Hill numbers are a unified family of biodiversity indices proposed by Mark Hill (1973) and popularised by Lou Jost (2006). Each Hill number is expressed as the effective number of equally abundant species — i.e. the number of species a perfectly even community would need to give the same diversity value. The order q controls sensitivity to rare species: q = 0 counts every species equally (richness), q = 1 weights species by Shannon entropy, q = 2 emphasises dominant species.

Use Hill numbers whenever you want diversity values that are directly comparable, additive, and on the same units (number of species) regardless of which order you compute. They are the modern recommended way to report biodiversity in peer-reviewed ecology.

You need a list of species counts (abundances) from one community or sampling unit. Each value is the number of individuals (or detections, occurrences, or basal area) of one species. A minimum of 5 species and 30 individuals is recommended; 100+ individuals across replicate plots gives stable estimates of all three orders.

Counts of zero should be excluded. Decimal abundances (e.g., basal area, biomass) are accepted — Hill numbers do not require integer counts.

⁰D = S is species richness — every species counts equally regardless of abundance. It is the most sensitive to rare species and to under-sampling. ¹D = exp(H′) is the exponential of Shannon entropy and equals the effective number of common species. ²D = 1/Σp² is the inverse of Simpson's concentration and represents the effective number of dominant species.

The relationship ⁰D ≥ ¹D ≥ ²D always holds, with equality only when the community is perfectly even.

Shannon (H′) and Simpson (D, λ) are not on the same scale and cannot be added or compared directly. Hill numbers convert them to effective species counts: ¹D = exp(H′) and ²D = 1/λ. Hill numbers also have the doubling property: a community with ²D = 10 has twice the effective dominant diversity of one with ²D = 5 — a property H′ does not have.

Hill numbers assume a closed community with a complete species list, equal sampling effort across species, and accurate identification. They are sensitive to sample size for q = 0 (richness), less sensitive for q = 1, and least sensitive for q = 2. Rarefaction or coverage-based standardisation (Chao & Jost 2012) is recommended for cross-site comparisons.

At minimum, 30 individuals and 5 species; ideally 100+ individuals across replicate plots, transects, or trap nights. Camera-trap studies should aim for 1,000+ trap nights. Use a species accumulation curve to confirm sampling adequacy before relying on q = 0 (richness), which is the most effort-sensitive of the three orders.

Yes, but only if sampling effort is standardised or rarefied to the same coverage level. Use Chao & Jost (2012) coverage-based rarefaction for unequal effort. Hill numbers are ideal for comparison because all three orders are on the same units (effective species), allowing meaningful subtraction and ratios across sites or time points.

Report all three orders together: ⁰D (species richness), ¹D (effective common species), ²D (effective dominant species), along with sample size N and survey effort. Cite Hill (1973) and Jost (2006). Include the diversity profile plot whenever possible — it is now considered best practice in biodiversity research.

Yes for exploratory analysis. For peer-reviewed publication, verify results with the iNEXT R package (Hsieh, Ma & Chao 2016) or the vegan package (Oksanen et al. 2022), which add bootstrap confidence intervals and rarefaction. Cite this tool as: Stats Unlock. (2026). Hill Numbers Calculator. https://statsunlock.com.

Common issues: (a) zero counts mistakenly entered, (b) species pooled instead of separated, (c) one taxon dominating the sample inflates ⁰D but collapses ²D, (d) very small N produces unstable estimates. Check the raw input in the Manual Entry tab and re-run with a sample dataset to confirm the tool is behaving correctly.