What range of values can the Shannon index take?

H ranges from 0 (only one species present, no diversity) up to ln(S), where S is species richness — the value H would take if every species were equally abundant. Most real ecological communities fall between 1.5 and 3.5.

Shannon Diversity Index Calculator — Biodiversity

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Walk-through

How to Use This Calculator

4 steps

1

List each species and its count

Add one row per species observed in your survey, sample, or community, with the number of individuals counted for each. You need at least two species with a positive count for the index to be meaningful.

2

Add or remove species rows

Use the add-species button to add more rows as you record more species. Remove a row for a species you didn't actually observe, or leave its count at zero to exclude it from the calculation.

3

Read the Shannon index and evenness

The calculator shows H (the Shannon diversity index), evenness (H rescaled to 0-1), and species richness (S), updating instantly as you edit species and counts.

4

Check the relative abundance chart and species table

The bar chart on the Shannon Index tab shows each species' share of the total sample. The Species Table tab breaks down exactly how much each species contributes to H, so you can see which species drive the overall diversity score.

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Reference

Formula & Methodology

2 formulas

Shannon diversity index

H = -sum(p_i * ln(p_i))

For each species i, p_i is its proportion of the total sample: count_i divided by N (the sum of all counts). Multiply each p_i by its natural log, sum those products across every species, and negate the result. Because ln(p_i) is always negative for p_i between 0 and 1, negating the sum gives a positive H.

Evenness

Evenness = H / ln(S)

S is species richness — the number of species with a positive count. ln(S) is the maximum possible value of H for that many species (achieved when every species has an identical count). Dividing H by ln(S) rescales the index to a 0-1 scale so communities with different numbers of species can be compared on evenness alone. Evenness is undefined when S = 1, since ln(1) = 0.

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General reference

Trust, Methodology & Sources

Written by Calculover Editorial Team · Updated 2026-07-31

Editorial accountability

Author: Calculover Editorial Team - Editor

Owner: Calculover Editorial Team - Editorial owner

Last reviewed: 2026-07-31

Last verified: 2026-07-31

Methodology

This tool computes the standard Shannon-Wiener formula from the counts you enter. It does not correct for unequal sampling effort between species, and it cannot tell you whether your sample size is large enough to represent the true community.

Limitations & guidance

Shannon diversity index H = -sum(pi·ln(pi)), where pi = counti / total count. Evenness = H / ln(S), where S is species richness.

Professional guidance:

Primary sources

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Glossary

Key Terms Explained

7 terms

Shannon index (H) A measure of diversity that combines species richness and evenness into a single number. It increases both when more species are present and when individuals are spread more evenly across those species. Typical values for real communities fall between 1.5 and 3.5.

Biodiversity The variety of species present in a given area or sample. Diversity indices like Shannon's H are a way to quantify biodiversity so different sites, time periods, or sampling methods can be compared numerically.

Species richness The simple count of distinct species present in a sample (S). Richness ignores how abundant each species is — a sample with 10 species, one of which makes up 99% of individuals, has the same richness as a sample with 10 perfectly balanced species, but a much lower Shannon index.

Evenness How uniformly individuals are distributed across the species present, on a 0-1 scale. High evenness means each species has a similar number of individuals; low evenness means one or a few species dominate the sample.

Relative abundance The proportion of the total sample made up by a single species (p_i = count_i / N). Relative abundances across all species in a sample always sum to 1.

Shannon-Wiener index Another name for the Shannon diversity index, sometimes written as the Shannon-Weaver index. All three names refer to the same H = -sum(p_i * ln(p_i)) formula, originally adapted from Claude Shannon's information theory.

Ecology survey A structured count of species and individuals within a defined area or time period, used as the raw data for diversity indices. Survey method (quadrat, transect, trap count) affects which species are detected and should stay consistent when comparing H across sites or time.

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Scenarios

Real-World Examples

3 worked examples

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Forest ecologist

5-species tree survey

Oak 24 Maple 18 Birch 9 Pine 4 Elm 3

With 58 total trees across 5 species, H comes out to about 1.42 — moderate diversity. Oak and maple together make up roughly 72% of the sample, so evenness (about 0.88) is pulled down slightly by that imbalance even though richness is decent.

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Comparing two plots

Even vs skewed community, same richness

Plot A: 3 species at 10 each 10 / 10 / 10 Plot B: 3 species at 28 / 1 / 1 28 / 1 / 1

Both plots have the same species richness (S = 3), but Plot A's H = ln(3) ≈ 1.099 with evenness = 1.0 (perfectly even), while Plot B's H ≈ 0.20 with evenness ≈ 0.18. Richness alone would call these plots identical — the Shannon index and evenness reveal Plot B is dominated by a single species.

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Edge case

Single-species sample

Species A 50

With only one species present, p_1 = 1 and ln(1) = 0, so H = 0 — the mathematical floor of the index, representing zero diversity. Evenness is undefined here (dividing by ln(1) = 0), since evenness only has meaning when there's more than one species to compare.

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Deep Dive

Understanding the Shannon Diversity Index

3 chapters · 4 min read

The Shannon diversity index (H) is one of the most widely used ways to summarize biodiversity from a species count into a single comparable number. It's used across ecology, conservation biology, and environmental monitoring to track how diverse a community is and whether that diversity is changing over time.

How the Shannon index works

The Shannon index combines two things that a simple species count misses: how many species are present (richness) and how evenly individuals are spread across them (evenness). The formula H = -sum(p_i · ln(p_i)) computes each species' proportion of the total sample, weights it by its own natural log, and sums the results. Because rare species contribute a large negative log term multiplied by a small proportion, and common species contribute a small negative log term multiplied by a large proportion, the formula balances contributions from both rare and abundant species — unlike richness alone, which treats every species equally regardless of abundance.

Inputs and what they mean

The calculator only needs a name and a count for each species you observed — the count can be individuals, colonies, or any consistent unit of abundance. Species richness (S) and total sample size (N) are derived automatically from your rows. The result is dimensionless: it depends only on the relative proportions between species, not on the units you used to count them, so H = 1.4 means the same thing whether your counts are in individuals, biomass, or percent cover, as long as you're consistent within one sample.

Limits and edge cases

The Shannon index assumes your sample is representative of the community you're studying — a small or biased survey can under- or over-estimate true diversity, especially for rare species that are easy to miss. The index also doesn't tell you which species are present, only how the abundance is distributed, so two very different communities can have the same H by coincidence. When comparing sites or time periods, keep sampling method and effort consistent, since a bigger sample generally detects more rare species and can inflate richness independent of any real ecological change. For communities with very skewed abundance, consider comparing H alongside Simpson's index, which weights dominant species more heavily and can tell a different story about which community is 'more diverse.'

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Questions

Frequently Asked Questions

6 questions

What is the formula for the Shannon diversity index?+

H = -sum(p_i · ln(p_i)), where p_i is each species' proportion of the total sample (its count divided by the total count N). You compute this term for every species and sum the results.

What range of values can H take?+

H ranges from 0 (only one species present) up to ln(S), where S is species richness — the maximum possible value, reached when every species has an identical count. Most real ecological communities fall between about 1.5 and 3.5.

What does evenness mean and how is it calculated?+

Evenness = H / ln(S). It rescales the Shannon index to a 0-1 scale, letting you compare how evenly individuals are distributed across species independent of how many species are present. An evenness of 1 means every species has exactly the same count.

What counts as a high Shannon index?+

There's no universal cutoff, but ecologists commonly treat H below 1.5 as low diversity, 1.5 to 3.0 as moderate, and above 3.0 as high — though the right benchmark depends heavily on the type of ecosystem and sampling method being compared.

How does the Shannon index differ from the Simpson index?+

Both are computed from the same species-count data but weight abundance differently. Shannon's H, using a logarithm, is more sensitive to rare species. Simpson's index squares each proportion, which weights dominant, abundant species more heavily. The two indices can rank the same communities differently when abundance is very skewed.

What units does the Shannon index use?+

The Shannon index is dimensionless — it depends only on the relative proportions between species, not on the units used to count them (individuals, colonies, biomass, percent cover), as long as you're consistent within a single sample.

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Shannon Diversity Index Calculator

Species Counts