Simpson Diversity Index Calculator (D, 1−D, and 1/D)

What this calculator does

Simpson’s diversity measures how evenly individuals are distributed among species in a community. It uses only species abundances (counts per species) and summarizes diversity in a single number. This page calculates three closely related outputs so you can use the version your course, lab, or paper expects:

• Simpson’s D (dominance / concentration): the probability that two individuals sampled at random without replacement belong to the same species.
• 1 − D (often called the Gini–Simpson index): the probability that two randomly selected individuals belong to different species.
• 1 / D (Simpson reciprocal index): an “effective number of species” style measure where larger values mean greater diversity.

How to use the calculator

1. Enter your species counts as a comma-separated list (for example: 10, 5, 3, 2).
2. Click Calculate.
3. Review D, 1 − D, and 1/D plus the parsed counts, total individuals N, and number of species S.

If your dataset is in a spreadsheet, you can usually copy a column of counts and paste it—this calculator accepts commas, spaces, tabs, and new lines.

Definitions and formulas

Suppose you observed S species. Let n_i be the count (abundance) of species i, and let:

• N = total individuals = $N=\sum _i{n}_i$

The classical finite-sample form of Simpson’s dominance index is:

Formula: D = (∑ i = 1 S n_i(n_i − 1)) / (N(N − 1))

$D=\frac{\sum _{i=1}^S{n}_i(n_i-1)}{N(N-1)}$

From that, the other common variants are:

• Gini–Simpson: 1 − D
• Reciprocal: 1 / D (defined only when D > 0)

How to interpret the results

• D (same-species probability): closer to 1 means one or a few species dominate; closer to 0 means the community is more even and diverse.
• 1 − D (different-species probability): closer to 1 means higher diversity; closer to 0 means lower diversity.
• 1/D: larger values indicate higher diversity; it can be easier to compare across sites because it increases roughly in proportion to “effective diversity.”

Important terminology note: Different textbooks and fields sometimes call different variants “Simpson’s diversity index.” Many ecology sources use D (dominance), while others use 1 − D (diversity). This calculator provides both so you can report the one required and cite the definition you used.

Worked example (complete)

Imagine a meadow with four plant species with counts:

10, 5, 3, 2

• Total individuals: N = 10 + 5 + 3 + 2 = 20
• Compute the numerator: 10×9 + 5×4 + 3×2 + 2×1 = 90 + 20 + 6 + 2 = 118
• Compute the denominator: N(N−1) = 20×19 = 380

So:

• D = 118 / 380 ≈ 0.3105
• 1 − D ≈ 0.6895
• 1 / D ≈ 3.22

Interpretation: There is about a 31% chance two randomly chosen individuals are the same species (dominance), and about a 69% chance they are different species (diversity). The reciprocal (~3.22) suggests diversity comparable to a perfectly even community of about 3.2 equally common species.

Comparison table: how the variants behave

Assumptions & limitations (read before using)

• Counts should be non-negative integers. This calculator accepts decimals but Simpson’s index is defined for counts; if you use proportions or weights, interpret results cautiously.
• Requires N ≥ 2. If the total number of individuals is 0 or 1, D is undefined because the denominator N(N−1) is 0.
• Zeros are allowed but don’t add information. A species with count 0 contributes nothing; consider omitting absent species from the list.
• Sampling assumptions matter. The probability interpretation assumes random sampling from a fixed community. Biased sampling or unequal detectability can distort diversity estimates.
• Not a full biodiversity profile. Simpson’s index emphasizes common species and is less sensitive to rare species than metrics like Shannon entropy.
• Comparisons require consistent effort. Comparing across sites/studies is meaningful only when sampling intensity and methods are comparable (or standardized).

Tips for clean inputs

• Paste counts separated by commas, spaces, tabs, or new lines.
• Use only numbers (e.g., 12, not 12 individuals).
• If you have a header row or species names, remove them before pasting.

FAQ

Introduction: Why does a smaller D mean higher diversity?

D is a same-species probability. In a highly even community, picking two individuals is less likely to yield the same species, so D is smaller.

Which value should I report in a lab report?

Report the variant your instructions specify, and include the definition (D vs 1−D vs 1/D). If unsure, 1 − D is commonly preferred because “higher means more diverse.”

What happens if one species dominates?

If most individuals belong to one species, D increases toward 1, while 1 − D decreases toward 0, reflecting low evenness.

Can I enter proportions instead of counts?

Simpson’s index is typically defined on counts. If you enter proportions, the finite-sample formula on this page no longer has the strict probability interpretation; use counts whenever possible.