Simpsons Diversity Index Calculator

What Simpson's Diversity Index Measures

Simpson's index summarizes how evenly individuals are distributed across species or categories. Higher Gini-Simpson diversity means more categories and a more even split. Compare with the Shannon Diversity Index Calculator or Index of Qualitative Variation Calculator.

Simpson Index Formula

For finite samples with species counts $n_i$ and total $N$:

$$D = \frac{\sum n_i(n_i - 1)}{N(N - 1)}$$

Gini-Simpson diversity is $1 - D$. Inverse Simpson index is $1/D$.

How to Interpret the Results

$D$ near 1 means low diversity because two random draws often land in the same category. Gini-Simpson near 1 means high diversity. Inverse Simpson can be read as an effective number of equally common categories.

Example

Five tree species with counts 42, 38, 55, 21, and 19 give $N = 175$, $D \approx 0.225$, and Gini-Simpson diversity $\approx 0.775$.

Frequently Asked Questions

What is the difference between D and 1 − D?

D rises when diversity falls. Gini-Simpson diversity 1 − D rises when categories are more even, which matches the usual intuition.

Can I use this outside ecology?

Yes. Any categorical distribution works, such as department headcount, product mix, or survey response categories.

Why use n_i(n_i − 1) instead of proportions squared?

The finite-sample formula adjusts for sampling without replacement. For large populations both forms converge.

What if one species dominates?

D moves toward 1 and Gini-Simpson toward 0 because most random pairs fall in the dominant category.

How is this different from Shannon diversity?

Shannon weights rare categories through logarithms. Simpson emphasizes the probability that two individuals match.

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