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) = 3108Sum of n×(n−1) over all species. - 3
Simpson's D = 1 − Σ nᵢ(nᵢ−1) ÷ N(N−1)
1 − 3108 ÷ (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.
Képlet
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.
Gyakran ismételt kérdések
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'.
Más néven
TG we-Calculate Editorial Team. (2026). SDI Calculator — Simpson's Diversity Index [Online calculator]. TG we-Calculate. https://we-calculate.com/hu/calculator/sdi-calculator
TG we-Calculate Editorial Team. "SDI Calculator — Simpson's Diversity Index." TG we-Calculate. 2026. https://we-calculate.com/hu/calculator/sdi-calculator.
TG we-Calculate Editorial Team, "SDI Calculator — Simpson's Diversity Index," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/hu/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/hu/calculator/sdi-calculator}}, year = {2026}, note = {TG we-Calculate} }
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