How this instrument works
Counting how many species live in a habitat (richness) only tells part of the diversity story — it treats a community of 100 individuals split 97/1/1/1 across four species the same as one split 25/25/25/25, even though the second is intuitively far more diverse. Simpson's index fixes this by also weighting how evenly individuals are distributed across those species, using each species' proportion of the total population.
Simpson's original index, D, is the sum of each proportion squared: D = Σ p_i². Because squaring emphasizes larger proportions disproportionately, D is actually highest when diversity is LOWEST (one dominant species pushes D toward 1) — which is counterintuitive for a 'diversity' index, so two standard transformations are used instead. Simpson's Diversity Index reports 1 − D, which rises toward 1 as diversity increases. Simpson's Reciprocal Index reports 1/D, which rises without an upper bound as diversity increases and can be read as 'the effective number of equally-common species' the community behaves like.
All three numbers come from the same underlying proportions and describe the same community from three different angles: D itself (dominance-weighted, rarely reported alone), 1−D (a bounded 0-to-1 diversity score, the most commonly cited version), and 1/D (an intuitive 'effective species count'). This calculator reports all three from one shared set of proportions so you don't have to compute D three separate ways.
- Enter each species' (or category's) share of the total population into Species proportions (must sum to 1), separated by commas, spaces, or new lines — for example 0.4, 0.3, 0.2, 0.1.
- Make sure the proportions sum to 1 (within a small tolerance); the calculator checks this and flags it if they don't.
- Read Simpson's index (D = Σp²) — the raw dominance-weighted sum, where higher values mean LOWER diversity.
- Read Simpson's Diversity Index (1 - D) — a 0-to-1 score where higher values mean higher diversity; this is the version most commonly cited.
- Read Simpson's Reciprocal Index (1 / D) — the 'effective number of equally-common species' this community behaves like.
Worked example — four species at proportions 0.4, 0.3, 0.2, 0.1
Enter 0.4, 0.3, 0.2, 0.1 into Species proportions (must sum to 1) — a community where the most common species makes up 40% of individuals and the rarest makes up 10%. The instrument squares each proportion and sums: 0.4² + 0.3² + 0.2² + 0.1² = 0.16 + 0.09 + 0.04 + 0.01 = 0.30.
Simpson's index (D = Σp²) reads 0.300000. Simpson's Diversity Index (1 - D) reads 0.700000 — a moderately high diversity score on its 0-to-1 scale. Simpson's Reciprocal Index (1 / D) reads 3.333333 — this unevenly-distributed four-species community behaves, diversity-wise, like about 3.3 equally-common species rather than a true 4, because the 40/30/20/10 split isn't perfectly even.
Questions
Why does a higher D mean lower diversity, when it's called a 'diversity' calculation?
Because squaring each proportion disproportionately boosts the contribution of whichever species is most dominant — D approaches 1 when one species makes up nearly the entire population (low diversity) and approaches its minimum when proportions are spread evenly across many species (high diversity). This inverted behavior is exactly why D is almost never reported on its own; instead, 1−D or 1/D is used so that a bigger number intuitively means 'more diverse,' matching what most people expect from a diversity score.
Should I report Simpson's Diversity Index (1-D) or the Reciprocal Index (1/D)?
Both are valid and widely used, and they carry the same underlying information, just rescaled differently. 1−D is bounded between 0 and 1, which makes it easy to interpret as a percentage-like diversity score and easy to compare across many samples on a fixed scale. 1/D has no upper bound and is often preferred by ecologists because it has an intuitive interpretation as 'the number of equally-common species this community's diversity is equivalent to' — a true even split of n species always gives a reciprocal index of exactly n.
How is Simpson's index different from Shannon entropy?
Both are diversity measures computed from the same kind of input (a set of proportions), but they weight rarity differently. Simpson's index emphasizes the most common species more heavily (because it squares proportions), making it more sensitive to dominance by a few abundant species. Shannon entropy weights all species more evenly by proportion and is more sensitive to the presence of rare species. Ecologists sometimes report both because they highlight slightly different aspects of the same community's diversity.
Why do the proportions need to sum to 1?
Because they're meant to represent every individual in the community, split across every species present — the proportions are shares of a whole population, and a complete accounting of that population has to sum to 1 (or 100%). If your proportions don't sum to 1, either a species is missing from your list or the underlying counts weren't converted to proportions correctly.
What's a 'good' diversity index value?
There's no universal threshold — it depends heavily on the type of ecosystem, the number of species present, and what you're comparing against. Diversity indices are most useful for comparison: tracking one site's diversity over time, or comparing diversity across several similar habitats sampled the same way, rather than judging a single number against some fixed 'good' or 'bad' cutoff.