Simpson's Diversity Index Calculator
Enter the count of individuals in each group or species, separated by commas or spaces, to get Simpson's index D, the Index of Diversity 1-D, and the reciprocal 1/D, along with your total N and number of groups.
Example: with Counts per group (comma or space separated) 40, 30, 20, 10 → Index of Diversity (1 - D): 0.707.
- Simpson's D (dominance)0.293
- Reciprocal (1/D)3.41
- Sample4 groups, N = 100 individuals
Computed by the calculator below using its default values. Change any input to see your own numbers.
Simpson's D = Σ n(n-1) / N(N-1). Report 1-D or 1/D as your diversity figure and say which one.
What Simpson's index actually measures
Simpson's index starts from a simple question: if you reach into the community and grab two individuals at random, how likely are they to be the same kind? That probability is D. Because it climbs as one or two groups take over, D is really a measure of dominance, not diversity.
Flip it and you get the number most people want. The Index of Diversity, 1-D, is the chance the two individuals are different, so it rises as the community becomes richer and more even. The Reciprocal Index, 1/D, rescales the same information into an effective number of equally common groups.
Counts, not proportions
Feed the calculator raw counts of each group, not percentages. The formula D = Σ n(n-1) / N(N-1) uses the actual number of individuals because it models sampling without replacement: pulling one individual changes what is left. With very large samples the correction barely matters and D approaches Σ p squared, but for the small quadrats and plots typical of fieldwork the n(n-1) form is the honest one.
How it’s calculated
Simpson's index uses the finite-sample form D = Σ [n_i(n_i - 1)] / [N(N - 1)], where n_i is the count in group i and N is the total count. The Index of Diversity is 1 - D and the Reciprocal Index is 1/D. Higher 1-D and higher 1/D both indicate greater diversity.
Counts should be whole individuals from one sampled community. The index says nothing about which groups are present or their roles, only how counts are spread across groups.
Reading the Index of Diversity (1 - D)
| 1 - D value | What it suggests |
|---|---|
| 0.00 - 0.20 | Very low diversity; one group dominates |
| 0.20 - 0.50 | Low to moderate diversity |
| 0.50 - 0.70 | Moderately diverse community |
| 0.70 - 0.90 | High diversity; groups fairly even |
| 0.90 - 1.00 | Very high diversity; many even groups |
General interpretation guide; exact cutoffs vary by field. 1 - D is the probability two random individuals belong to different groups.
Common mistakes
- Confusing D with 1-D. D near 1 means low diversity (one group dominates), while 1-D near 1 means high diversity. Always state which you are reporting.
- Entering percentages instead of counts. The n(n-1) formula needs real individual counts; proportions give the Σ p squared approximation, a slightly different number.
- Comparing indices from samples of very different sizes without noting it, since both the finite correction and richness shift with N.
Frequently asked questions
What is the formula for Simpson's Diversity Index?
The core index is D = Σ n(n-1) / N(N-1), where n is each group's count and N is the total. Simpson's Index of Diversity is 1 - D, the probability that two randomly picked individuals belong to different groups. The Reciprocal Index is 1/D.
Is a high Simpson's value good or bad?
It depends which version you mean. A high D near 1 means low diversity, because two random picks are usually the same group. A high 1-D near 1 means high diversity. This tool reports both so there is no ambiguity.
Should I enter counts or percentages?
Enter raw counts of individuals in each group. The n(n-1) formula models drawing individuals without replacement, so it needs actual numbers. If you only have proportions, the result approximates Σ p squared instead.
What is the reciprocal Simpson's index?
It is 1/D. It represents the effective number of equally abundant groups that would produce the same D, which makes comparisons between communities more intuitive than the raw probability.
Does the index tell me which species are present?
No. Simpson's index only summarizes how individuals are spread across groups. Two very different communities can share the same value, so report richness and the group list alongside it.