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Shannon Diversity Index Calculator

Calculate the Shannon diversity index (H'), species richness, evenness (Pielou's J), and Simpson's index from species abundance data.

Frequently Asked Questions

What is a high vs low Shannon diversity index?

H' = 0 means only one species is present. Values above 3 indicate high diversity typical of diverse forests or coral reefs. Most ecological communities fall between 1.5 and 3.5. The maximum possible H' equals ln(S) where S is species richness.

What is Pielou's evenness and why does it matter?

Pielou's J = H' / ln(S) ranges from 0 to 1. J = 1 means all species are equally abundant (maximum evenness). Low evenness means a few species dominate. Two communities can have the same H' but very different evenness if one has more species.

What is the difference between Shannon's H' and Simpson's D?

Shannon's H' weighs rare species more heavily and is sensitive to species richness. Simpson's D is the probability that two randomly chosen individuals belong to the same species - it weighs abundant species more. 1-D and 1/D are common diversity measures derived from Simpson's D.

What is the effective number of species (Hill numbers)?

Hill numbers express diversity as an equivalent count of equally abundant species, which is easier to interpret than raw index values. Converting Shannon's H' gives the Shannon effective number, exp(H'). For the worked example above, exp(1.182) ≈ 3.26, meaning the community is as diverse as about 3.26 equally common species. The inverse Simpson 1/D is the same idea derived from Simpson's index and gives a slightly lower number because it discounts rare species more. Both are Hill numbers of different order (q = 1 for Shannon, q = 2 for Simpson).

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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How This Calculator Works

This calculator takes a list of species abundances (the number of individuals of each species in your sample) and computes several standard diversity indices used in ecology. Enter one count per line, or separate counts with commas. All counts must be positive numbers; fractional counts are accepted for estimated biomass or coverage data.

The three major indices computed here - Shannon, Simpson, and evenness - each capture a slightly different aspect of diversity. Using all three together gives a fuller picture of community structure than any single index alone.

Shannon Index (H')

The Shannon index (also called Shannon entropy or Shannon-Wiener index) is calculated as:

H' = -sum of (p_i × ln p_i) for all species i

where p_i is the proportion of the total that species i represents. Natural log is used. H' equals zero when the community contains only one species, and reaches its maximum value of ln(S) when all S species are equally abundant. Typical values in ecological field studies range from about 1.5 to 3.5, although highly diverse tropical communities can exceed 5.

H' is sensitive to rare species: adding one rare species increases H' by a small but non-zero amount. It is also sensitive to sample size - undersampling tends to underestimate the true H' because rare species are missed.

Pielou's Evenness (J)

Evenness measures how uniformly individuals are distributed across species, independently of how many species there are. Pielou's J is defined as:

J = H' / H'_max = H' / ln(S)

J ranges from 0 to 1. A value of 1 means all species are equally abundant (maximum evenness). A value close to 0 means one or a few species dominate. J can be more informative than H' when comparing communities with very different species richness, because it removes the effect of species number.

Simpson's Index

Simpson's D is the probability that two individuals drawn at random from the community belong to the same species:

D = sum of p_i squared

D ranges from 0 (infinite diversity) to 1 (single species). Because a high D value means low diversity, ecologists often report one of two transforms: Simpson's diversity 1 - D (ranges 0 to 1, higher is more diverse), or the inverse Simpson 1/D (also called the effective number of species, or the number of equally abundant species that would produce the same D).

Compared with Shannon's H', Simpson's index gives more weight to dominant species and less weight to rare ones. It is less sensitive to undersampling than H'.

Worked Example

Suppose you count four bird species in a woodland plot: 45, 32, 18, and 5 individuals. Total N = 100. Proportions: 0.45, 0.32, 0.18, 0.05.

H' = -(0.45 × ln 0.45 + 0.32 × ln 0.32 + 0.18 × ln 0.18 + 0.05 × ln 0.05)
H' = -(0.45 × (-0.799) + 0.32 × (-1.139) + 0.18 × (-1.715) + 0.05 × (-2.996))
H' = -((-0.3595) + (-0.3645) + (-0.3087) + (-0.1498)) = 1.182
S = 4, H'_max = ln(4) = 1.386, J = 1.182 / 1.386 = 0.853
D = 0.45^2 + 0.32^2 + 0.18^2 + 0.05^2 = 0.2025 + 0.1024 + 0.0324 + 0.0025 = 0.3398
1 - D = 0.660, 1/D = 2.94 effective species

The relatively high J (0.85) tells us the community is fairly even. The inverse Simpson of about 2.9 means this community behaves like a hypothetical community of roughly 3 equally abundant species.

Note that this inverse-Simpson effective count (1/D = 2.94) is not the same as Shannon's own effective-species count, exp(H') = exp(1.182) = 3.26. The two numbers differ because Shannon weights rare species a little more heavily, so they are not expected to match; report whichever effective-species metric goes with the index you are using.

Tips and FAQ

How many species do I need?

At least two. With one species H' = 0 and J is undefined. Most meaningful ecological studies include at least 5 to 10 species.

Can I enter decimal abundances?

Yes. Fractional values are valid for percentage cover, relative biomass, or estimated density. Only the proportions matter mathematically, so multiplying all values by a constant leaves all indices unchanged.

Which index should I use?

Use Shannon H' for a general diversity comparison that gives moderate weight to rare species. Use Simpson's 1/D (inverse Simpson) when you want an intuitive "effective number of species" metric that emphasises dominant species. Use Pielou's J when you want to separate evenness from species richness, for example when comparing plots that differ greatly in the number of species.

Why does the order of species not matter?

Both Shannon and Simpson indices are symmetric: they sum over all species without regard to identity or order. Only the set of proportions matters, not which species is which or how you list them.

What is a good H' value?

There is no universal threshold. Context matters: a temperate grassland with H' = 2.5 may be highly diverse, while a tropical rainforest understory with H' = 2.5 might be considered depauperate. Compare values within the same ecosystem type and sampling method.