SDI Calculator — Simpson's Diversity Index
Enter counts for each species (or category) and get Simpson's Diversity Index, Shannon–Wiener entropy, Pielou's evenness, and Berger–Parker dominance — the standard suite of ecological diversity statistics.
0 = no diversity (one species dominates), 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
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Simpson's Diversity Index D = 1 − Σ nᵢ(nᵢ−1) / N(N−1). Enter species counts to get D (0–1, higher = more diverse), Shannon–Wiener H (in nats), Pielou's evenness J (H / ln S, 0–1), and Berger–Parker dominance (max species fraction). Works for any categorical frequency data, not just ecology.
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How this is calculated
Simpson's Diversity Index (D) measures the probability that two individuals drawn at random from the same sample belong to different species. It is computed as D = 1 − Σ nᵢ(nᵢ−1) / N(N−1), where nᵢ is the count of each species and N is the total. D ranges from 0 (one species dominates entirely) to approaching 1 (many equally abundant species). The complementary statistic — Simpson's dominance index — is 1 − D, which measures the probability that both random individuals belong to the same species.
The Shannon–Wiener entropy H = −Σ pᵢ ln(pᵢ) (where pᵢ = nᵢ/N) measures uncertainty or information content — higher H means more species at more even abundances. It is unbounded but practically ranges from 0 to ln(S). Pielou's evenness J = H / ln(S) normalises Shannon entropy by its theoretical maximum, giving a 0–1 scale where 1 means all species are equally abundant.
Berger–Parker dominance is the simplest measure: the fraction of individuals belonging to the most abundant species. Higher values indicate stronger dominance. Use Simpson's D when you want a single probability-based summary; use Shannon H when you want to weight rare species more strongly. Both require a representative, well-counted sample — small sample sizes increase variance in all these indices.
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A D of 0.8 means there is an 80% probability that two randomly chosen individuals belong to different species — indicating fairly high diversity. A D of 0.2 indicates low diversity where one or a few species strongly dominate.
Both measure diversity, but they weight rare species differently. Shannon H treats rare species more heavily because it uses the logarithm of proportions; Simpson's D emphasises the most abundant species because it squares proportions. In practice they usually rank samples the same way, but disagree when rare species are numerous.
Yes. Simpson's D and Shannon H apply to any frequency distribution: market share by company, word frequency in a text, language distribution in a region, or survey response categories. The mathematics is identical — 'species' just means 'category'.
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TG we-Calculate Editorial Team. (2026). SDI Calculator — Simpson's Diversity Index [Online calculator]. TG we-Calculate. https://we-calculate.com/ga/calculator/sdi-calculator
TG we-Calculate Editorial Team. "SDI Calculator — Simpson's Diversity Index." TG we-Calculate. 2026. https://we-calculate.com/ga/calculator/sdi-calculator.
TG we-Calculate Editorial Team, "SDI Calculator — Simpson's Diversity Index," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/ga/calculator/sdi-calculator
@misc{wecalculate_sdi_calculator, title = {SDI Calculator — Simpson's Diversity Index}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/ga/calculator/sdi-calculator}}, year = {2026}, note = {TG we-Calculate} }
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