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.

Entering your species counts

The only thing this tool needs is one number per species: how many individuals you tallied for each. Type or paste them into the box in any order—10, 5, 3, 2 gives the same answer as 2, 3, 5, 10—and press Calculate. You don't enter species names, percentages, or a grand total; the calculator counts the species (S) and sums the individuals (N) for you.

If your data already lives in a spreadsheet, select the column of counts and paste it straight in. The parser is deliberately forgiving about separators—commas, spaces, tabs, and line breaks all work—so a pasted column drops in without reformatting. Strip out any header row or species-name column first, though; text tokens like Oak or count get flagged as ignored entries rather than silently treated as zero.

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)

Reading D, 1 − D, and 1/D

All three numbers describe the same community from different angles, so pick the one that matches how your question is phrased:

• D — the same-species probability. Think of it as the odds that two individuals grabbed at random turn out to be the same species. A single stand of near-monoculture pushes D toward 1; a well-mixed community with no clear winner pulls it toward 0. Because a bigger D signals less diversity, some people find it counterintuitive to report on its own.
• 1 − D — the different-species probability (Gini–Simpson). This flips the scale so it reads the intuitive way: near 1 the next two individuals are almost certainly different species, near 0 they are almost certainly the same. If someone just wants "how diverse is this site, higher is better," this is the number to hand them.
• 1/D — the reciprocal, or effective number of species. A value of 4 means the community is about as diverse as four equally common species would be, even if you actually counted twelve. It stays roughly proportional to real diversity, which makes it the fairest of the three for comparing one site against another.

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.

Questions that come up in the field and the lab

Why does a smaller D mean higher diversity?

Because D counts sameness, not variety. It answers "how often will two individuals match?"—and in a genuinely diverse, even community that match is rare, so D lands low. The moment one species starts to dominate, matches become common and D climbs. It feels backwards only until you remember you're reading a dominance score, not a diversity score.

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.