ln(4) ≈ 0.309.
Result
This community has a Shannon index of about 0.428, with low evenness (0.309): one species heavily dominates the other three.
Frequently asked questions
Why does the Shannon index depend on both the number of species and their distribution?
The index actually measures the uncertainty about the identity of the species of a randomly drawn individual in the sample: the more possible species there are and the closer their counts, the higher this uncertainty (and thus the index). A single dominant species sharply reduces this uncertainty, even if other rarer species are technically present.
What is the usual range of values for this index?
In real ecological samples, the Shannon index typically falls between 1.5 and 3.5, the exact value depending heavily on the ecosystem studied and the number of species recorded. There is no universal threshold for "good" or "bad" diversity: the index is mainly useful for comparing several samples measured with the same method.
Why is evenness not defined with a single species?
Pielou's evenness divides the Shannon index by the logarithm of the number of species observed. With a single species, that logarithm equals ln(1) = 0, which would make the division impossible: this special case is mathematically undefined, so rather than returning an arbitrary value, this calculator shows evenness as not applicable in that case.