How this works
Alpha diversity asks two questions about a community sample at the same time: how many different species are present (richness), and how evenly are individuals distributed across them (evenness). The classical indices roll those two ideas into a single number, weighted differently. The calculator above takes a list of counts — one per species, in any reasonable text format — and returns the four most-used summaries: Shannon-Wiener H′, Gini-Simpson 1−D, inverse Simpson 1/D, and Pielou's evenness J′. All four are computed from the same proportion vector (p_i = n_i / N), and the differences come down to which mathematical operation gets applied to those proportions.
Shannon-Wiener H′ = −Σ p_i ln(p_i) is the entropy of the distribution: it asks "how surprised would I be to draw an individual at random?", which is high when many species are present and abundances are even. It's reported in nats when you use natural log (the default here), or bits if you use log₂ — the choice doesn't affect comparisons between samples as long as you're consistent. Simpson's D = Σ p_i² is the probability that two individuals drawn at random belong to the same species; the more even the community, the lower D. The Gini-Simpson 1−D inverts this so that higher means more diverse (the form most people mean when they say "Simpson diversity"). Inverse Simpson 1/D has the appealing property of behaving like an "effective number of species" — a community where 1/D = 5 has the same diversity as a perfectly even community of 5 species, regardless of how many rare species are actually in the tail. Pielou's J′ = H′ / ln(S) divides Shannon by its theoretical maximum and gives an evenness score from 0 to 1, useful for comparing samples with different species counts.
A few practical points. (1) These indices are only meaningful for a fixed sampling effort. A 16S rRNA sample with 50,000 reads will look more diverse than the same community sequenced to 5,000 reads, simply because deeper sampling discovers more rare species. Standard practice in microbiome work is to rarefy all samples to the same read depth before computing diversity, or to use a coverage-based estimator. (2) The choice of "what counts as a species" matters as much as the index. In microbiome studies, OTU clustering at 97% vs ASV resolution gives meaningfully different diversity numbers from the same data. Be explicit about your unit of analysis. (3) Shannon and Simpson disagree about how much weight to give rare species. Shannon weights them more (because ln(p) blows up as p approaches zero), Simpson barely weights them at all. If your community has a long tail of singletons that you suspect are sequencing errors, Simpson will be more robust; if those rare species are biologically real and matter to your question, Shannon respects them.
The formula
n_i is the count for species i, N is the total of all counts (Σ n_i), and S is the number of species with n_i > 0 (richness). The calculator uses natural log throughout, so Shannon H′ is in nats; multiply by 1/ln(2) ≈ 1.443 to convert to bits if you need that unit. Pielou's J′ is undefined when S = 1 (only one species — there's no theoretical max diversity to compare against), so the calculator shows it as not-applicable in that case. Singleton species (n_i = 1) contribute fully to richness and to Shannon, but very little to Simpson because their p_i² is tiny.
Example calculation
- Sample with 5 species, counts: 50, 25, 15, 7, 3 (total N = 100).
- Proportions: 0.50, 0.25, 0.15, 0.07, 0.03.
- Shannon H′ = −(0.50·ln 0.50 + 0.25·ln 0.25 + 0.15·ln 0.15 + 0.07·ln 0.07 + 0.03·ln 0.03) ≈ 1.265 nats.
- Simpson D = 0.50² + 0.25² + 0.15² + 0.07² + 0.03² ≈ 0.344. Gini-Simpson 1−D ≈ 0.656. Inverse 1/D ≈ 2.91. Pielou J′ = 1.265/ln(5) ≈ 0.786.
Frequently asked questions
Should I report Shannon, Simpson, or both?
Both, when space allows. They emphasise different things: Shannon is more sensitive to species richness and to rare species, Simpson is more sensitive to evenness among the dominant species. A community where Shannon and Simpson disagree (one says "very diverse", the other says "moderate") is usually one with a long tail of rare species — and which answer is "right" depends on what your scientific question is. For ecology papers, reporting both alongside richness (S) is normal and lets readers interpret your data their own way. For microbiome work, the convention has converged on reporting at least Shannon and inverse Simpson, often alongside Faith's phylogenetic diversity (which this calculator doesn't compute — for that you need a tree). If you have to pick one for a single-number summary, inverse Simpson is the easiest to interpret because it has units of "effective species" — a number a non-specialist can immediately reason about.
Why does deeper sequencing make my Shannon look higher?
Because deeper sampling discovers more rare species, and rare species push richness up — Shannon includes a richness term, so it rises mechanically with read count. The same community sequenced to 1,000 vs 50,000 reads can show meaningfully different Shannon values purely due to sampling depth, not biology. Two standard fixes. (1) Rarefy: subsample every sample down to the lowest read depth in your dataset before computing diversity. Loses real data but makes samples directly comparable. (2) Use coverage-based or model-based estimators (e.g. Hill numbers via the iNEXT framework, or Chao1 for richness alone) that explicitly account for sampling effort. For a single one-off calculation on a single sample, the raw Shannon is fine to report alongside the read count; for cross-sample comparisons, never compare raw Shannon between samples sequenced to different depths.
What input formats does the calculator accept?
Anything that contains a list of numeric counts. The parser extracts every numeric token from the pasted text and treats each as one species count, so you can paste a single column of numbers from a spreadsheet, a comma-separated list, a tab-separated table with species names in one column and counts in another, or even a sentence like "Species A had 12 individuals, Species B had 7". Species names are ignored — only the counts matter for the indices. Zero counts are dropped (a species with zero observations isn't in the sample). Negative numbers are silently ignored as input errors. If you have a spreadsheet with multiple samples and want diversity for each, run them one at a time; the calculator computes a single sample's diversity per submission, not a matrix.
My Pielou evenness is 1.00 — is that right?
Yes — J′ = 1 means the community is perfectly even, i.e. every species has the same count. Mathematically that's when Shannon hits its theoretical maximum of ln(S), and J′ = H′/ln(S) = 1. It's rare to see in real ecological or microbiome data because real communities almost always have at least some unevenness; if you're seeing exactly 1.00, double-check that your input wasn't accidentally a list of identical numbers (e.g. you pasted relative frequencies after rounding to the same value, or you have a constant column from a spreadsheet). At the other extreme, J′ approaches 0 as one species comes to dominate completely; J′ = 0 would mean a single-species "community", which the calculator flags as not-applicable for evenness because there's no theoretical maximum to compare against (S = 1 makes ln(S) = 0).