Simpson's Diversity Index Calculator
Enter the count of individuals observed for each species - up to 10 - and this calculator returns all three standard forms of Simpson's Diversity Index: the dominance index D, the complement 1-D (also called the Gini-Simpson index), and the reciprocal 1/D. You also get species richness, species evenness, and a step-by-step breakdown of the arithmetic so you can follow every number.
What is Simpson's Diversity Index?
Simpson's Diversity Index is a measure of biodiversity that quantifies how evenly individuals are distributed across species in a community. Developed by Edward H. Simpson in 1949, it is based on the probability that two randomly selected individuals from a sample belong to the same species. Three closely related values are commonly reported: Simpson's Index D (dominance), the Gini-Simpson Index (1 - D), and the Reciprocal Index (1/D). Because D is a measure of dominance rather than diversity, ecologists usually prefer the complement 1 - D or the reciprocal 1/D, both of which increase as diversity rises.
The three Simpson formulas explained
Simpson's Index D uses the formula D = sum of [n_i * (n_i - 1)] divided by [N * (N - 1)], where n_i is the count of individuals in species i and N is the total count across all species. This finite-sample version (without replacement) is preferred for field surveys where the sample is a small fraction of the total population. For very large or estimated populations you can use D = sum of (p_i squared), where p_i = n_i / N is the proportional abundance. The Gini-Simpson Index (1 - D) gives the probability that two randomly chosen individuals come from different species, so it ranges from 0 (one species only) to 1 (maximum diversity). The Reciprocal Index (1/D) starts at 1 and rises toward S, the total species count, when all species are equally abundant - making it the most intuitive of the three for communicating diversity to a general audience.
Species richness vs. species evenness
Simpson's index captures both the number of species (richness) and how evenly individuals are spread among them (evenness). A community with 10 species is not necessarily more diverse than one with 5 if 9 of those 10 species each have only 1 individual and the tenth has 10,000. Species evenness - calculated here as (1/D) / S - ranges from 0 to 1 and measures how close the actual distribution is to the theoretical maximum. An evenness score of 1.0 means every species has exactly the same count; a very low evenness signals that a single dominant species drives the index. Because richness and evenness can pull in opposite directions, always report both alongside Simpson's index when comparing communities.
How to use this calculator
Enter the individual count for each species in your sample, from Species 1 through to however many you observed (up to 10). Leave unused rows at 0. Choose the finite-sample formula if your counts come directly from a field survey; choose the infinite-population formula if you are working with estimated proportions scaled to a large reference population. The results panel shows D, 1 - D, 1/D, total N, species richness, and species evenness. The Steps panel traces every arithmetic step so you can verify or reproduce the calculation by hand. The chart shows how the Gini-Simpson index would change if the same total population were spread evenly across different numbers of species, giving you a benchmark for your actual result.
Interpreting Simpson's Diversity Index values
| Gini-Simpson (1 - D) | Interpretation | Typical context |
|---|---|---|
| 0.00 - 0.29 | Low diversity | Monoculture or heavily disturbed habitat |
| 0.30 - 0.49 | Moderate-low diversity | Species-poor community, one or two dominants |
| 0.50 - 0.69 | Moderate diversity | Mixed community with some dominant species |
| 0.70 - 0.84 | High diversity | Species-rich, relatively balanced community |
| 0.85 - 1.00 | Very high diversity | Highly diverse, near-equal species abundance |
Gini-Simpson (1 - D) ranges and their typical ecological interpretation. Values near 1 indicate high species diversity.
Frequently asked questions
What is the difference between Simpson's Index D and the Gini-Simpson Index?
Simpson's Index D measures dominance - the probability that two randomly selected individuals belong to the same species. Lower D means more diversity. The Gini-Simpson Index (1 - D) is simply the complement: the probability they belong to different species. It ranges from 0 (no diversity) to 1 (maximum diversity), making it easier to read intuitively. Most modern ecology papers report the Gini-Simpson Index rather than D directly.
When should I use the finite vs. infinite formula?
Use the finite (without replacement) formula - D = sum[n_i*(n_i-1)] / [N*(N-1)] - whenever your data come from an actual count of individuals in a bounded sample, which is the most common situation in ecology. Use the infinite (with replacement) formula - D = sum(p_i squared) - only when you are working with true proportional abundances or estimated probabilities for a population so large that sampling without replacement makes no practical difference. For most field surveys the finite formula is correct.
What does a Gini-Simpson index of 0 or 1 mean?
A value of 0 means there is only one species: any two randomly chosen individuals must belong to it, so the probability of picking two different species is zero. A value of 1 is the theoretical maximum, approached when the sample contains a very large number of species that each have exactly one individual. In practice, real communities rarely reach 0.95 or above.
How is species evenness calculated here?
This calculator divides the Reciprocal Index (1/D) by species richness S. When all species are equally abundant, 1/D equals S and evenness is 1.0. When one species dominates, 1/D stays close to 1 regardless of how many other species are present, and evenness approaches 1/S (near zero). This ratio is sometimes called the Simpson evenness index.
What is the effective number of species?
The Reciprocal Index (1/D) is sometimes called the effective number of species. It answers the question: how many equally abundant species would produce the same Simpson's D as the observed community? If 1/D = 4.2, your community is as diverse as a hypothetical one containing 4.2 equally common species, even if your sample actually contains 8 species. It makes comparisons across communities with different richness more meaningful.
How does Simpson's index compare to the Shannon-Wiener index?
Both indices measure alpha diversity (diversity within a single community). The Shannon-Wiener index (H') is log-based and gives more weight to rare species, so it rises more steeply when rare species are added. Simpson's index is based on dominance probabilities and is more sensitive to the most common species. For communities dominated by a few species, Shannon-Wiener will report higher diversity than Simpson's. Using both together gives a fuller picture.