Shannon Weiner Index Calculator - Calculator Academy

Enter the proportion of individuals of each species and their natural logarithms into the calculator to determine the Shannon Weiner Index.

Shannon Weiner Index Formula

The Shannon Weiner Index is a biodiversity measure used to describe both richness (how many species are present) and evenness (how evenly individuals are distributed among those species). It is also commonly called the Shannon-Wiener or Shannon-Weaver diversity index.

H' = -\sum_{i=1}^{S} p_i \ln(p_i)

If you begin with species counts instead of proportions, convert each species count into a proportion first.

p_i = \frac{n_i}{N}

H’ = Shannon Weiner Index
S = total number of species in the sample
p_i = proportion of the total sample belonging to species i
n_i = count of individuals in species i
N = total number of individuals across all species
ln = natural logarithm

How to Use the Shannon Weiner Index Calculator

Determine the share of the sample represented by each species.
Enter each species proportion into the calculator.
Make sure all proportions are between 0 and 1.
The proportions should sum to 1. If one value is missing, it can be found by subtracting the known proportions from 1.

p_{missing} = 1 - \sum p_i

Once the proportions are known, the calculator multiplies each proportion by its natural logarithm, adds those terms together, and applies a negative sign to produce the final diversity value.

How to Interpret the Result

A larger Shannon value means the community is more diverse. The index rises when more species are present and when their abundances are more evenly distributed. It falls when one or a few species dominate most of the sample.

0 \leq H' \leq \ln(S)

The minimum value is 0, which occurs when the sample is entirely dominated by a single species. The maximum depends on the number of species and occurs when every species has the same proportion.

H'_{max} = \ln(S)

For example, if there are three species and each makes up one-third of the community, the index reaches its maximum for a three-species system.

H'_{max} = \ln(3) \approx 1.099

Community Pattern	What Happens to the Index
One species is overwhelmingly dominant	The index is low
Several species are present, but one is still much more common	The index is moderate
Many species are present with similar abundances	The index is high
Species counts become more evenly distributed	The index increases

Example Calculation

Assume a habitat contains three species with proportions 0.50, 0.30, and 0.20.

H' = -[(0.50\ln 0.50) + (0.30\ln 0.30) + (0.20\ln 0.20)]

H' \approx 1.03

This indicates a reasonably diverse community, but not the maximum possible diversity for three equally abundant species.

Why Ecologists Use This Index

The Shannon Weiner Index is popular because it captures two important features of biodiversity at the same time:

Richness: more species generally increase the index.
Evenness: a more balanced distribution also increases the index.

Because of this, the index is often used in ecology, conservation biology, environmental monitoring, forestry, soil science, and water quality studies.

Common Input Mistakes

Entering raw counts instead of proportions.
Using proportions that do not add up to 1.
Entering negative values or values greater than 1.
Comparing results from samples collected with very different methods or effort levels.

Helpful Notes

The index is dimensionless, so it has no units.
The natural logarithm is the standard version used in most ecological applications.
Species with zero observed individuals do not increase the index.
Adding a rare species usually increases the index slightly; adding a common species in a more balanced way increases it more.

Related Diversity Concept: Evenness

If you want to know how evenly species are distributed apart from richness, you can compute Pielou’s evenness using the Shannon result.

J' = \frac{H'}{\ln(S)}

An evenness value closer to 1 indicates that the species present are represented in more similar proportions.