Simpson's Diversity Index Calculator
Enter the count of individuals in each species (or category) and get Simpson's Diversity Index alongside Shannon–Wiener entropy, Pielou's evenness, and Berger–Parker dominance — the standard suite of ecological diversity statistics.
0 = all individuals are the same species; 1 = maximum diversity
- 1
Total individuals (N)
Σ nᵢ = 100 - 2
Σ nᵢ(nᵢ − 1)
Σ nᵢ(nᵢ − 1) = 3,108Sum of n×(n−1) over all species. - 3
Simpson's D = 1 − Σ nᵢ(nᵢ−1) ÷ N(N−1)
1 − 3,108 ÷ (100 × 99) = 0.6861
How does this calculator work?
D = 1 − Σ nᵢ(nᵢ−1) / N(N−1): enter counts per species to get D (0–1, higher = more diverse), Shannon H (in nats), Pielou's evenness J (H / ln S, 0–1), and Berger–Parker dominance (max species fraction). Works for any categorical data, not only ecology.
Formula
How this is calculated
Simpson's Diversity Index D measures the probability that two individuals randomly drawn from the same community belong to different species. It is computed as D = 1 − Σ nᵢ(nᵢ−1) / (N(N−1)), where nᵢ is the count in each species and N is the total. D ranges from 0 (one species dominates entirely) to approaching 1 (many equally abundant species). Its complement 1 − D is Simpson's Dominance index — the probability that both individuals belong to the same species.
The Shannon–Wiener entropy H = −Σ pᵢ ln(pᵢ), where pᵢ = nᵢ/N, measures diversity as information content. Unlike Simpson's D, Shannon H weights rare species more strongly because it uses the logarithm of proportions. Pielou's evenness J = H / ln(S) normalises Shannon entropy by its theoretical maximum ln(S), giving a 0–1 scale where 1 means all species are equally abundant. Berger–Parker dominance max(nᵢ)/N is the simplest measure: the fraction of individuals belonging to the most abundant species.
All four indices assume a fully enumerated, representative sample. Small sample sizes inflate variance in all estimates — interpret with caution when N is low. The formulas work for any frequency data, not just ecology: market share by company, language distribution, or any categorical count.
Frequently asked questions
D = 0.85 means there is an 85% probability that two randomly chosen individuals belong to different species — indicating high diversity. Conversely, the dominance index is 0.15, meaning only a 15% chance both individuals are the same species.
Both measure diversity but weight species differently. Shannon H emphasises rare species more because it uses the logarithm of proportions; Simpson's D emphasises the most common species because it squares proportions. For most communities the two indices rank samples the same way.
Yes. The mathematics is identical for any categorical frequency distribution: brand market share, vote shares, word frequencies in a corpus, or response categories in a survey. 'Species' simply means 'category'.
Also known as
TG we-Calculate Editorial Team. (2026). Simpson's Diversity Index Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/simpsons-diversity-index-calculator
TG we-Calculate Editorial Team. "Simpson's Diversity Index Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/simpsons-diversity-index-calculator.
TG we-Calculate Editorial Team, "Simpson's Diversity Index Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/simpsons-diversity-index-calculator
@misc{wecalculate_simpsons_diversity_index_calculator, title = {Simpson's Diversity Index Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/simpsons-diversity-index-calculator}}, year = {2026}, note = {TG we-Calculate} }
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