Biodiversity Index Calculator

Enter species counts to compute biodiversity indices and visualise community structure.

Worked example — Biodiversity Index Calculator

Richness (S)	5
Total individuals	50
Shannon H	1.6094
Hmax	1.6094
Evenness (E)	1.0000
Simpson 1−D	0.8163
Species counts (comma-separated)	10Sp110Sp210Sp310Sp410Sp5

These are the values the calculator shows when the page opens. Change any input above to recompute them.

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Two indices, and they disagree on purpose 🖖

Measuring biodiversity is not just about counting species; it is about assessing the distribution of life. The Shannon diversity index H is derived from Claude Shannon's information entropy: H = -Σ p_i ln p_i. In ecology, this measures the uncertainty in predicting the species of a randomly chosen individual. If an ecosystem is dominated by a single species, uncertainty is low, and the Shannon index is close to zero. If species are equally abundant, uncertainty and diversity are maximized. Similarly, the Simpson index measures the probability that two randomly selected individuals belong to the same species. By translating biological diversity into thermodynamic and information-theoretic terms, ecologists can mathematically evaluate ecosystem stability, resilience to disturbance, and the impact of conservation efforts.

Evenness matters as much as species count 🖖

Two communities can list the same number of species yet be worlds apart. A plot with 90 individuals of one species and just one each of four others has the same richness (S = 5) as a plot with 20 of each — but far less real diversity, because one species drowns out the rest. That is why this tool reports evenness (Pielou's J) beside the raw count: diversity is about how evenly individuals are spread, not only how many species are present.

The same formula that spots monopolies 🖖

Simpson's dominance λ = Σpᵢ² is mathematically identical to the Herfindahl-Hirschman Index that economists use to gauge market concentration — regulators apply the very same sum of squared shares to decide whether a merger creates a monopoly. Low ecological diversity and a monopolised market are, arithmetically, the same thing. Fittingly, Edward Simpson introduced the index in 1949 after wartime service as a Bletchley Park codebreaker.

Problem solved in full

Five species with ten individuals each and a Simpson's index of 0.8163 5 steps
Five species, ten individuals each. Shannon says 1.6094 and evenness is exactly 1. Work out why Simpson's index reads 0.8163 rather than the 0.8000 the standard formula gives.
1. With every species equally abundant, each proportion is 1/5, and the Shannon sum collapses to the logarithm of the number of species.
  
  $H = - \sum p_{i} ln p_{i} = - 5 (0.2) ln 0.2 = ln 5 = 1.6094$
2. That is also the maximum Shannon value any five-species community can have, so evenness — the ratio of the two — is exactly 1. This community is as even as five species can be, and both numbers say so by being identical.
  
  $H_{m a x} = ln S = ln 5 ⟹ E = \frac{H}{H _{m a x}} = 1.0000$
3. Simpson's index asks a different question: the chance that two individuals drawn from the community are different species.
4. Drawn with replacement, the answer is 1 − Σp², which is 0.8000 — the version in most textbooks.
  
  $1 - \sum p_{i}^{2} = 1 - 5 (0.04) = 0.8000 (with replacement)$
5. But you cannot sample the same individual twice. Drawing without replacement changes the second draw's odds, and with only 50 individuals that correction is not negligible.
  
  $1 - \frac{\sum n _{i} ( n _{i} - 1 )}{N ( N - 1 )} = 1 - \frac{450}{2450} = 0.8163 (without)$
Answer

The tool prints H = 1.6094, evenness 1.0000 and Simpson 1 − D = 0.8163. The gap of 0.0163 is not a different index, it is the finite-sample correction — and it shrinks as the community grows, vanishing entirely in the infinite-population limit the textbook formula assumes. Worth knowing before comparing published values, because both versions are called "Simpson's index". The other lesson is in what these two indices disagree about: click the dominant preset, where one species holds 80 of the 100 individuals. Richness is unchanged at 5, but Shannon falls to 0.78 and evenness to 0.48. Counting species is not measuring diversity.

$E = 1 is maximal evenness; 0.8163 - 0.8000 = 0.0163 is the N = 50 correction$

References (2)

The index the tool computes, from the paper that introduced the entropy it borrows: C. E. Shannon, "A Mathematical Theory of Communication." The Bell System Technical Journal 27(3), 379–423, 1948.
The second index, and why it answers a different question: E. H. Simpson, "Measurement of Diversity." Nature 163, 688, 1949.

By the 42Math team · Updated 2026-06-29

Reviewed against published sources. Corrections welcome. Editorial policy · Corrections

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Example problems

Even - Five species in equal numbers: Shannon H is 1.6094, exactly Hmax, so evenness comes out at 1.0000.
Dominant - The same five species with one dominating: H falls to 0.7777 and evenness to 0.4832.
Tropical - Twelve species among 74 individuals gives H = 2.2399 against an Hmax of 2.4849.
Post-extinction - Lose a species and richness drops to 4, taking Simpson 1−D down to 0.6414.