How this calculator works
The Shannon index, borrowed from information theory, takes the proportion of each species and multiplies it by its logarithm, then adds the results and changes the sign. When one species dominates, almost every individual belongs to it, the uncertainty is low, and H is close to zero. When many species are equally common, the uncertainty is high and H approaches the logarithm of the number of species. The choice of logarithm base only rescales the number: natural logs give nats, base 2 gives bits and base 10 gives hartleys, and all three rank communities the same way. Pielou evenness divides H by its maximum for the same richness, so it runs from zero to one and measures how evenly the individuals are spread across species. The Simpson index is a different summary: it gives the probability that two individuals picked at random belong to the same species, so a lower value means more diversity. Species with a count of zero are not included in richness.
Formula
p = count / total for each species. H = -sum(p x ln p) / ln(base). J = H / (ln(S) / ln(base)), where S is the number of species present. Simpson index D = sum(p^2). The rank abundance curve plots the proportions in descending order.
Worked example
Counts of 50, 30 and 20 give a total of 100 and proportions of 0.5, 0.3 and 0.2. The natural-log contributions are 0.3466, 0.3612 and 0.3219, which add to H = 1.0297 nats. With three species the maximum is ln 3 = 1.0986, so evenness is 1.0297 / 1.0986 = 0.937. Simpson D is 0.25 + 0.09 + 0.04 = 0.38.
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Frequently asked questions
Which index should I use, Shannon or Simpson?
Shannon gives more weight to rare species and Simpson more weight to common ones, so Shannon is more sensitive to species that appear in small numbers. Many studies report both. If the ranking of sites matters, the two usually agree; if it does not, the choice is part of your result.
Do I need counts or can I use biomass?
Both work, but the answer means different things. Counts describe the diversity of individuals, while biomass or cover describes the diversity of the material present. Do not mix the two in one dataset.
Should zero counts be included?
No. A species with zero individuals was not observed and adds nothing to the proportions. Excluding it is why richness here is the number of species present, not the number of species you typed.
Is the result comparable between studies?
Only if the sampling effort and area are similar. A larger sample finds more rare species, which raises both richness and H. Rarefaction, which standardises the sample size, is the usual fix.