Simpson Diversity Index Calculator
Simpson's diversity index quantifies how dominated a community is by its most common species. Enter the count of individuals per species, separated by commas. The calculator computes Simpson's index D (the probability two random individuals share a species), the Simpson index of diversity 1-D, and the reciprocal Simpson index 1/D, which equals the effective number of species. Because Simpson's measure weights abundant species heavily, it complements the Shannon index and is widely used in ecology and conservation.
Simpson diversity index formula
pi = ni / N (proportion of species i)
D = sum( pi^2 )
Index of diversity = 1 - D
Reciprocal Simpson = 1 / D
N is the total count of individuals. D ranges from near 0 (very diverse) to 1 (a single species dominates). The 1-D form is bounded between 0 and 1 and increases with diversity; 1/D gives the effective number of species.
Simpson index context
- Simpson's index emphasises dominance and is less affected by rare species than the Shannon index.
- The 1-D form (Gini-Simpson index) is the most commonly reported because higher values mean greater diversity.
- The reciprocal 1/D is a true diversity of order 2, expressed as an effective number of equally common species.
- For small samples, an unbiased estimator using ni(ni-1)/N(N-1) is preferred; this tool uses the proportion form suited to larger N.
- Always compare communities sampled with equal effort and consistent taxonomic resolution.
Simpson diversity index: frequently asked questions
What is Simpson's diversity index?
Simpson's index (D) measures the probability that two individuals drawn at random from a community belong to the same species. It is the sum over all species of pi squared, where pi is the proportion of individuals in species i. Lower D means higher diversity, so it is often reported as 1 minus D or 1 divided by D.
What is the difference between D, 1-D, and 1/D?
D is the dominance (probability two individuals are the same species). The Simpson index of diversity, 1-D, is the probability they are different, ranging from 0 to 1 with higher values meaning more diversity. The reciprocal Simpson index, 1/D, is the effective number of species and ranges from 1 upward.
Should I use the sample or population formula?
The population (finite) version uses pi = ni/N and squares the proportions. The unbiased sample estimator uses ni(ni-1) divided by N(N-1). This calculator reports the population form using proportions, the version most commonly taught and applied when N is large.
How does Simpson's index compare to Shannon's index?
Both measure diversity, but Simpson's index gives more weight to common (dominant) species, while Shannon's index is more sensitive to rare species. Reporting both gives a fuller picture of a community's structure.
What does a reciprocal Simpson value of 4 mean?
A reciprocal Simpson index (1/D) of 4 means the community has the same dominance as a community of 4 equally abundant species. It is interpreted as the effective number of species, a true diversity of order 2.
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.