The Shannon diversity index, sometimes called the Shannon-Wiener or Shannon-Weaver index, condenses a table of species counts into a single number that rises with both the number of species present and the evenness of their abundances. It is borrowed directly from information theory, where the same quantity measures the uncertainty in a message. In ecology it answers a related question: if you picked one individual at random from this community, how uncertain would you be about which species it belonged to?
Arb Digital publishes free ecology and environmental tools that show their working rather than returning a bare number. This page reports H alongside the three things that determine how it should be read — species richness, Pielou's evenness, and the effective number of species — plus Simpson's index as a second opinion. That extra context matters, because the single most common misuse of this index is comparing two H values from communities with very different species counts.
What This Shannon Diversity Index Calculator Does
It parses your abundance table, converts each count to a proportion of the total, and computes H. It then divides H by its theoretical maximum for that number of species to give Pielou's evenness J, which always sits between 0 and 1. The exponential of H gives the effective number of species — the number of equally abundant species that would produce the same H — which is the form most ecologists now prefer because it is on a linear scale you can actually reason about.
Simpson's index is computed alongside, in both its dominance form D and its complement 1 − D, because the two indices weight rarity differently and looking at both is a cheap check. A proportion bar for every species shows where the abundance actually sits, so a community that looks diverse in the number but is in fact dominated by one species is obvious at a glance.
How to Use It
- Paste your counts. One species per line, with an optional name before the number. Individuals, biomass or percentage cover all work as long as the unit is consistent.
- Pick a logarithm base — natural log unless you are matching a paper that used another — and record which one you chose.
- Read H with the evenness beside it. A high H with low evenness means many species with one dominating; a high H with high evenness means a genuinely balanced community.
- Use the effective species number for comparisons. It is on a linear scale, so a doubling of the figure means a doubling of effective diversity, which is not true of H itself.
- Check the sample size. Rare species missed by a small survey depress H, and the tool reports the total count so you can judge the effort behind the number.
The Formula and a Worked Example
Let pᵢ be the proportion of the community made up by species i. Then H = −Σ pᵢ ln(pᵢ), summed over all species present. Pielou's evenness is J = H ÷ ln(S) where S is the number of species, since ln(S) is the largest H can be when all species are equally abundant. The effective number of species is eH, and Simpson's dominance index is D = Σ pᵢ². The NIST Dataplot reference page for the Shannon diversity index gives both the index and the equitability form in exactly these terms.
Work the default by hand. Four species with counts 40, 30, 20 and 10 total 100 individuals, so the proportions are 0.4, 0.3, 0.2 and 0.1. Then H = −(0.4 ln 0.4 + 0.3 ln 0.3 + 0.2 ln 0.2 + 0.1 ln 0.1) = 1.2799 nats. The maximum for four species is ln 4 = 1.3863, so J = 1.2799 ÷ 1.3863 = 0.9232 — a very even community. The effective number of species is e^1.2799 = 3.60, meaning this community is as diverse as 3.6 equally common species would be. Simpson's D is 0.4² + 0.3² + 0.2² + 0.1² = 0.30, so 1 − D = 0.70.
Why H Alone Can Mislead When Richness Differs
Consider two survey plots. Plot A holds four species in the counts above and scores H = 1.28. Plot B holds four species too, but the counts are 91, 3, 3 and 3: one overwhelming dominant and three stragglers. Plot B scores H = 0.40, with an evenness of 0.29 and an effective species number of just 1.49. Same richness, same number of individuals, radically different communities — and only the evenness figure makes that legible immediately.
The harder case runs the other way. A species-rich but very uneven community can score the same H as a species-poor but perfectly even one, because H trades richness against evenness on a single axis and cannot tell you which contributed. That is not a defect in the formula; it is a consequence of compressing two dimensions into one. The remedy is to report richness, evenness and H together, which is why all three appear in the result grid here rather than being buried. Where a decision depends on the difference, plot richness against evenness for all your sites instead of ranking them by H.
Choosing Between Shannon and Simpson
The two indices weight abundance differently. Shannon's H is relatively sensitive to rare species: adding a single individual of a new species raises H noticeably. Simpson's index is dominated by the common species and barely moves when a rare one appears or disappears. Neither is more correct — they answer different questions.
If your concern is the detection of rare or declining taxa, Shannon is the more responsive instrument, but it is also the more sensitive to sampling effort, because whether you find the rare species at all depends on how hard you looked. If your concern is dominance — whether one species is taking over a site — Simpson is more stable and less dependent on catching the tail. Regulatory biomonitoring programmes often use composition-based indices for precisely this reason; the EPA's guidance on benthic macroinvertebrates as a biological indicator describes how community variety is used to assess waterbody condition.
Sampling Effort Is Part of the Result
H is not a property of the community alone; it is a property of the community as sampled. Double the survey effort and you will usually find additional rare species, which raises richness and typically raises H a little. This means two H values are only comparable when the sampling effort behind them is comparable — same method, same area, similar total count, ideally the same observer.
Where effort genuinely differs, the honest options are rarefaction, which subsamples the larger dataset down to the smaller one's size, or reporting the indices with an explicit note about effort. Simply comparing the raw numbers and declaring one site more diverse is the error this whole field warns about most often. The total count is shown in the panel below the result specifically so that this check is available at a glance, and any figure you publish should carry it too.
What the Index Cannot Tell You
Shannon's H treats all species as interchangeable tokens. It does not know that one of them is a keystone predator, an endangered endemic, or an invasive species that arrived last year. A site can gain diversity, in the index's terms, by acquiring three invasive weeds — and the number will go up while the ecosystem's condition goes down. Diversity indices are descriptive summaries, not condition assessments.
Nor does H account for phylogenetic or functional distance: four species from one genus count the same as four from four different families, though the second community is far more distinct ecologically. Nor does it handle spatial structure, which is why beta and gamma diversity exist alongside the alpha diversity this index measures. Treat H as one line in a table that also carries richness, evenness, species identity and the survey method — never as the headline conclusion on its own.
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The index needs proportions, so the unit of abundance has to be consistent across every row. Counts of individuals are the usual choice and the easiest to defend. Biomass and percentage cover both work — the latter is standard for vegetation surveys where counting individual plants is impossible — but they answer subtly different questions, because a single large individual can dominate a biomass-based index while contributing one count to an individual-based one. Never mix units within one table.
Two edge cases come up often. Species recorded as present but not counted cannot be included without inventing a number, so either count them or exclude them and say so. And taxa identified only to genus or family sit at a different taxonomic resolution from the rest, which inflates or deflates richness depending on how you treat them; the usual convention is to keep the resolution consistent across the whole table even if that means aggregating some well-identified species upwards. Both decisions change H, and both belong in the method note rather than being made silently.
Common Mistakes to Avoid
- Reporting H without the logarithm base — the same community scores 1.28 in nats and 1.85 in bits.
- Comparing H across surveys of different effort, since rare species found only by the larger survey inflate its score.
- Reading H as a condition score — an index can rise because invasive species arrived.
- Ignoring evenness, which is the only way to tell a balanced community from one dominated by a single species.
- Including zero counts — an absent species contributes nothing, and the logarithm of zero is undefined.
Related Free Tools From Arb Digital
Estimate what a tree contributes to a site with the tree benefits calculator, size a compost heap with the compost calculator, work out the runoff from a catchment with the rainfall volume calculator, summarise any dataset with the descriptive statistics calculator, or count occurrences with the frequency distribution calculator. Everything else is on the free online tools hub.
Frequently Asked Questions
The uncertainty in predicting the species of an individual drawn at random from the community. It rises both with the number of species present and with how evenly the individuals are spread among them.
Most ecological communities fall between about 1.5 and 3.5 in natural logarithms, but the range depends entirely on the taxa and the sampling method, so there is no universal good or bad value.
The Shannon index divided by the natural logarithm of the number of species, which is the largest value H could take for that richness. It runs from 0 to 1, with 1 meaning all species are equally abundant.
Because it is on a linear scale. Doubling the effective species number means twice the diversity, whereas doubling H does not, since H is a logarithmic quantity.
It changes the value but not the ordering of communities. Natural logarithms give nats, base 2 gives bits, and figures from different bases must never be compared without converting.
Shannon is more responsive to rare species and to sampling effort. Simpson is dominated by the common species and is more stable. Report both when the choice would change your conclusion.
Only when the sampling effort and method are comparable. A larger survey finds more rare species and scores higher for that reason alone, so rarefy to a common sample size before comparing.
This tool is provided for educational and analytical use. A diversity index describes a sample of a community and is not on its own an assessment of ecological condition.
