Simpson's Diversity Index Calculator
Calculate Simpson’s diversity index from species abundance data.
Zeros and blanks are ignored. Each value is the abundance (count) of one species.
Simpson's Index of Diversity (1 − D)
Higher values (closer to 1) indicate greater diversity.
Simpson's Index / Dominance (λ)
Reciprocal Index (1/λ)
Species Richness (S)
Total Individuals (N)
Interpretation
What Simpson's Index Measures
Simpson's index quantifies biodiversity by accounting for both richness (the number of species present) and evenness (how individuals are distributed among those species). In its most intuitive form, Simpson's index of diversity represents the probability that two individuals drawn at random from a community belong to different species.
A community dominated by a single species has a low probability that two random individuals differ, and therefore low diversity. A community where individuals are spread evenly across many species has a high probability that two random individuals differ, and therefore high diversity. This calculator uses the finite-population form, which samples without replacement and is appropriate for counted, real-world data.
The Three Forms of Simpson's Index
The same underlying calculation is reported in three related but distinct ways. With ni the number of individuals of species i and N the total number of individuals:
Simpson's Index / Dominance (λ)
λ = Σ [ ni(ni − 1) ] / [ N(N − 1) ]
The probability that two randomly selected individuals belong to the same species. Ranges from 0 to 1; higher values mean lower diversity (more dominance).
Simpson's Index of Diversity (1 − λ)
The probability that two randomly selected individuals belong to different species. Ranges from 0 to 1; higher values mean greater diversity. This is the headline result above and the most commonly reported figure.
Simpson's Reciprocal Index (1/λ)
Ranges from 1 to S (the number of species). It can be interpreted as the effective number of equally-common species. A value of 1 means a single species dominates entirely; higher values indicate more — and more even — species.
Simpson vs Shannon
Simpson's index and the Shannon (Shannon-Wiener) index are the two most widely used diversity measures, but they emphasize different aspects of a community:
- Sensitivity to dominance: Simpson's index is weighted toward the most abundant (dominant) species and is relatively insensitive to rare species. Shannon's index gives more weight to rare species and species richness.
- Interpretation: Simpson's diversity has a clear probabilistic meaning (chance two individuals differ). Shannon's index is rooted in information theory (the uncertainty in predicting the species of a random individual).
- Range: Simpson's index of diversity is bounded between 0 and 1, which makes communities easy to compare. Shannon's index has no fixed upper bound — it grows with richness.
- When to use: Choose Simpson's index when dominance and evenness matter most; choose Shannon's index when rare species and overall richness are the focus. Reporting both is common practice.
Related Calculators
Educational Disclaimer: This Simpson's Diversity Index calculator is intended for educational and informational purposes. Diversity indices summarize a single sample and depend on consistent, complete sampling effort; they do not by themselves account for sampling bias, detection probability, spatial scale, or undetected rare species. For formal ecological assessments, consult qualified ecologists and primary literature.