Diversity index calculator

Formulas and symbols

Below, pᵢ = nᵢ / N, where nᵢ is the count (or cover) of species i, N is the total, and S is the number of species.

Shannon-Wiener diversity H′

H′ = −Σ pᵢ log pᵢ

The logarithm base changes the value of H′: with the natural log (ln) it is ln 10 ≈ 2.3026 times the log₁₀ value, and ln 2 ≈ 0.6931 times the log₂ value. Values in different bases cannot be compared directly, so a report must state which base it used.

Pielou evenness J′

J′ = H′ / log S

The numerator and denominator use the same base, so evenness does not depend on it. With a single species, J′ is defined as 0.

Simpson indices

λ = Σ pᵢ²　　1 − λ　　1 / λ

λ is dominance (the chance that two individuals drawn at random are the same species), 1 − λ is often called Simpson diversity, and 1 / λ is the inverse Simpson index, also Hill number N2. The literature does not agree on which of these "the Simpson index" means, so quote the formula. For whole counts the unbiased estimate λ̂ = Σ nᵢ(nᵢ − 1) / [N(N − 1)] is listed too.

Margalef richness

D = (S − 1) / ln N

Effective number of species, Hill N1

N1 = e^H′(ln) = 10^{H′(log₁₀)}

N1 is the number of equally common species that would give the same diversity. It does not depend on the base, which makes it good for comparing sites and years.