Simpson index calculator
Four species with 10, 20, 5 and 15 individuals give lambda 0.3 and a Gini–Simpson diversity of 0.7: enter your counts and get Simpson's D, its complement, lambda and the inverse Simpson index together. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Abundances
- 10, 20, 5, 15
- Species count
- 4
- Total individuals
- 50
- Simpson d
- 0.2857142857
- Simpson diversity
- 0.7142857143
Ecologists, field biologists, and conservation analysts measure how unevenly individuals are distributed among species with the Simpson index: the probability that two randomly drawn individuals belong to the same species. High D means a few species dominate the sample; low D and a high complement 1−D mean greater evenness and diversity. This Simpson index species dominance calculator accepts a list of non-negative abundance counts, applies the finite-sample formula D equals the sum of n times n minus one over N times N minus one, and also reports the infinite-population form lambda equals the sum of squared proportions, the Gini–Simpson complement, and the inverse Simpson effective-species number. Validation rejects empty lists, negative counts, and totals below two individuals so you never get a hollow index when two draws are impossible.
What the Simpson index measures and how D and 1−D are defined
Simpson’s dominance index asks a simple sampling question: if you pick two individuals at random from a finite community sample without replacement, what is the probability they belong to the same species? When one species holds almost every individual, D approaches one and the stand is strongly dominated. When abundances are equal across many species, D is small and the sample is even.
Ecologists often prefer the complement one minus D, sometimes called Simpson’s index of diversity or the finite-sample Gini–Simpson index: it is the probability that the two draws are different species, so larger values mean more diversity rather than more dominance. Species with zero count do not contribute to richness or to the sums, but they may appear in the echoed abundances array when you pad a fixed species list.
What to enter and what you get back
Each entry is the abundance of one species in the sample—classically integer counts, though non-negative reals are accepted for aggregated or rarefied tables. At most ten thousand entries are allowed. The total number of individuals N must be at least two; a single individual cannot support a two-draw probability, so N less than two is rejected with a clear message rather than returning NaN.
Numeric fields are rounded to twelve significant digits for stable goldens across runtimes. Example: abundances ten, twenty, five, and fifteen give N equals fifty, four species, a moderate D below zero point three, and diversity one minus D above zero point seven, reflecting a mixed stand rather than a monoculture.
Where the Simpson index helps most
Biodiversity monitoring programs reduce each plot’s raw counts to a short list of diversity indices before storing time series or comparing sites; automating Simpson D and one minus D removes spreadsheet drift when technicians copy formulas across sheets. Environmental impact assessments and restoration scorecards need reproducible dominance metrics when arguing that a post-disturbance community is still dominated by a few opportunistic taxa.
Teaching labs and online ecology courses use a live calculator so students can type abundances from a bird point-count or a quadrat and see dominance and diversity update without installing R. Research notebooks that already compute Shannon entropy can add inverse Simpson as a second evenness-sensitive lens without pulling a full vegan package for a single closed formula.
What you can do with it
Plot and transect survey summaries
Turn per-species counts from a vegetation plot or bird point-count into Simpson D, 1−D, and inverse Simpson for site comparison tables.
Impact and restoration reporting
Document whether a community remains dominated by few taxa after disturbance by reporting finite-sample D and its diversity complement.
Teaching labs and LMS checks
Let students submit abundance vectors and auto-grade Simpson dominance and diversity against a deterministic oracle.
FAQ
How do I calculate the Simpson index from species abundances?
Send a non-empty abundances array of non-negative counts with total N ≥ 2.
Are zero abundances allowed?
An all-zero vector is rejected because N would be zero.
Why must the sample contain at least two individuals?
Because the index is the probability that two individuals drawn without replacement belong to the same species. With fewer than two individuals two draws are impossible, so the calculator stops instead of returning an empty result.
What is the difference between Simpson's D and 1−D?
D is the probability that two random individuals are the same species, so high values mean a few species dominate. 1−D is the chance they differ, so larger values mean more diversity rather than more dominance.
What does the inverse Simpson index tell me?
It reads as an effective number of equally abundant species: the higher it is, the more evenly the sample is shared. It equals one divided by lambda, the sum of squared proportions, and is a Hill number of order two.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/bio/simpson-index-ecology \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"abundances":[10,20,5,15]}'const res = await fetch("https://api.kit.forhosting.com/bio/simpson-index-ecology", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"abundances": [
10,
20,
5,
15
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/bio/simpson-index-ecology",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"abundances": [
10,
20,
5,
15
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/bio/simpson-index-ecology", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"abundances":[10,20,5,15]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"abundances":[10,20,5,15]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/bio/simpson-index-ecology", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"abundances": [
10,
20,
5,
15
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "bio.simpson_index_ecology",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
What the Simpson index measures and how D and 1−D are defined
With abundance n_i for species i and total individuals N equal to the sum of all n_i, that probability is D equals the sum over i of n_i times (n_i minus one), all divided by N times (N minus one). An infinite-population companion uses proportions p_i equals n_i over N and defines lambda equals the sum of p_i squared; one minus lambda is the classic Gini–Simpson diversity, and one over lambda is the inverse Simpson index, a Hill number of order two that reads as an effective number of equally abundant species. This calculator returns all five numbers together so you can match textbook footnotes that use D, 1−D, lambda, or 1/lambda without re-deriving the algebra by hand.
Input contract, response fields, and validation errors
POST a JSON body with a required abundances field: a non-empty array of non-negative finite numbers (or a comma, space, or semicolon separated string of the same). Aliases counts, n, abundances_list, and species_counts are accepted. Missing field, empty list, non-numeric tokens, negative values, and all-zero vectors fail with invalid_input and are not billed. On success the body echoes the cleaned abundances, species_count (number of strictly positive abundances), total_individuals N, simpson_d (finite-sample D), simpson_diversity (one minus D), lambda (sum of p_i squared), gini_simpson (one minus lambda), inverse_simpson (one over lambda), plus formula and method strings for display and audit. Pair the numbers with your own species names client-side; this endpoint is deliberately name-free so privacy and i18n stay in your UI.
Where a Simpson dominance API earns its keep
Mobile field apps can call the same parse endpoint from offline-synced count lists once connectivity returns, billing only successful tasks at the published $0.002 base price with no model tokens and no outbound network from the worker.
Technical questions
What is the difference between simpson_d and simpson_diversity?
simpson_d is dominance (probability two random individuals are the same species). simpson_diversity is the complement 1−D (probability they are different species)—higher means more diversity.
Why must total individuals be at least 2?
Finite-sample D divides by N(N−1). With fewer than two individuals you cannot draw a pair, so the index is undefined and the task fails with invalid_input.
What does the Simpson index calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.