Shannon Diversity Index Calculator — Species Diversity & Evenness

What is the Shannon Diversity Index?

The Shannon diversity index (also known as the Shannon–Wiener diversity index, abbreviated H′) is a widely used metric in ecology for measuring species diversity within a community. It was developed from Claude Shannon's information entropy formula and captures two key properties of a community: richness (how many species are present) and evenness (how evenly individuals are distributed among species).

How to Use the Shannon Diversity Index Calculator

To get the Shannon–Wiener diversity index for your data set:

1. Enter the name of each species or sample group (optional but recommended).
2. Enter the number of individuals observed for each species.
3. Add rows as needed — up to 40 samples are supported.
4. Select the base of the logarithm (natural log e is the default; base 2 and base 10 are also available).
5. Click Calculate to see the results.

At the bottom of the results panel you will see:

• H′ — Shannon diversity index
• J′ — Evenness (Pielou's J)
• S — Species richness (number of species)
• N — Total number of individuals
• Average population size — N/S

Shannon Diversity Index Formula

The mathematical formula for the Shannon diversity index is:

H′ = −∑ [ p_i × log(p_i) ]

where:

• H′ — Shannon diversity index;
• p_i — proportion of individuals belonging to species i in the whole community = n_i / N;
• n_i — number of individuals of species i;
• N — total number of individuals in the community;
• ∑ — sum over all species; and
• log — logarithm (natural log is standard, but base 2 and base 10 are also common).

Evenness (Pielou's J)

Evenness is calculated as:

J′ = H′ / H_max   where H_max = log(S)

Evenness ranges from 0 (no evenness) to 1 (perfect evenness), indicating how uniformly the individuals are distributed among species.

How to Calculate the Shannon Diversity Index — Step by Step

1. Count all individuals in each species and record n_i.
2. Sum all counts to get the total N.
3. Calculate p_i for each species: p_i = n_i / N.
4. Compute p_i × ln(p_i) for each species.
5. Sum all values from step 4.
6. Negate the sum (multiply by −1) to get H′.

Example: How to Calculate the Shannon Diversity Index

Suppose a meadow contains three species of birds:

N = 20 · Sum of p_i × ln(p_i) = −1.0297 · H′ = −(−1.0297) ≈ 1.030

H_max = ln(3) ≈ 1.099 · Evenness J′ = 1.030 / 1.099 ≈ 0.937

This indicates high diversity with very even distribution among the three species.

Shannon Diversity Index Range of Values

• H′ = 0 — only one species is present (no diversity).
• H′ < 1 — low diversity; community is dominated by very few species.
• 1 ≤ H′ < 2 — moderate diversity.
• 2 ≤ H′ < 3 — high diversity.
• H′ ≥ 3 — very high diversity; typical of tropical rainforests and coral reefs.
• J′ close to 1 — species are equally abundant (high evenness).
• J′ close to 0 — one species dominates (low evenness).

Note: The absolute value of H′ depends on the logarithm base used. Values calculated with natural log (nats), log₂ (bits), or log₁₀ (decibels/Hartleys) cannot be directly compared with each other.

FAQs

What is a good Shannon diversity index value?

There is no universal "good" value — it depends on the ecosystem. Tropical forests typically show H′ between 2.5 and 4.5, temperate forests between 1.5 and 3.5, and heavily disturbed habitats below 1.5.

What is the difference between Shannon diversity and species richness?

Species richness (S) simply counts the number of species, treating all as equally important. Shannon diversity also accounts for the relative abundance of each species, giving a more complete picture of the community structure.

Which logarithm base should I use?

The natural logarithm (base e) is most common in ecology and is the default in this calculator. Use base 2 when comparing results in information theory, and base 10 in some geology and geography studies. Always specify the base when reporting H′.

Can the Shannon index be used for non-biological data?

Yes. The formula applies to any set of categories and counts — for example, languages spoken in a region, types of land use, or customer segments.

What is the maximum possible Shannon diversity index?

The theoretical maximum H′ = log(S) is achieved when all species have exactly the same number of individuals (perfect evenness). This is why the evenness index J′ = H′ / log(S) ranges from 0 to 1.