Calculate Simpson's Diversity Index, Shannon Index, evenness, richness, and Hill numbers for any categorical dataset. Includes visual distribution bars and detailed breakdown.
The Simpson's Diversity Index Calculator computes multiple diversity metrics including Simpson's D, Shannon-Wiener H', Pielou's evenness, Berger-Parker dominance, Margalef richness, and Hill numbers. Enter category counts and instantly see a complete diversity analysis.
Diversity indices quantify how evenly individuals are distributed across categories. In ecology, this measures species diversity in a habitat. In business, it measures market concentration. In demographics, it measures population diversity. The Simpson's Diversity Index (1-D) gives the probability that two randomly selected individuals belong to different categories.
This calculator provides both the most common diversity metrics and advanced measures like Hill numbers, which unify richness to dominance indices in a single framework. Visual proportion bars, a step-by-step computation table, and preset datasets make the tool accessible for students and researchers alike. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case. Use the example pattern when troubleshooting unexpected results.
Diversity analysis requires computing multiple indices, each capturing different aspects of distribution. This calculator provides them all in one place, with visual aids and step-by-step computation tables that make results transparent and verifiable.
Ecologists studying biodiversity, social scientists analyzing demographic diversity, business analysts measuring market concentration, and students learning diversity metrics all benefit from this comprehensive tool. The Hill numbers framework provides a unified perspective that helps interpret seemingly contradictory index values.
Simpson's D = Σpᵢ². Diversity = 1 - D. Reciprocal = 1/D. Shannon H' = -Σ(pᵢ × ln pᵢ). Evenness J = H'/H'max. Margalef = (S-1)/ln(N).
Result: Simpson's 1-D = 0.7300, Shannon H' = 1.4405, Evenness J = 0.8947
Total = 100. Proportions: 0.40, 0.25, 0.20, 0.10, 0.05. D = 0.40² + 0.25² + 0.20² + 0.10² + 0.05² = 0.27. Diversity = 1 - 0.27 = 0.73 (73% probability two random individuals differ).
In ecology, Simpson's Diversity Index is used to compare species diversity across habitats, monitor biodiversity over time, and assess the impact of environmental changes. A declining index may indicate habitat degradation, invasive species, or pollution. Conservation biologists use these metrics to prioritize protection efforts.
Hill numbers, introduced by Mark Hill in 1973, provide a unified mathematical framework for diversity measurement. At order q=0, they reduce to species richness. At q=1, they equal the exponential of Shannon entropy. At q=2, they equal Simpson's reciprocal. This framework eliminates the apparent contradiction between different indices by showing they're all part of one family with different sensitivity to rare vs. common categories.
Despite sharing a name, Simpson's Diversity Index and Simpson's Paradox are unrelated — named after different statisticians (E.H. Simpson for the index, Edward Simpson for the paradox). However, both remind us that aggregated statistics can be misleading: a habitat with high overall diversity might have low diversity within each microhabitat.
It measures the probability that two randomly selected individuals from the sample belong to different categories. Ranges from 0 (no diversity, one category dominates) to nearly 1 (maximum diversity, all categories equal). Higher values indicate more diversity.
Simpson's index is more sensitive to dominant categories (commons), while Shannon's is more sensitive to rare categories. Simpson's has a clear probability interpretation; Shannon's is measured in "nats" (information units). Both increase with diversity.
Evenness (Pielou's J) measures how equally individuals are distributed across categories, ranging from 0 (all individuals in one category) to 1 (perfectly equal distribution). It's calculated as H'/H'max, where H'max = ln(S).
Hill numbers unify diversity indices into a family parameterized by order q. q=0 gives richness (number of categories), q=1 gives exp(H') (Shannon diversity), q=2 gives 1/D (Simpson diversity). Higher q gives more weight to common categories.
Absolutely! Diversity indices apply to any categorical data: market concentration (companies), ethnic diversity (demographics), vocabulary richness (linguistics), or portfolio diversification (finance). The math is identical.
The Berger-Parker index equals the proportional abundance of the most dominant category. It ranges from 1/S (perfect evenness) to 1 (total dominance). Lower values indicate more even distributions.