ForHosting KIT · Developer Utilities

Logistic growth rate calculator

A logistic growth rate calculator answers one ecology question: how fast is a population changing right now, given its size, its intrinsic per-capita rate, and the carrying capacity of the habitat.

● BetaFree · in your browser

Run — free How it works & API

Use it from WebAPIEmailTelegramApp soon

The Verhulst identity dN/dt equals r times N times one minus N over K is the instantaneous slope of the classic S-shaped logistic curve. When the population sits far below K the unused-capacity factor is near one and growth is nearly exponential; at half of carrying capacity the slope reaches its maximum rK/4; at K the slope is zero; above K a positive r produces a decline back toward the ceiling. This endpoint evaluates that identity for any finite non-negative population, any finite intrinsic rate, and any positive carrying capacity, and it also returns the per-capita rate, the unused-capacity fraction, the density ratio N/K, and the theoretical peak slope. It does not integrate N(t) forward in time and it does not replace an exponential-only model. The same deterministic module powers the free browser runner and the API, so a lecture slide, an LMS homework check, and a wildlife-management script never disagree on whether fifty individuals at r = 0.1 and K = 100 grow at 2.5 individuals per unit time.

How to use it

Enter your values in the form above. The tool checks them before calculating and shows the result on the same page.

Check your inputs

Use the labels and units shown next to each field. If something is missing or outside the allowed range, the page points to the field to fix.

Use it again or automate it

Use the browser tool for individual checks and the API when you need the same capability in an automated workflow.

What you can do with it

Get an answer now

Enter one set of values and see the result without building a spreadsheet or script.

Compare scenarios

Change one value at a time and rerun the calculation to understand what affects the result.

Automate repeated work

Use the API when the same calculation needs to run inside your product or workflow.

FAQ

How do I use this capability?

Complete the fields above and run it on this page. The form highlights anything that needs attention.

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

POSThttps://api.kit.forhosting.com/bio/logistic-growth-rate-dndt

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/logistic-growth-rate-dndt \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"population":50,"intrinsic_rate":0.1,"carrying_capacity":100}'

const res = await fetch("https://api.kit.forhosting.com/bio/logistic-growth-rate-dndt", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "population": 50,
    "intrinsic_rate": 0.1,
    "carrying_capacity": 100
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/bio/logistic-growth-rate-dndt",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "population": 50,
    "intrinsic_rate": 0.1,
    "carrying_capacity": 100
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/bio/logistic-growth-rate-dndt", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"population":50,"intrinsic_rate":0.1,"carrying_capacity":100}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"population":50,"intrinsic_rate":0.1,"carrying_capacity":100}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/bio/logistic-growth-rate-dndt", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "population": 50,
  "intrinsic_rate": 0.1,
  "carrying_capacity": 100
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "bio.logistic_growth_rate_dndt",
  "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

Per request$0.002

Published price — no tokens, no invented credits. A failed task is never charged.

Limits

max_abs 1000000000000000

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.

Read the full KIT documentation →