Foundations · Diversity & concentration
Simpson's Diversity Index Calculator
How diverse is a community? Enter the count of each species (or category) to get Simpson's index D, the Diversity Index 1 − D, and the Reciprocal 1/D — the effective number of equally-common species — alongside species richness, the Shannon index and evenness. Because diversity is not just how many kinds there are, but how evenly the individuals are spread among them.
Counts of individuals in each category. Labels are optional — “Oak: 35”, “Oak = 35”, “Oak 35” or a bare “35” all work. Proportions (e.g. 0.35) work too.
Result
In plain English
Diversity has two ingredients: richness (how many different species there are) and evenness (how equally the individuals are divided between them). A wood with 1,000 oaks and one each of four other trees has five species but feels like an oak wood. Simpson's index captures both at once by asking a simple question: pick two individuals at random — how likely are they to be the same species?
- Simpson's index, D
- The probability that two individuals drawn at random are the same species. High D means low diversity (one or two species dominate). It runs from near 0 to 1.
- Diversity Index, 1 − D
- The probability that two random individuals are different species. Higher means more diverse. This is what “Simpson's Diversity Index” usually refers to.
- Reciprocal, 1/D
- The “effective number of species”: how many equally-common species would give the same D. A reading of 4.0 means the community is as diverse as four perfectly balanced species, however many it actually has.
- richness (S)
- Simply the number of species present — diversity's first ingredient, but blind to evenness on its own.
- Shannon index (H) & evenness
- An alternative diversity measure from information theory, −Σ p ln p, with evenness H ∕ ln S scaling it to 0–1 (1 = perfectly even).
Frequently asked
How do you calculate Simpson's Diversity Index?
Count the individuals of each species (n) and the total (N). Simpson's index is D = Σ [n(n − 1)] ∕ [N(N − 1)] — the chance two randomly picked individuals are the same species. The Diversity Index is 1 − D (the chance they differ), and the Reciprocal is 1 ∕ D. For proportions or very large populations the equivalent formula is D = Σ p², where p is each species' share.
What's a good Simpson's Diversity Index value?
The Diversity Index 1 − D runs from 0 (no diversity — a single species) to almost 1 (very diverse). There is no universal “good” cut-off; it only means something compared with another community sampled the same way. The Reciprocal 1 ∕ D is often easier to interpret: it is the effective number of equally-common species, so 1 ∕ D = 5 is meaningfully more diverse than 1 ∕ D = 2.
What is the difference between Simpson's and Shannon's index?
Both combine richness and evenness, but weight them differently. Simpson's index is dominated by the commonest species, so it is really a measure of dominance (or its inverse). Shannon's index, −Σ p ln p, gives comparatively more weight to rare species. Report whichever your field expects — and ideally both, since they answer slightly different questions.
What is the difference between richness and evenness?
Richness is simply how many different species (or categories) are present; evenness is how equally the individuals are spread among them. A wood with 1,000 oaks and one each of four other trees is rich — five species — but very uneven, so it scores low for diversity and feels like an oak wood. A good diversity index such as Simpson’s rewards both: you need many types and a balanced spread to score high.