Simpson's diversity index calculator
Enter the number of individuals of each species in your sample. The calculator gives Simpson's index D, the chance that two individuals picked at random belong to different species (1 − D), the effective number of species (1/D), evenness and the share of the most common species.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Count the individuals of each species in your sample and enter one number per species.
- Choose the sample formula for counts of individuals or the community formula for proportions.
- Read 1 − D and 1/D; D itself, evenness and Berger–Parker dominance are shown below.
- Sample: D = Σ nᵢ(nᵢ − 1) ÷ (N(N − 1)), where nᵢ is the count of species i and N the total.
- Community: λ = Σ pᵢ², where pᵢ = nᵢ ÷ N.
- Simpson’s diversity: 1 − D, from 0 (one species) towards 1.
- Inverse Simpson: 1/D, from 1 up to S.
- Evenness: (1/D) ÷ S, from 0 to 1.
- Berger–Parker: the largest nᵢ ÷ N.
Worked example
Counts 12, 8, 5, 3 and 2: S = 5 species, N = 30 individuals.
- Σ n(n − 1) = 132 + 56 + 20 + 6 + 2 = 216; N(N − 1) = 870; D = 0.2483;
- 1 − D = 0.7517: three times out of four, two random individuals are different species;
- 1/D = 4.0278, evenness 4.0278 ÷ 5 = 0.8056;
- the most common species makes up 12 ÷ 30 = 0.4 of the sample.
Tips
- Species with a count of 0 are left out and do not change S.
- Compare samples of similar size and effort; S grows with sampling, D much less.
- Use the same formula for every sample you compare.
Frequently asked questions
What does Simpson's index measure?
The probability that two individuals drawn at random from the sample belong to the same species. A high D means one or a few species dominate. Because a higher D means less diversity, results are usually reported as 1 − D (the chance of two different species) or 1/D.
Which formula should I use, n(n − 1) or p²?
Σ n(n − 1) ÷ N(N − 1) treats the counts as a sample and draws without replacement; it is the usual choice for field counts. Σ p² describes a whole community, or proportions like percentage cover. For 12, 8, 5, 3 and 2 individuals the sample form gives D = 0.2483 and the community form 0.2733.
What is 1/D?
The inverse Simpson index, the effective number of species: how many equally common species would give the same D. Here 1/D = 4.0278, close to the 5 species present, because the community is fairly even. Divided by S it gives Simpson's evenness, 0.8056.
How does it differ from the Shannon index?
Simpson's index is driven by the common species and barely changes when you add a rare one; Shannon's H gives rare species more weight. Reporting both, or Hill numbers, gives a fuller picture. The Shannon calculator shows D next to H.