# Simpson's Diversity Index Calculator

Free Simpson's diversity index calculator. Calculate D, 1-D, and 1/D from species counts. Measure biodiversity and community evenness for ecology research.

## What this calculates

Calculate Simpson's diversity index from species abundance data. Enter the number of individuals for each species and get D, the diversity index (1-D), and the reciprocal index (1/D).

## Inputs

- **Species 1 Count** — min 0 — Number of individuals of species 1.
- **Species 2 Count** — min 0 — Number of individuals of species 2.
- **Species 3 Count** — min 0 — Number of individuals of species 3 (optional).
- **Species 4 Count** — min 0 — Number of individuals of species 4 (optional).
- **Species 5 Count** — min 0 — Number of individuals of species 5 (optional).
- **Species 6 Count** — min 0 — Number of individuals of species 6 (optional).
- **Species 7 Count** — min 0 — Number of individuals of species 7 (optional).
- **Species 8 Count** — min 0 — Number of individuals of species 8 (optional).

## Outputs

- **Simpson's Index (D)** — Probability that two randomly chosen individuals belong to the same species.
- **Simpson's Diversity (1 - D)** — Probability that two randomly chosen individuals belong to different species.
- **Simpson's Reciprocal (1/D)** — The reciprocal index. Higher values indicate more diversity.
- **Total Individuals (N)** — Total number of individuals across all species.
- **Number of Species** — Number of species with at least one individual.
- **Interpretation** — formatted as text — What the diversity index means for this community.

## Details

Simpson's diversity index measures the probability that two randomly selected individuals from a community belong to the same species. It accounts for both species richness and evenness.

**The Formula:**
D = Σ [nᵢ(nᵢ - 1)] / [N(N - 1)]

Where nᵢ is the count of species i and N is the total number of individuals. This version uses the finite-sample correction (sampling without replacement).

**Three Related Measures:**

- **Simpson's Index (D):** Ranges from 0 to 1. Higher values mean lower diversity (dominated by one species).
- **Simpson's Diversity Index (1 - D):** Ranges from 0 to 1. Higher values mean higher diversity.
- **Simpson's Reciprocal Index (1/D):** Starts at 1 and increases with diversity. Maximum value equals the number of species (when all species have equal counts).

**Example:**
A forest with 50 oaks, 30 maples, and 20 pines has N = 100. D = [50(49) + 30(29) + 20(19)] / [100(99)] = 3700/9900 = 0.374. The diversity index is 1 - 0.374 = 0.626, indicating moderate diversity.

## Frequently Asked Questions

**Q: What is the difference between D, 1-D, and 1/D?**

A: D is the probability that two randomly chosen individuals belong to the same species (higher D = lower diversity). 1-D flips this so higher values mean more diversity. 1/D is the reciprocal index that ranges from 1 to the number of species, making it more intuitive for comparing communities.

**Q: When should I use Simpson's index vs. Shannon's index?**

A: Simpson's index is more sensitive to dominant species, while Shannon's index is more sensitive to rare species. If you care about which species dominate the community, Simpson's is a better choice. If you want to capture the contribution of rare species, Shannon's is often preferred.

**Q: Can Simpson's index be used for non-ecological data?**

A: Yes. Simpson's index works for any categorical data where you want to measure diversity or concentration. It is used in economics (market concentration), linguistics (vocabulary diversity), genetics (allelic diversity), and other fields.

**Q: What does a diversity index of 0.9 mean?**

A: A 1-D value of 0.9 means there is a 90% probability that two randomly selected individuals belong to different species. This indicates high diversity with individuals spread fairly evenly across species.

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Source: https://vastcalc.com/calculators/statistics/simpsons-diversity-index
Category: Statistics
Last updated: 2026-04-08