# Simpson’s Diversity Index Calculator URL: https://speedycalculator.com/calculators/statistics/simpsons-diversity-index/ Last updated: 2026-10-30 > The Simpson's diversity index calculator takes the number of individuals of each species and returns Simpson's index D, the diversity index 1 − D, the reciprocal index 1/D, species richness, evenness and the infinite-population form Σp². ## Inputs - Number of individuals of each species ## Results - Simpson's index D - Simpson's diversity index 1 − D - Simpson's reciprocal index 1/D - Species richness S - Total individuals N - Simpson's evenness (1/D) ÷ S - Infinite-population form Σp² - 1 − Σp² (with replacement) - Diversity level ## Formula ``` D = Σnᵢ(nᵢ − 1) ÷ (N(N − 1)) · Gini–Simpson = 1 − D · Inverse Simpson = 1/D · evenness E = (1/D) ÷ S ``` ## Explanation Simpson's index, introduced by Edward Simpson in 1949, captures two things at once: how many species a community holds (richness) and how evenly the individuals are spread among them (evenness). D is the probability that two individuals picked at random, without putting the first back, belong to the same species. A community dominated by one species has D close to 1; a rich, even community has D close to 0. Because "bigger means less diverse" is confusing, ecologists usually report the Simpson's diversity index 1 − D, the probability that the two individuals are different species, or the reciprocal index 1/D, which can be read as the "effective number" of equally common species. A meadow with 1/D = 3.7 is as diverse as one with about 3.7 equally abundant species. Simpson's measures are weighted towards the common species, so adding a few rare species barely changes them – unlike the Shannon index, which is more sensitive to rare species. The same formula is used outside ecology: in economics Σp² is the Herfindahl–Hirschman index of market concentration, and in genetics 1 − Σp² is the expected heterozygosity. ### How to use the Simpson's Diversity Index Calculator - **Number of individuals of each species** Results update as you type, and everything is calculated in your browser. ### How it works Enter the count of individuals for each species. The calculator adds them to get N, sums nᵢ(nᵢ − 1) over the species and divides by N(N − 1) to get D. Then it derives 1 − D, 1/D, evenness and the with-replacement form Σ(nᵢ ÷ N)². ### Worked example A pond survey counts 40, 25, 20, 10 and 5 individuals of five species (N = 100). Σn(n − 1) = 1,560 + 600 + 380 + 90 + 20 = 2,650 and N(N − 1) = 9,900, so D = 0.2677, 1 − D = 0.7323 and 1/D = 3.736. Evenness is 3.736 ÷ 5 = 0.747. The with-replacement form gives Σp² = 0.275 and 1 − Σp² = 0.725. ### Same richness, different evenness Community (4 species)1 − D1/D25, 25, 25, 250.7584.1340, 30, 20, 100.7073.4185, 5, 5, 50.2731.38 ### What each result means - **Simpson's index D** = simpson([Number of individuals of each species]) - **Simpson's diversity index 1 − D** = 1 - [Simpson's index D] - **Simpson's reciprocal index 1/D** = 1÷[Simpson's index D] - **Species richness S** = count([Number of individuals of each species]) - **Total individuals N** = sum([Number of individuals of each species]) - **Simpson's evenness (1/D) ÷ S** = [Simpson's reciprocal index 1÷D]÷[Species richness S] - **Infinite-population form Σp²** = ss([Number of individuals of each species])÷sum([Number of individuals of each species])^2 - **1 − Σp² (with replacement)** = 1 - [Infinite-population form Σp²] ## Worked example Inputs — Number of individuals of each species: 40, 25, 20, 10, 5. Results — Simpson's index D = 0.2677; **Simpson's diversity index 1 − D = 0.7323**; Simpson's reciprocal index 1/D = 3.7358; Species richness S = 5; Total individuals N = 100; Simpson's evenness (1/D) ÷ S = 0.7472; Infinite-population form Σp² = 0.275; 1 − Σp² (with replacement) = 0.725; Diversity level = High. ## Key terms - **Species richness**: The number of different species in the sample. - **Species evenness**: How similar the abundances of the species are. - **Simpson's index (D)**: The probability that two individuals drawn without replacement are the same species. - **Effective number of species**: 1/D – the number of equally common species that would give the same diversity. ## FAQ **What does Simpson's diversity index tell you?** 1 − D is the chance that two randomly chosen individuals are of different species. 0.73 means a 73% chance of picking two different species. **What is the range of Simpson's index?** D and 1 − D lie between 0 and 1. 1/D ranges from 1 (a single species) up to the number of species S when all are equally common. **What is the difference between D, 1 − D and 1/D?** They carry the same information on different scales: D measures dominance, 1 − D diversity as a probability and 1/D diversity as an effective number of species. **Which formula should I use, n(n − 1) or p²?** Use Σn(n − 1) ÷ N(N − 1) for counted samples (sampling without replacement). Σp² is the version for an infinite population or for percentages; the two agree closely for large samples. **What is Simpson's index of 300, 335 and 365 individuals?** N = 1,000, Σn(n − 1) = 334,450, so D = 334,450 ÷ 999,000 = 0.335, 1 − D = 0.665 and 1/D = 2.99. **Simpson or Shannon – which is better?** Neither. Simpson is dominated by common species and is robust to sample size; Shannon gives more weight to rare species. Many studies report both. **Can Simpson's index be used outside ecology?** Yes – for market shares (Herfindahl–Hirschman index), genetic diversity, language diversity, or the variety of answers to a survey question. ## Sources - [Wikipedia – Diversity index (Simpson index)](https://en.wikipedia.org/wiki/Diversity_index) - [Simpson (1949), Measurement of diversity, Nature 163: 688](https://doi.org/10.1038/163688a0) - [Khan Academy – Biodiversity](https://www.khanacademy.org/science/biology/ecology)