Shannon Diversity Index Calculator

Ten species with one holding 90 percent scores far below ten species in equal numbers.

Shannon index1.285395 species, 100 individuals

Maximum possible1.60944ln of the species count, reached only at perfect evenness

Evenness0.79866the index against its maximum, from 0 to 1

Simpson's index0.6782the chance two random individuals differ in species

Species richness5

Most abundant share45%

If all were equally abundant1.60944the index would rise to its maximum

Shannon is sensitive to rare species and Simpson to common ones — Simpson is essentially the chance that two individuals picked at random are different species. Neither is correct; they answer different questions, which is why both are usually reported.

The formula

H' = -sum(p ln p) ; evenness = H' / ln(species)

Two things at once

The Shannon index rises both with the number of species and with how evenly individuals are spread between them. A wood with ten species where one holds 90 % of the trees scores far lower than a wood with ten species in equal numbers, even though the species count is identical. That is the point: a community dominated by one thing is not diverse in any useful sense.

The maximum is ln(S)

Perfect evenness across S species gives exactly the natural logarithm of S, which is why dividing by it gives an evenness score between 0 and 1. Four equally abundant species score ln 4 = 1.386 and no arrangement of four species scores higher.

Shannon against Simpson

Simpson's index weights the common species much more heavily — it is essentially the chance that two individuals picked at random are different species. Shannon is more sensitive to the rare ones. Neither is correct; they answer different questions, and reporting both is standard practice for exactly that reason.

How much to trust a footprint

Life-cycle figures for the same product routinely differ by a factor of two between studies, because deciding what to count — the farm, the packaging, the shop, the drive home, the disposal — is a methodological choice rather than a measurement. The numbers here are central estimates from published meta-analyses. They are reliable for comparing one option against another, which is what people actually use them for, and not reliable to the second significant figure.

The other thing worth keeping in view is scale. Individual choices matter and they are not where the emissions are: the difference between the best and worst quartile of beef producers is larger than most people's entire dietary footprint, and that is a question about agriculture policy rather than about shopping.