What this calculator does
Simpson's Diversity Index measures how mixed a community is, whether that community is species in a habitat, categories in a data set, or any other collection split into groups. A value near 1 means individuals are spread evenly across many groups; a value near 0 means one group dominates almost everything.
The calculation behind it, the simpson's diversity index formula, actually starts from the opposite question: if you picked two individuals at random from the whole population, how likely is it that they belong to the same group? That probability is Simpson's Index itself. Subtracting it from 1 flips it into the more commonly quoted diversity figure, where a higher number now means more diversity rather than less.
The formula
Simpson's Index (D) is the sum, across every category, of n(n−1), divided by N(N−1), where n is the count in each category and N is the total count across all categories. That sum is the probability of drawing two individuals from the same category by chance. Simpson's Diversity Index is simply 1 minus that figure, and the Reciprocal Simpson's Index is 1 divided by it, which behaves like an effective number of equally common categories.
| Term | Meaning |
|---|---|
| n | The count of individuals in a single category or species. |
| N | The total count of individuals across every category. |
| Simpson's Index (D) | The probability two randomly picked individuals belong to the same category: Σ[n(n−1)] ÷ [N(N−1)]. |
| Diversity Index (1−D) | One minus Simpson’s Index. Higher means more diverse. |
The inputs explained
| Field | What to enter |
|---|---|
| Count for each species or category (comma or space separated) | Enter the count for each species or category, separated by commas or spaces, in any order. |
When to use it
Comparing two habitats
Two sites can have the same number of species recorded, yet very different diversity, if one site is dominated by a single common species and the other has counts spread more evenly. The index captures that difference in one number.
Tracking diversity over time
Recalculating the index each season or year from repeated survey counts shows whether a community is becoming more even or more dominated by fewer groups.
Summarising a market or portfolio split
The same formula applies outside ecology to any set of category counts, such as market share by company or holdings by asset, where a lower diversity index flags concentration in a small number of categories.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the index changes from an even split to a dominated one
The same total of 30 individuals across five categories, arranged from perfectly even to heavily dominated by one.
| Category counts | Simpson's Diversity Index (1−D) | Reciprocal Simpson's Index (1/D) |
|---|---|---|
| 6, 6, 6, 6, 6 | 0.8276 | 5.80 |
| 10, 8, 5, 4, 3 | 0.7885 | 4.73 |
| 15, 6, 4, 3, 2 | 0.7011 | 3.35 |
| 22, 3, 2, 2, 1 | 0.4575 | 1.84 |
| 26, 1, 1, 1, 1 | 0.2529 | 1.34 |
Diversity Index for a five-species count
A single worked example, matching the default values on the calculator.
| Category counts | Number of categories | Total individuals counted |
|---|---|---|
| 10, 8, 5, 3, 1 | 5 | 27 |
Questions
What is a good Simpson's Diversity Index value?
It ranges from 0 (no diversity, a single category holds everything) to just under 1 (very high diversity, spread evenly across many categories). What counts as high or low depends entirely on the field and the number of categories being compared, so it is most useful compared across sites, samples or time periods measured the same way.
How do I calculate Simpson's diversity index by hand?
Square each category’s count and subtract the count itself to get n(n−1) per category, sum those, divide by N(N−1) for the total population, and subtract the result from 1. This calculator does that arithmetic automatically from a plain list of counts.
What is the difference between Simpson's Index and Simpson's Diversity Index?
Simpson's Index (D) is the probability two random individuals share a category, so a low D means high diversity. Simpson's Diversity Index (1−D) flips that around so a higher number consistently means more diversity, which is why the flipped version is the one usually reported.
Does the number of categories alone determine the index?
No. Evenness matters as much as the count of categories. Five categories split evenly produce a higher index than five categories where one holds almost all the individuals, even though both cases have exactly five categories.
To see the percentage and angle each category takes on a chart rather than a diversity score, use the pie chart percentages calculator. For the mean and spread of a numeric data set, see the descriptive statistics calculator.