Simpson Diversity Index Calculator
The Simpson index asks a simple question with a clear meaning: if you pick two individuals at random, how likely are they to be different species? This calculator computes the popular 1 minus D form from a list of species counts. First each count is divided by the grand total to get its proportion, then each proportion is squared and the squares are summed to give D, the chance that two random individuals are the same species. Subtracting D from 1 gives the Gini-Simpson index, which runs from 0 to 1 so that higher always means more diverse. A community of four species with counts of 40, 30, 20 and 10 has squared proportions of 0.16, 0.09, 0.04 and 0.01, summing to 0.30, so the index is 1 minus 0.30, which is 0.70. Compared with the Shannon index, Simpson is more sensitive to the dominant species and is naturally bounded, which makes communities easy to compare side by side. A value near 1 signals many species spread evenly, while a value near 0 signals one species in charge. Enter your counts to get the index. Every figure is computed deterministically from the formula, never estimated, with the method and a worked example shown below for verification.
The Simpson index subtracts the sum of squared proportions from one: 1 - D = 1 - sum(p^2). Species counts of 40, 30, 20 and 10 give an index of 0.7000.
Simpson index formula
D = sum over species of p_i^2
p_i = count of species i / total count
Simpson index = 1 - D (Gini-Simpson form)
ranges from 0 (one species) to near 1 (very diverse)
D is the chance two random individuals are the same species. Subtracting it from 1 gives the chance they differ, so higher means more diverse.
Worked example
Four species have counts of 40, 30, 20 and 10, a total of 100.
- Proportions: 0.4, 0.3, 0.2, 0.1
- Squares: 0.16, 0.09, 0.04, 0.01
- D = 0.16 + 0.09 + 0.04 + 0.01 = 0.30
- Simpson index = 1 - 0.30 = 0.70
The Simpson index is 0.7000. These are the calculator's default inputs, so the result above matches the widget exactly.
Index for equally abundant species
With perfect evenness, 1 minus D equals 1 minus 1 over the species count.
| Species (equal) | 1 - D |
|---|---|
| 2 | 0.5000 |
| 4 | 0.7500 |
| 5 | 0.8000 |
| 10 | 0.9000 |
Biodiversity and community ecology metrics: US Geological Survey (USGS).
Simpson diversity index calculator: frequently asked questions
What is the Simpson diversity index?
The Simpson index measures the probability that two individuals drawn at random belong to different species. In the common 1 minus D form, it is one minus the sum of each species' squared proportion, so a higher value means greater diversity.
What is the difference between D and 1 minus D?
D, the sum of squared proportions, is the probability that two random individuals are the same species, so a higher D means lower diversity. The form 1 minus D, called the Gini-Simpson index, flips this so higher means more diverse, which is more intuitive. This calculator reports 1 minus D.
How does Simpson differ from Shannon?
Both measure diversity, but Simpson is more sensitive to the most abundant species while Shannon weights rare and common species more evenly. Simpson is bounded between 0 and 1 in its 1 minus D form, which makes it easy to compare across communities.
What does a value near 1 mean?
A 1 minus D close to 1 means two randomly chosen individuals are very likely to be different species, indicating high diversity with many species spread evenly. A value near 0 means one species dominates, so most pairs are the same species.
Is the result computed automatically?
Yes. The page computes each proportion, squares it, sums the squares and subtracts from 1 deterministically. No value is estimated or hard-coded, so changing the counts updates the index instantly.
Official sources
- Biodiversity and community ecology metrics: US Geological Survey (USGS). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.