Brillouin Index Calculator

The Brillouin Index (H) is a measure of species diversity developed by Louis Brillouin. Unlike the Shannon Index, it is specifically designed for situations where you have conducted a complete census of a community — meaning every individual has been counted — rather than working with a sample. It accounts for the exact number of individuals rather than estimated proportions.

The Brillouin Index is calculated as H = (1/N) × ln(N! / ∏n_i!), where N is the total number of individuals and n_i is the count for each species. Because factorials of large numbers are involved, the calculation uses the log-gamma function (Stirling's approximation or summing logarithms) for numerical stability.

Use the Brillouin Index when your data represents a complete census — every individual in the community has been counted and identified. Use the Shannon Index when you are working with a random sample from a larger, unknown population. Using the Shannon Index on census data can introduce a small bias that Brillouin corrects for.

A higher H value indicates greater diversity — the community contains many species distributed relatively evenly across individuals. A value near H_max means the population is as diverse as it could be given the number of species and total individuals present.

Evenness (E = H / H_max) measures how close the observed diversity is to the theoretical maximum. A value of 1.0 means all species are represented equally. Values closer to 0 indicate that one or a few species dominate the community, even if many species are present.

H_max is the maximum possible Brillouin diversity for a community with the same total number of individuals (N) and the same number of species (S). It is computed assuming individuals are distributed as evenly as possible across all species. It serves as a benchmark for interpreting how diverse the observed community is.

This calculator supports up to 8 species. Enter a count of 0 (or leave blank) for any species slot you do not need — those entries will be automatically excluded from the calculation. For studies with more species, the same formula applies and can be extended manually.

Yes, but the index becomes less informative when N (total individuals) is very small (e.g. fewer than 5). The factorial-based formula is mathematically exact for any N, but ecologically meaningful interpretation generally requires a reasonably sized community with at least several individuals per species.