Shannon diversity index calculator
Counts of ten, twenty, thirty and forty individuals across four species give a Shannon index of 1.279854. Enter the abundances from a quadrat, net or camera trap and get one number you can compare between sites. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Counts
- 10, 20, 30, 40
- Total
- 100 nats
- Shannon index
- 1.2798542258
- Richness
- 4
- Species count
- 4
The Shannon diversity index, also called the Shannon–Wiener or Shannon–Weaver index, measures how mixed a biological community is from the population counts of each species. It is not a species list and it is not a simple richness tally: two plots can hold the same number of taxa and still differ because one is dominated by a single abundant species while the other splits individuals more evenly. Zero counts contribute nothing, because the limit of p times ln p as p approaches zero is zero.
How the Shannon diversity index is computed
Sum those counts once to obtain the community size N. A total of zero means every relative abundance would be zero over zero, so the engine rejects that input rather than inventing an index. A zero count contributes nothing: the well-known limit of p ln p as p approaches zero is zero, which is the ecological convention used in every standard textbook.
When every positive count is identical, H prime collapses to the natural log of the number of occupied taxa, which is also the theoretical maximum H_max for that richness. A single occupied species always yields H prime of zero because p equals one and ln of one is zero. Pielou evenness J prime is H prime divided by ln of richness; a community of one species is treated as perfectly even, so evenness is one rather than an undefined zero over zero.
What you send, what you get back, and what fails
One number is one species. Fractional abundances are allowed so a biomass or cover series does not have to be rounded to integers first. Zero entries are allowed and stay in the returned counts and proportions arrays; they do not increase richness.
Any negative count fails and names the offending index, because a negative population is not a sample. When every count is zero the total is zero and the task fails with a message that the Shannon index is undefined when N equals zero. Classic checks include ten, twenty, thirty, forty, whose index is about 1.279854, and three equal counts, whose index is the natural log of three.
Wire the free browser form for a field notebook, then call the identical contract from scripts when you need answer keys or a monitoring pipeline.
Who uses the Shannon index and why
Field ecologists, conservation agencies and classroom labs use a deterministic Shannon calculator to turn a vector of counts from a quadrat, a mist-net session or a camera-trap night into a single comparable number they can put next to a site name, instead of arguing about whether the plot felt diverse.
Restoration projects compare a pre-treatment sample with a post-treatment sample by sending the two count lists independently and reading the change in H prime and evenness; the engine does not invent a statistical test, it just returns the same formula both times. Failed validation does not consume balance. Keep lists inside the published item limit, pin the rounded fields in tests, and you get a reproducible diversity product without standing up a statistics stack of your own.
If you later need Simpson dominance, rarefaction curves or a permutation test of two communities, treat those as separate search intents rather than overloading this Shannon index page.
What you can do with it
Quadrat and transect field notes
Turn a row of species counts from a plot, net or trap night into H′, richness and evenness you can store next to the site identifier.
Classroom answer keys
Generate the Shannon index for textbook abundance lists so teachers and auto-graders share one ground truth instead of drifting logarithms.
Restoration and monitoring pipelines
Compare pre-treatment and post-treatment communities by sending each count vector independently and reading the change in H′ and evenness.
FAQ
Do zero counts change the index?
No. A zero abundance contributes nothing because the limit of p ln p as p approaches zero is zero. Zeros also do not increase richness, which counts only strictly positive entries.
What is evenness in the response?
Pielou evenness J′ = H′ / ln(S), the index divided by the maximum possible H′ for that richness. A single occupied species is treated as perfectly even, so evenness is 1.
What does it cost?
The browser tool is free and runs locally.
What is the Shannon diversity index?
It measures how mixed a community is from the number of individuals of each species. Two plots with the same number of species can score differently if one is dominated by a single abundant species.
What is the highest Shannon index a sample can reach?
When every species has the same count, the index equals the natural log of the number of species, the maximum for that richness. Three equal counts give ln 3, while a single species always gives zero.
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/eco/shannon-index \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"counts":[10,20,30,40]}'const res = await fetch("https://api.kit.forhosting.com/eco/shannon-index", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"counts": [
10,
20,
30,
40
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/eco/shannon-index",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"counts": [
10,
20,
30,
40
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/eco/shannon-index", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"counts":[10,20,30,40]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"counts":[10,20,30,40]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/eco/shannon-index", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"counts": [
10,
20,
30,
40
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "eco.shannon_index",
"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.
Limits
max_items | 10000 |
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
This calculator takes a list of non-negative population counts, converts each count into a relative abundance p_i equal to n_i over N, then returns H prime equal to minus the sum of p_i times the natural logarithm of p_i. A negative count is not a population, and a total of zero leaves every proportion undefined, so those cases fail with invalid_input instead of returning NaN.
How the Shannon diversity index is computed
Start with a non-empty list of species population counts n_1 through n_S, each a finite non-negative number. For each species compute the relative abundance p_i equals n_i divided by N. The Shannon–Wiener index in nats is then H prime equals minus the sum of p_i times the natural logarithm of p_i, taken only over species whose count is strictly positive. The pipeline is ordinary floating-point arithmetic with no random seeds, no wall-clock timestamps, and no network lookup, so identical counts always produce identical JSON.
What you send, what you get back, and what fails
Send a JSON object with one required field named counts, or the aliases populations, abundances, values, or n, holding either a JSON array of finite non-negative numbers or a plain string with numbers separated by commas, spaces, or semicolons. Missing fields, empty arrays, empty strings, booleans, objects, NaN, Infinity, and tokens that are not plain decimal or scientific numbers fail with invalid_input and are not charged. On success the response reports shannon_index as the primary H prime in nats, richness as the number of strictly positive counts, species_count as the length of the input including zeros, total as N, evenness as Pielou J prime, the cleaned counts and proportions in input order, log_base e, unit nats, and the compact formula string. Successful API calls use the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where a Shannon-index API earns its keep
Long-term monitoring programmes that already store species-by-site abundance tables can post one task per row and store shannon_index, richness and evenness beside the visit identifier without opening a spreadsheet of logarithms.
Technical questions
What is the Shannon diversity index?
H′ = −Σ p_i ln(p_i), where p_i is the relative abundance n_i / N of each species. It is reported here in nats (natural logarithm). Higher H′ means a more mixed community.
Why are negative counts and a total of zero rejected?
A negative population is not a sample. When every count is zero, N is zero and every p_i is undefined, so the index cannot be computed. Both cases fail with invalid_input.