How this instrument works
The Shannon diversity index, adapted from Claude Shannon's 1948 information theory into ecology, measures biodiversity by combining two things a simple species count can't capture on its own: how many different species are present (richness), and how evenly individuals are spread across them (evenness). A community of five species where one dominates 90% of individuals is intuitively less diverse than a community of the same five species split evenly — H′ reflects that difference, while a raw species count would treat both communities as identically diverse.
The formula, H′ = −Σ(pᵢ × ln(pᵢ)), sums each species' proportion of the total community (pᵢ) multiplied by the natural log of that same proportion, across all species, then flips the sign to make the result positive. Because ln of a fraction less than 1 is always negative, each term in the sum is negative, and negating the total sum turns H′ into a positive number that grows with more species and with more even representation among them.
H′ has no fixed upper bound in general, but for any given number of species S, it's mathematically capped at ln(S) — the value it takes exactly when every species is equally represented — which is why ecologists often report H′ alongside species count, since the same H′ value means something different in a 3-species community than in a 30-species one.
- Enter each species' proportion of the total community in Proportion of each species (0-1), separated by commas, spaces, or new lines — for example 0.5, 0.3, 0.2.
- Make sure your proportions describe the community correctly — they represent each species' share of the total individuals sampled, values strictly between 0 and 1.
- Read Shannon diversity index (H′) directly — higher values mean greater diversity, combining both richness and evenness.
- Enter at least two species; with only one species present there's no diversity to measure, and the instrument will prompt for more.
Worked example — a 3-species community at 0.5, 0.3, 0.2
A community has three species with relative abundances 0.5, 0.3, and 0.2. Each term is pᵢ × ln(pᵢ): 0.5 × ln(0.5) ≈ −0.34657, 0.3 × ln(0.3) ≈ −0.36119, and 0.2 × ln(0.2) ≈ −0.32189, summing to ≈ −1.02965.
Negating that sum gives H′ ≈ 1.02965. For comparison, the maximum possible H′ for three equally-abundant species would be ln(3) ≈ 1.0986 — this community's actual H′ falls a bit below that ceiling because one species (at 50%) noticeably dominates the other two, pulling evenness, and therefore H′, down from the theoretical maximum for three species.
Questions
What counts as a 'good' or 'high' Shannon diversity index value?
There's no universal cutoff — H′ depends heavily on how many species are present, since its maximum possible value is ln(species count). A well-studied ecological community often reports H′ somewhere between about 1.5 and 3.5, but the right way to interpret any single value is by comparing it either against ln(S) for the same community, or against H′ values from other, comparable communities sampled the same way, not against a fixed universal scale.
Why does H′ use natural log instead of log base 10 or base 2?
The choice of logarithm base is a convention rather than a mathematical necessity — the original information-theory version of this formula (Shannon entropy) is most commonly expressed and taught using natural log in ecology, though base-2 and base-10 versions exist and simply rescale H′ by a constant factor. This calculator uses natural log, the standard convention in ecological literature, so results are directly comparable to the vast majority of published Shannon diversity figures.
What's the difference between species richness and the Shannon index?
Species richness is simply a count of how many different species are present, with no regard for how abundant each one is. The Shannon index folds richness together with evenness — how evenly individuals are distributed across those species — so two communities with identical richness can have very different H′ values if one is dominated by a single species and the other is more evenly balanced.
Why must each proportion be greater than zero and no more than one?
A proportion of exactly zero represents a species that isn't actually present in the sample, so it contributes nothing and shouldn't be listed at all; the formula's natural log of zero is undefined regardless. A proportion above 1 is not a valid share of a whole community by definition, since each pᵢ represents that species' fraction of the total, and no single species can be more than 100% of it.
Do my proportions need to add up to exactly 1?
In a correctly constructed dataset, yes — the proportions represent every species' share of the same total community, so they should sum to 1 (or very close to it, allowing for rounding). If your proportions come from raw counts rather than pre-calculated shares, divide each species' count by the total count across all species first to get proportions that sum to 1 before entering them here.