Shannon Diversity Index Calculator
The Shannon diversity index (H) measures the diversity of a biological community by combining species richness and evenness in a single number. Enter the count of individuals for each species, separated by commas, and the calculator computes each species proportion, the Shannon index using natural logarithms, the species richness, the Shannon (Pielou) evenness, and the effective number of species as the exponential of H. Higher values indicate communities that are both species-rich and evenly balanced, the hallmark of high biodiversity.
Shannon diversity index formula
pi = ni / N (proportion of species i)
H = -sum( pi * ln(pi) )
S = number of species
Evenness J = H / ln(S)
Effective species = exp(H)
N is the total number of individuals across all species. The sum runs over every species with a positive count. Evenness is undefined when there is only one species (ln 1 = 0), so it is reported only when S is at least 2.
Diversity index context
- The Shannon index originates from information theory, where it measures the uncertainty in predicting the species of a randomly chosen individual.
- Typical Shannon index values in ecological studies range from about 1.5 to 3.5, though there is no fixed upper bound.
- The index is sensitive to rare species relative to Simpson's index, which weights common species more heavily.
- Reporting exp(H) as effective species count makes comparisons across communities more intuitive.
- Use consistent sampling effort across communities before comparing their Shannon indices.
Shannon diversity index: frequently asked questions
What is the Shannon diversity index?
The Shannon diversity index (H, sometimes H') quantifies the diversity of a community by accounting for both the number of species (richness) and how evenly individuals are distributed among them (evenness). It is defined as the negative sum over all species of pi times the natural log of pi, where pi is the proportion of individuals belonging to species i.
How is the Shannon index calculated?
First compute each species proportion pi by dividing its count by the total count. Then for each species calculate pi times ln(pi). Sum these values across all species and multiply by minus one. The result is H. Higher H means greater diversity.
What is Shannon evenness?
Shannon evenness (also called Pielou's evenness, J) equals H divided by ln(S), where S is the number of species. It ranges from 0 to 1, with 1 meaning all species are equally abundant. Evenness isolates the equitability component of diversity from richness.
What does the exponential of H mean?
Exp(H), the exponential of the Shannon index, is the effective number of species or true diversity of order 1. It expresses diversity as the number of equally common species that would yield the same H, which is more intuitive than H itself.
What units does the Shannon index use?
When using the natural logarithm (ln), H is expressed in natural units called nats. If you use log base 2 it is in bits, and log base 10 gives decits. This calculator uses the natural logarithm, the most common convention in ecology.
Official sources
- U.S. Environmental Protection Agency: Indicators Used in National Aquatic Resource Surveys.
- U.S. Geological Survey: Biodiversity Research.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.